One can describe electronically excited states at a level of theory similar to that associated with coupledcluster theory for the ground state by applying either linear response theory [351] or equationofmotion methods [352]. A number of groups have demonstrated that excitation energies based on a coupledcluster singles and doubles ground state are generally very accurate for states that are primarily single electron promotions. The error observed in calculated excitation energies to such states is typically 0.1–0.2 eV, with 0.3 eV as a conservative estimate, including both valence and Rydberg excited states. This, of course, assumes that a basis set large and flexible enough to describe the valence and Rydberg states is employed. The accuracy of excited state coupledcluster methods is much lower for excited states that involve a substantial double excitation character, where errors may be 1 eV or even more. Such errors arise because the description of electron correlation of an excited state with substantial double excitation character requires higher truncation of the excitation operator. The description of these states can be improved by including triple excitations, as in the EOM(2,3) or EOMCCSD(dT)/(fT) methods.
QChem includes coupledcluster methods for excited states based on the optimized orbital coupledcluster doubles (OD), and the coupled cluster singles and doubles (CCSD) methods, described earlier. OD excitation energies have been shown to be essentially identical in numerical performance to CCSD excited states [353].
These methods, while far more computationally expensive than TDDFT, are nevertheless useful as proven high accuracy methods for the study of excited states of small molecules. Moreover, they are capable of describing both valence and Rydberg excited states, as well as states of a chargetransfer character. Also, when studying a series of related molecules it can be very useful to compare the performance of TDDFT and coupledcluster theory for at least a small example to understand its performance. Along similar lines, the CIS(D) method described earlier as an economical correlation energy correction to CIS excitation energies is in fact an approximation to EOMCCSD. It is useful to assess the performance of CIS(D) for a class of problems by benchmarking against the full coupledcluster treatment. Finally, QChem includes extensions of EOM methods to treat ionized or electron attachment systems, as well as di and triradicals.
EOMEE
EOMIP
EOMEA
EOMSF
QChem features the most complete set of EOMCCSD models [354] that enables accurate, robust, and efficient calculations of electronically excited states (EOMEECCSD or EOMEEOD) [355, 356, 352, 353, 357]; ground and excited states of diradicals and triradicals (EOMSFCCSD and EOMSFOD [358, 357]); ionization potentials and electron attachment energies as well as problematic doublet radicals, cation or anion radicals, (EOMIP/EACCSD) [359, 360, 361], as well as EOMDIPCCSD and EOM2SFCCSD. Conceptually, EOM is very similar to configuration interaction (CI): target EOM states are found by diagonalizing the similarity transformed Hamiltonian ,
(6.30) 
where and are general excitation operators with respect to the reference determinant . In the EOMCCSD models, and are truncated at single and double excitations, and the amplitudes satisfy the CC equations for the reference state :
(6.31)  
(6.32) 
The computational scaling of EOMCCSD and CISD methods is identical, i.e., , however EOMCCSD is numerically superior to CISD because correlation effects are “folded in” in the transformed Hamiltonian, and because EOMCCSD is rigorously sizeintensive.
By combining different types of excitation operators and references , different groups of target states can be accessed as explained in Fig. 6.1. For example, electronically excited states can be described when the reference corresponds to the ground state wave function, and operators conserve the number of electrons and a total spin [352]. In the ionized/electron attached EOM models [360, 361], operators are not electron conserving (i.e., include different number of creation and annihilation operators)—these models can accurately treat ground and excited states of doublet radicals and some other openshell systems. For example, singly ionized EOM methods, i.e., EOMIPCCSD and EOMEACCSD, have proven very useful for doublet radicals whose theoretical treatment is often plagued by symmetry breaking. Finally, the EOMSF method [358, 357] in which the excitation operators include spinflip allows one to access diradicals, triradicals, and bondbreaking.
QChem features EOMEE/SF/IP/EACCSD methods for both closed and openshell references (RHF/UHF/ROHF), including frozen core/virtual options. All EOM models take full advantage of molecular point group symmetry. Analytic gradients are available for RHF and UHF references, for the full orbital space, and with frozen core/virtual orbitals [362]. Properties calculations (permanent and transition dipole moments, , , etc.) are also available. The current implementation of the EOMXXCCSD methods enables calculations of mediumsize molecules, e.g., up to 15–20 heavy atoms. Using RI approximation 5.7.5 or Cholesky decomposition 5.7.6 helps to reduce integral transformation time and disk usage enabling calculations on much larger systems.
The CCMAN module of QChem includes two implementations of EOMIPCCSD. The proper implementation [363] is used by default is more efficient and robust. The EOM_FAKE_IPEA keyword invokes is a pilot implementation in which EOMIPCCSD calculation is set up by adding a very diffuse orbital to a requested basis set, and by solving EOMEECCSD equations for the target states that include excitations of an electron to this diffuse orbital. The implementation of EOMEACCSD in CCMAN also uses this trick. Fake IP/EA calculations are only recommended for Dyson orbital calculations and debug purposes.
CCMAN2 features proper implementations of EOMIP and EOMEA (including Dyson orbitals).
The computational cost of EOMIP calculations can be considerably reduced (with negligible decline in accuracy) by truncating virtual orbital space using FNO scheme (see Section 6.7.7).
Finally, a more economical CI variant of EOMIPCCSD, IPCISD is also available. This is an N approximation of IPCCSD, and is recommended for geometry optimizations of problematic doublet states [364].
EOM and CI methods are handled by the CCMAN/CCMAN2 modules.
The spinflip method [358, 316, 365] addresses the bondbreaking problem associated with a singledeterminant description of the wavefunction. Both closed and open shell singlet states are described within a single reference as spinflipping, (e.g., excitations from the triplet reference state, for which both dynamical and nondynamical correlation effects are smaller than for the corresponding singlet state. This is because the exchange hole, which arises from the Pauli exclusion between samespin electrons, partially compensates for the poor description of the coulomb hole by the meanfield HartreeFock model. Furthermore, because two electrons cannot form a bond, no bond breaking occurs as the internuclear distance is stretched, and the triplet wavefunction remains essentially singlereference in character. The spinflip approach has also proved useful in the description of di and triradicals as well as some problematic doublet states.
The spinflip method is available for the CIS, CIS(D), CISD, CISDT, OD, CCSD, and EOM(2,3) levels of theory and the spin complete SFXCIS (see Section 6.2.4). An N noniterative triples corrections are also available. For the OD and CCSD models, the following nonrelaxed properties are also available: dipoles, transition dipoles, eigenvalues of the spinsquared operator (), and densities. Analytic gradients are also for SFCIS and EOMSFCCSD methods. To invoke a spinflip calculation the EOM_SF_STATES $rem should be used, along with the associated $rem settings for the chosen level of correlation (CORRELATION, and, optionally, EOM_CORR). Note that the high multiplicity triplet or quartet reference states should be used.
Several double SF methods have also been implemented [366]. To invoke these methods, use
EOM_DSF_STATES.
Doubleionization potential (DIP) is another nonelectronconserving variant of EOMCCSD [367, 368, 369]. In DIP, target states are reached by detaching two electrons from the reference state:
(6.33) 
and the excitation operator has the following form:
(6.34)  
(6.35)  
(6.36) 
As a reference state in the EOMDIP calculations one usually takes a wellbehaved closedshell state. EOMDIP is a useful tool for describing molecules with electronic degeneracies of the type “ electrons on degenerate orbitals”. The simplest examples of such systems are diradicals with twoelectronsontwoorbitals pattern. Moreover, DIP is a preferred method for fourelectronsonthreeorbitals wavefunctions.
Accuracy of the EOMDIPCCSD method is similar to accuracy of other EOMCCSD models, i.e., 0.1–0.3 eV. The scaling of EOMDIPCCSD is , analogous to that of other EOMCCSD methods. However, its computational cost is less compared to, e.g., EOMEECCSD, and it increases more slowly with the basis set size.
An EOMDIP calculation is invoked by using EOM_DIP_STATES, or EOM_DIP_SINGLETS and
EOM_DIP_TRIPLETS.
While conventional coupledcluster and equationofmotion methods allow one to tackle electronic structure ranging from wellbehaved closed shell molecules to various openshell and electronically excited species [354], metastable electronic states, socalled resonances, present a difficult case for theory. By using complex scaling and complex absorbing potential techniques, we extended these powerful methods to describe autoionizing states, such as transient anions, highly excited electronic states, and coreionized species [370, 371]. In addition, users can employ stabilization techniques using charged sphere and scaled atomic charges options [369]. These methods are only available within CCMAN2. The complex CC/EOM code is engaged by COMPLEX_CCMAN; the specific parameters should be specified in the $complex_ccman section.
COMPLEX_CCMAN
Requests complexscaled or CAPaugmented CC/EOM calculations.
TYPE:
LOGICAL
DEFAULT:
FALSE
OPTIONS:
TRUE
Engage complex CC/EOM code.
RECOMMENDATION:
Not available in CCMAN. Need to specify CAP strength or complexscaling parameter in $complex_ccman section.
The $complex_ccman section is used to specify the details of the complexscaled/CAP calculations, as illustrated below. If user specifies CS_THETA, complex scaling calculation is performed.
$complex_ccman CS_THETA 10 Complexscaling parameter theta=0.01, r>r exp(i*theta) CS_ALPHA 10 Real part of the scaling parameter alpha=0.01, r>alpha r exp(itheta) $end
Alternatively, for CAP calculations, the CAP parameters need to be specified.
$complex_ccman CAP_ETA 1000 CAP strength in 105 a.u. (0.01) CAP_X 2760 CAP onset along X in 10^3 bohr (2.76 bohr) CAP_Y 2760 CAP onset along Y in 10^3 bohr (2.76 bohr) CAP_Z 4880 CAP onset along Z in 10^3 bohr (4.88 bohr) CAP_TYPE 1 Use cuboid cap (CAP_TYPE=0 will use spherical CAP) $end
CS_THETA is specified in radian 10. CS_ALPHA, CAP_X/Y/Z are specified in a.u. 10, i.e., CS_THETA=10 means =0.01; CAP_ETA is specified in a.u. 10. When CAP calculations are performed, CC_EOM_PROP=TRUE by default; this is necessary for calculating firstorder deperturbative correction.
Advanced users may find the following options useful. Several ways of conducing complex calculations are possible, i.e., complex scaling/CAPs can be either engaged at all levels (HF, CCSD, EOM), or not. By default, if COMPLEX_CCMAN is specified, the EOM calculations are conducted using complex code. Other parameters are set up as follows:
$complex_ccman CS_HF=true CS_CCSD=true $end
Alternatively, the user can disable complex HF. These options are experimental and should only be used by advanced users. For CAPEOMCC, only CS_HF=TRUE and CS_CCSD=TRUE is implemented. Finally, only RHF references are supported in complexscaled and CAPaugmented calculations.
Unfortunately, the performance of EOMDIP deteriorates when the reference state is unstable with respect to electrondetachment [368, 369], which is usually the case for dianion references employed to describe neutral diradicals by EOMDIP. Similar problems are encountered by all excitedstate methods when dealing with excited states lying above ionization or electrondetachment thresholds.
To remedy this problem, one can employ charge stabilization methods, as described in Refs. [368, 369]. In this approach (which can also be used with any other electronic structure method implemented in QChem), an additional Coulomb potential is introduced to stabilize unstable wave functions. The following keywords invoke stabilization potentials: SCALE_NUCLEAR_CHARGE and ADD_CHARGED_CAGE. In the former case, the potential is generated by increasing nuclear charges by a specified amount. In the latter, the potential is generated by a cage built out of point charges comprising the molecule. There are two cages available: dodecahedral and spherical. The shape, radius, number of points, and the total charge of the cage are set by the user.
Note: A perturbative correction estimating the effect of the external Coulomb potential on EOM energy will be computed when target state densities are calculated, e.g., when CC_EOM_PROP is set to TRUE.
Note: Charge stabilization techniques can be used with other methods such as EOMEE, CIS, and TDDFT to improve the description of resonances. It can also be employed to describe metastable ground states.
Large computational savings are possible if the virtual space is truncated using the frozen natural orbital (FNO) approach (see Section 5.10). Extension of the FNO approach to ionized states within EOMCC formalism was recently introduced and benchmarked [278]. In addition to groundstate coupledcluster calculations, FNOs can also be used in EOMIPCCSD, EOMIPCCSD(dT/fT) and EOMIPCC(2,3). In IPCC the FNOs are computed for the reference (neutral) state and then are used to describe several target (ionized) states of interest. Different truncation scheme are described in Section 5.10.
An EOMCC eigen problem is solved by an iterative diagonalization procedure that avoids full diagonalization and only looks for several eigenstates, as specified by the XX_STATES keywords.
The default procedure is based on the modified Davidson diagonalization algorithm, as explained in Ref. [357]. In addition to several keywords that control the convergence of algorithm, memory usage, and fine details of its execution, there are several important keywords that allow user to specify how the target state selection will be performed.
By default, the diagonalization looks for several lowest eigenstates, as specified by XX_STATES. The guess vectors are generated as singly excited determinants selected by using the Koopmans theorem; the number of guess vectors is equal to the number of target states. If necessary, the user can increase the number of singly excited guess vectors (EOM_NGUESS_SINGLES), include doubly excited guess vectors (EOM_NGUESS_DOUBLES), and even preconverge them (EOM_PRECONV_SINGLES and EOM_PRECONV_DOUBLES).
If a state of a particular character is desired (e.g., HOMOLUMO+10 excitation or HOMO10 ionization), the user can specify this by using EOM_USER_GUESS keyword and $eom_user_guess section, as illustrated by an example below. The algorithm will attempt to find an eigenstate that has the maximum overlap with this guess vector. Note that the point group symmetry of user defined guess vectors should be consistent with the symmetry of the transition specified by XX_STATES. The multiplicity of the state is determined as in the regular calculations, by using the EOM_XX_SINGLETS and EOM_EE_TRIPLETS keywords. This option is useful for looking for highlying states such as coreionized states.
The examples below illustrate how to use userspecified guess in EOM calculations:
$eom_user_guess 4 Calculate excited state corresponding to 4(OCC)>5(VIRT) transition. 5 $end
In IP/EA calculations, only one orbital is specified:
$eom_user_guess 4 $end
If IP_STATES is specified, this will invoke calculation of the EOMIP state corresponding to the ionization from 4th occupied MO. If EA_STATES is requested, then EOMEA equations will be solved for a root corresponding to electronattachment to the 4th virtual MO.
The symmetries of the MOs should be consistent with the EE_STATES value, which should only request one state in the correct irrep. The orbitals are ordered by energy as printed at the beginning of the CCMAN2 output.
Alternatively, the user can specify an energy shift by EOM_SHIFT. In this case, the solver looks for the XX_STATES eigenstates that are closest to this energy; the guess vectors are generated accordingly, using the Koopmans theorem. This option is useful when highly excited states (i.e., interior eigenstates) are desired.
Finally, a new diagonalization technique, socalled GPLMR (or GPLHR), is available[372]. This solver is engaged by EOM_GPLMR keyword and is only available in CCMAN2. The GPLMR method usually converges in fewer iterations relative to Davidson and can use less memory, but it performs more floating point operations. Similarly to the Davidson procedure, GPLMR can be applied to look for either the lowest eigenstates, or for an interior set, as specified by EOM_SHIFT. The convergence is controlled by the same keywords as in the Davidson algorithm. One additional keyword controlling the maximum subspace size in the GPLMR solver is EOM_GPLMR_MSUBSIZE.
It is important to ensure there are sufficient resources available for the necessary integral calculations and transformations. For CCMAN/CCMAN2 algorithms, these resources are controlled using the $rem variables CC_MEMORY, MEM_STATIC and MEM_TOTAL (see Section 5.13).
Equationofmotion methods require a coupledcluster reference state, which is computed when METHOD is set to EOMCCSD or EOMOD. In addition, a specification of the number of target states is required through XX_STATES (XX designates the type of the target states, e.g., EE, SF, IP, EA, DIP, DSF, etc.). Users must be aware of the point group symmetry of the system being studied and also the symmetry of the initial and target states of interest, as well as symmetry of transition. It is possible to turn off the use of symmetry by CC_SYMMETRY. If set to FALSE the molecule will be treated as having symmetry and all states will be of symmetry.
Note: In finitedifference calculations, the symmetry is turned off automatically, and the user must ensure that XX_STATES is adjusted accordingly.
Note: Mixing different EOM models in a single calculation is only allowed in Dyson orbitals calculations.
By default, the level of correlation of the EOM part of the wavefunction (i.e., maximum excitation level in the EOM operators ) is set to match CORRELATION, however, one can mix different correlation levels for the reference and EOM states by using EOM_CORR. To request a CI calculation, set CORRELATION=CI and select type of CI expansion by EOM_CORR. The table below shows default and allowed CORRELATION and EOM_CORR combinations.
CORRELATION 
Default 
Allowed 
Target states 
CCMAN/CCMAN2 
EOM_CORR 
EOM_CORR 

CI 
none 
CIS, CIS(D) 
EE,SF 
y/n 
CISD 
EE,SF,IP 
y/n 

SDT, DT 
EE,SF,DSF 
y/n 

CIS(D) 
CIS(D) 
N/A 
EE,SF 
y/n 
CCSD, OD 
CISD 
EE,SF,IP,EA,DIP 
y/y 

SD(dT),SD(fT) 
EE,SF, fake IP/EA 
y/n 

SD(dT),SD(fT), SD(sT) 
IP 
y/n 

SDT, DT 
EE,SF,IP,EA,DIP,DSF 
y/n 
The table below shows the correct combinations of CORRELATION and EOM_CORR for standard EOM and CI models.
Method 
CORRELATION 
EOM_CORR 
Target states selection 
CIS 
CI 
CIS 
EE_STATES 
EE_SNGLETS,EE_TRIPLETS 

SFCIS 
CI 
CIS 
SF_STATES 
CIS(D) 
CI 
CIS(D) 
EE_STATES 
EE_SNGLETS,EE_TRIPLETS 

SFCIS(D) 
CI 
CIS(D) 
SF_STATES 
CISD 
CI 
CISD 
EE_STATES 
EE_SNGLETS,EE_TRIPLETS 

SFCISD 
CI 
CISD 
SF_STATES 
IPCISD 
CI 
CISD 
IP_STATES 
CISDT 
CI 
SDT 
EE_STATES 
EE_SNGLETS,EE_TRIPLETS 

SFCISDT 
CI 
SDT or DT 
SF_STATES 
EOMEECCSD 
CCSD 
EE_STATES 

EE_SNGLETS,EE_TRIPLETS 

EOMSFCCSD 
CCSD 
SF_STATES 

EOMIPCCSD 
CCSD 
IP_STATES 

EOMEACCSD 
CCSD 
EA_STATES 

EOMDIPCCSD 
CCSD 
DIP_STATES 

DIP_SNGLETS,DIP_TRIPLETS 

EOM2SFCCSD 
CCSD 
SDT or DT 
DSF_STATES 
EOMEE(2,3) 
CCSD 
SDT 
EE_STATES 
EE_SNGLETS,EE_TRIPLETS 

EOMSF(2,3) 
CCSD 
SDT 
SF_STATES 
EOMIP(2,3) 
CCSD 
SDT 
IP_STATES 
EOMSFCCSD(dT) 
CCSD 
SD(dT) 
SF_STATES 
EOMSFCCSD(fT) 
CCSD 
SD(fT) 
SF_STATES 
EOMIPCCSD(dT) 
CCSD 
SD(dT) 
IP_STATES 
EOMIPCCSD(fT) 
CCSD 
SD(fT) 
IP_STATES 
EOMIPCCSD(sT) 
CCSD 
SD(sT) 
IP_STATES 
The most relevant EOMCC input options follow.
EE_STATES
Sets the number of excited state roots to find. For closedshell reference, defaults into EE_SINGLETS. For openshell references, specifies all lowlying states.
TYPE:
INTEGER/INTEGER ARRAY
DEFAULT:
0
Do not look for any excited states.
OPTIONS:
Find excited states in the first irrep, states in the second irrep etc.
RECOMMENDATION:
None
EE_SINGLETS
Sets the number of singlet excited state roots to find. Valid only for closedshell references.
TYPE:
INTEGER/INTEGER ARRAY
DEFAULT:
0
Do not look for any excited states.
OPTIONS:
Find excited states in the first irrep, states in the second irrep etc.
RECOMMENDATION:
None
EE_TRIPLETS
Sets the number of triplet excited state roots to find. Valid only for closedshell references.
TYPE:
INTEGER/INTEGER ARRAY
DEFAULT:
0
Do not look for any excited states.
OPTIONS:
Find excited states in the first irrep, states in the second irrep etc.
RECOMMENDATION:
None
SF_STATES
Sets the number of spinflip target states roots to find.
TYPE:
INTEGER/INTEGER ARRAY
DEFAULT:
0
Do not look for any excited states.
OPTIONS:
Find SF states in the first irrep, states in the second irrep etc.
RECOMMENDATION:
None
DSF_STATES
Sets the number of doubly spinflipped target states roots to find.
TYPE:
INTEGER/INTEGER ARRAY
DEFAULT:
0
Do not look for any DSF states.
OPTIONS:
Find doubly spinflipped states in the first irrep, states in the second irrep etc.
RECOMMENDATION:
None
IP_STATES
Sets the number of ionized target states roots to find. By default, electron will be removed (see EOM_IP_BETA).
TYPE:
INTEGER/INTEGER ARRAY
DEFAULT:
0
Do not look for any IP states.
OPTIONS:
Find ionized states in the first irrep, states in the second irrep etc.
RECOMMENDATION:
None
EOM_IP_ALPHA
Sets the number of ionized target states derived by removing electron (M=).
TYPE:
INTEGER/INTEGER ARRAY
DEFAULT:
0
Do not look for any IP/ states.
OPTIONS:
Find ionized states in the first irrep, states in the second irrep etc.
RECOMMENDATION:
None
EOM_IP_BETA
Sets the number of ionized target states derived by removing electron (M=, default for EOMIP).
TYPE:
INTEGER/INTEGER ARRAY
DEFAULT:
0
Do not look for any IP/ states.
OPTIONS:
Find ionized states in the first irrep, states in the second irrep etc.
RECOMMENDATION:
None
EA_STATES
Sets the number of attached target states roots to find. By default, electron will be attached (see EOM_EA_ALPHA).
TYPE:
INTEGER/INTEGER ARRAY
DEFAULT:
0
Do not look for any EA states.
OPTIONS:
Find EA states in the first irrep, states in the second irrep etc.
RECOMMENDATION:
None
EOM_EA_ALPHA
Sets the number of attached target states derived by attaching electron (M=, default in EOMEA).
TYPE:
INTEGER/INTEGER ARRAY
DEFAULT:
0
Do not look for any EA states.
OPTIONS:
Find EA states in the first irrep, states in the second irrep etc.
RECOMMENDATION:
None
EOM_EA_BETA
Sets the number of attached target states derived by attaching electron (M=, EASF).
TYPE:
INTEGER/INTEGER ARRAY
DEFAULT:
0
Do not look for any EA states.
OPTIONS:
Find EA states in the first irrep, states in the second irrep etc.
RECOMMENDATION:
None
DIP_STATES
Sets the number of DIP roots to find. For closedshell reference, defaults into DIP_SINGLETS. For openshell references, specifies all lowlying states.
TYPE:
INTEGER/INTEGER ARRAY
DEFAULT:
0
Do not look for any DIP states.
OPTIONS:
Find DIP states in the first irrep, states in the second irrep etc.
RECOMMENDATION:
None
DIP_SINGLETS
Sets the number of singlet DIP roots to find. Valid only for closedshell references.
TYPE:
INTEGER/INTEGER ARRAY
DEFAULT:
0
Do not look for any singlet DIP states.
OPTIONS:
Find DIP singlet states in the first irrep, states in the second irrep etc.
RECOMMENDATION:
None
DIP_TRIPLETS
Sets the number of triplet DIP roots to find. Valid only for closedshell references.
TYPE:
INTEGER/INTEGER ARRAY
DEFAULT:
0
Do not look for any DIP triplet states.
OPTIONS:
Find DIP triplet states in the first irrep, states in the second irrep etc.
RECOMMENDATION:
None
Note: It is a symmetry of a transition rather than that of a target state which is specified in excited state calculations. The symmetry of the target state is a product of the symmetry of the reference state and the transition. For closedshell molecules, the former is fully symmetric and the symmetry of the target state is the same as that of transition, however, for openshell references this is not so.
Note: For the XX_STATES options, QChem will increase the number of roots if it suspects degeneracy, or change it to a smaller value, if it cannot generate enough guess vectors to start the calculations.
EOM_FAKE_IPEA
If TRUE, calculates fake EOMIP or EOMEA energies and properties using the diffuse orbital trick. Default for EOMEA and Dyson orbital calculations in CCMAN.
TYPE:
LOGICAL
DEFAULT:
FALSE (use proper EOMIP code)
OPTIONS:
FALSE, TRUE
RECOMMENDATION:
None. This feature only works for CCMAN.
Note: When EOM_FAKE_IPEA is set to TRUE, it can change the convergence of HartreeFock iterations compared to the same job without EOM_FAKE_IPEA, because a very diffuse basis function is added to a center of symmetry before the HartreeFock iterations start. For the same reason, BASIS2 keyword is incompatible with EOM_FAKE_IPEA. In order to read HartreeFock guess from a previous job, you must specify EOM_FAKE_IPEA (even if you do not request for any correlation or excited states) in that previous job. Currently, the second moments of electron density and Mulliken charges and spin densities are incorrect for the EOMIP/EACCSD target states.
EOM_USER_GUESS
Specifies if userdefined guess will be used in EOM calculations.
TYPE:
LOGICAL
DEFAULT:
FALSE
OPTIONS:
TRUE
Solve for a state that has maximum overlap with a transn specified in $eom_user_guess.
RECOMMENDATION:
The orbitals are ordered by energy, as printed in the beginning of the CCMAN2 output. Not available in CCMAN.
EOM_SHIFT
Specifies energy shift in EOM calculations.
TYPE:
INTEGER
DEFAULT:
0
OPTIONS:
corresponds to hartree shift (i.e., 11000 = 11 hartree); solve for eigenstates around this value.
RECOMMENDATION:
Not available in CCMAN.
EOM_GPLMR
Specifies whether to engage GPLMR solver in EOM calculations.
TYPE:
LOGICAL
DEFAULT:
FALSE
OPTIONS:
TRUE
Use GPLMR.
RECOMMENDATION:
Not available in CCMAN.
EOM_NGUESS_DOUBLES
Specifies number of excited state guess vectors which are double excitations.
TYPE:
INTEGER
DEFAULT:
0
OPTIONS:
Include guess vectors that are double excitations
RECOMMENDATION:
This should be set to the expected number of doubly excited states (see also EOM_PRECONV_DOUBLES), otherwise they may not be found.
EOM_NGUESS_SINGLES
Specifies number of excited state guess vectors that are single excitations.
TYPE:
INTEGER
DEFAULT:
Equal to the number of excited states requested
OPTIONS:
Include guess vectors that are single excitations
RECOMMENDATION:
Should be greater or equal than the number of excited states requested.
EOM_PRECONV_SINGLES
When not zero, singly excited vectors are converged prior to a full excited states calculation. Sets the maximum number of iterations for preconverging procedure
TYPE:
INTEGER
DEFAULT:
0
OPTIONS:
0
do not preconverge
N
perform N Davidson iterations preconverging singles.
RECOMMENDATION:
Sometimes helps with problematic convergence.
EOM_PRECONV_DOUBLES
When not zero, doubly excited vectors are converged prior to a full excited states calculation. Sets the maximum number of iterations for preconverging procedure
TYPE:
INTEGER
DEFAULT:
0
OPTIONS:
0
do not preconverge
N
perform N Davidson iterations preconverging doubles.
RECOMMENDATION:
Occasionally necessary to ensure a doubly excited state is found. Also used in DSF calculations instead of EOM_PRECONV_SINGLES
EOM_PRECONV_SD
When not zero, EOM vectors are preconverged prior to a full excited states calculation. Sets the maximum number of iterations for preconverging procedure
TYPE:
INTEGER
DEFAULT:
0
OPTIONS:
0
do not preconverge
N
perform N Davidson iterations preconverging singles and doubles.
RECOMMENDATION:
Occasionally necessary to ensure that all lowlying states are found. Also, very useful in EOM(2,3) calculations.
None
EOM_DAVIDSON_CONVERGENCE
Convergence criterion for the RMS residuals of excited state vectors
TYPE:
INTEGER
DEFAULT:
5
Corresponding to
OPTIONS:
Corresponding to convergence criterion
RECOMMENDATION:
Use default. Should normally be set to the same value as EOM_DAVIDSON_THRESHOLD.
EOM_DAVIDSON_THRESHOLD
Specifies threshold for including a new expansion vector in the iterative Davidson diagonalization. Their norm must be above this threshold.
TYPE:
INTEGER
DEFAULT:
00105
Corresponding to 0.00001
OPTIONS:
Integer code is mapped to
RECOMMENDATION:
Use default unless converge problems are encountered. Should normally be set to the same values as EOM_DAVIDSON_CONVERGENCE, if convergence problems arise try setting to a value less than EOM_DAVIDSON_CONVERGENCE.
EOM_DAVIDSON_MAXVECTORS
Specifies maximum number of vectors in the subspace for the Davidson diagonalization.
TYPE:
INTEGER
DEFAULT:
60
OPTIONS:
Up to vectors per root before the subspace is reset
RECOMMENDATION:
Larger values increase disk storage but accelerate and stabilize convergence.
EOM_DAVIDSON_MAX_ITER
Maximum number of iteration allowed for Davidson diagonalization procedure.
TYPE:
INTEGER
DEFAULT:
30
OPTIONS:
Userdefined number of iterations
RECOMMENDATION:
Default is usually sufficient
EOM_GPLMR_MSUBSIZE
Specifies the number of Krylovspace residuals in GPLMR.
TYPE:
INTEGER
DEFAULT:
3
OPTIONS:
Generate residuals at each iteration.
RECOMMENDATION:
Use default. The convergence is faster for larger , but the memory usage and the overall cost will increase.
EOM_IPEA_FILTER
If TRUE, filters the EOMIP/EA amplitudes obtained using the diffuse orbital implementation (see EOM_FAKE_IPEA). Helps with convergence.
TYPE:
LOGICAL
DEFAULT:
FALSE (EOMIP or EOMEA amplitudes will not be filtered)
OPTIONS:
FALSE, TRUE
RECOMMENDATION:
None
CC_FNO_THRESH
Initialize the FNO truncation and sets the threshold to be used for both cutoffs (OCCT and POVO)
TYPE:
INTEGER
DEFAULT:
None
OPTIONS:
range
000010000
Corresponding to %
RECOMMENDATION:
None
CC_FNO_USEPOP
Selection of the truncation scheme
TYPE:
INTEGER
DEFAULT:
1
OCCT
OPTIONS:
0
POVO
RECOMMENDATION:
None
SCALE_NUCLEAR_CHARGE
Scales charge of each nuclei by a certain value. The nuclear repulsion energy is calculated for the unscaled nuclear charges.
TYPE:
INTEGER
DEFAULT:
0 no scaling.
OPTIONS:
n a total positive charge of (1+n/100)e is added to the molecule.
RECOMMENDATION:
NONE
ADD_CHARGED_CAGE
Add a point charge cage of a given radius and total charge.
TYPE:
INTEGER
DEFAULT:
0 no cage.
OPTIONS:
0 no cage.
1 dodecahedral cage.
2 spherical cage.
RECOMMENDATION:
Spherical cage is expected to yield more accurate results, especially for small radii.
CAGE_RADIUS
Defines radius of the charged cage.
TYPE:
INTEGER
DEFAULT:
225
OPTIONS:
n radius is n/100 .
RECOMMENDATION:
None
CAGE_POINTS
Defines number of point charges for the spherical cage.
TYPE:
INTEGER
DEFAULT:
100
OPTIONS:
n n point charges are used.
RECOMMENDATION:
None
CAGE_CHARGE
Defines the total charge of the cage.
TYPE:
INTEGER
DEFAULT:
400 Add a cage charged +4e.
OPTIONS:
n total charge of the cage is n/100 a.u.
RECOMMENDATION:
None
Example 6.130 EOMEEOD and EOMEECCSD calculations of the singlet excited states of formaldehyde
$molecule 0 1 O C,1,R1 H,2,R2,1,A H,2,R2,1,A,3,180. R1=1.4 R2=1.0 A=120. $end $rem method eomod basis 631+g ee_states [2,2,2,2] $end @@@ $molecule read $end $rem method eomccsd basis 631+g ee_singlets [2,2,2,2] ee_triplets [2,2,2,2] $end
Example 6.131 EOMEECCSD calculations of the singlet excited states of PYP using Cholesky decomposition
$molecule 0 1 ...too long to enter... $end $rem method eomccsd basis augccpVDZ purecart 1112 n_frozen_core fc cc_t_conv 4 cc_e_conv 6 cholesky_tol 2 using CD/1e2 threshold ee_singlets [2,2] $end
Example 6.132 EOMSFCCSD calculations for methylene from highspin B reference
$molecule 0 3 C H 1 rCH H 1 rCH 2 aHCH rCH = 1.1167 aHCH = 102.07 $end $rem method eomccsd basis 631G* scf_guess core sf_states [2,0,0,2] Two singlet A1 states and singlet and triplet B2 states $end
Example 6.133 EOMIPCCSD calculations for NO using closedshell anion reference
$molecule 1 1 N O 1 r1 O 1 r2 2 A2 O 1 r2 2 A2 3 180.0 r1 = 1.237 r2 = 1.237 A2 = 120.00 $end $rem method eomccsd basis 631G* ip_states [1,1,2,1] ground and excited states of the radical $end
Example 6.134 EOMIPCCSD calculation using FNO with OCCT=99%.
$molecule 0 1 O H 1 1.0 H 1 1.0 2 100. $end $rem method eomccsd basis 6311+G(2df,2pd) ip_states [1,0,1,1] cc_fno_thresh 9900 99% of the total natural population recovered $end
Example 6.135 DSFCIDT calculation of methylene starting with quintet reference
$molecule 0 5 C H 1 CH H 1 CH 2 HCH CH = 1.07 HCH = 111.0 $end $rem method cisdt basis 631G dsf_states [0,2,2,0] eom_nguess_singles 0 eom_nguess_doubles 2 $end
Example 6.136 EOMEACCSD job for cyano radical. We first do HartreeFock calculation for the cation in the basis set with one extremely diffuse orbital (EOM_FAKE_IPEA) and use these orbitals in the second job. We need make sure that the diffuse orbital is occupied using the OCCUPIED keyword. No SCF iterations are performed as the diffuse electron and the molecular core are uncoupled. The attached states show up as “excited” states in which electron is promoted from the diffuse orbital to the molecular ones.
$molecule +1 1 C N 1 bond bond 1.1718 $end $rem jobtype sp method hf basis 6311+G* purecart 111 scf_convergence 8 eom_fake_ipea true $end @@@ $molecule 0 2 C N 1 bond bond 1.1718 $end $rem jobtype sp basis 6311+G* purecart 111 scf_guess read max_scf_cycles 0 method eomccsd cc_dov_thresh 2501 use threshold for CC iterations with problematic convergence ea_states [2,0,0,0] eom_fake_ipea true $end $occupied 1 2 3 4 5 6 14 1 2 3 4 5 6 $end
Example 6.137 EOMDIPCCSD calculation of electronic states in methylene using charged cage stabilization method.
$molecule 2 1 C 0.000000 0.000000 0.106788 H 0.989216 0.000000 0.320363 H 0.989216 0.000000 0.320363 $end $rem jobtype = sp basis = 6311g(d,p) scf_algorithm = diis_gdm symmetry = false method = eomccsd cc_symmetry = false dip_singlets = [1] ! Compute one EOMDIP singlet state dip_triplets = [1] ! Compute one EOMDIP triplet state eom_davidson_convergence = 5 cc_eom_prop = true ! Compute excited state properties add_charged_cage = 2 ! Install a charged sphere around the molecule cage_radius = 225 ! Radius = 2.25 A cage_charge = 500 ! Charge = +5 a.u. cage_points = 100 ! Place 100 point charges cc_memory = 256 ! Use 256Mb of memory, increase for larger jobs $end
Example 6.138 EOMEECCSD calculation of excited states in NO using scaled nuclear charge stabilization method.
$molecule 1 1 N 1.08735 0.0000 0.0000 O 1.08735 0.0000 0.0000 $end $rem jobtype = sp input_bohr = true basis = 631g symmetry = false cc_symmetry = false method = eomccsd ee_singlets = [2] ! Compute two EOMEE singlet excited states ee_triplets = [2] ! Compute two EOMEE triplet excited states cc_ref_prop = true ! Compute ground state properties cc_eom_prop = true ! Compute excited state properties cc_memory = 256 ! Use 256Mb of memory, increase for larger jobs scale_nuclear_charge = 180 ! Adds +1.80e charge to the molecule $end
Example 6.139 EOMEECCSD calculation for phenol with userspecified guess requesting the EE transition from the occupied orbital number 24 (3 A") to the virtual orbital number 2 (23 A’)
$molecule 0 1 C 0.935445 0.023376 0.000000 C 0.262495 1.197399 0.000000 C 1.130915 1.215736 0.000000 C 1.854154 0.026814 0.000000 C 1.168805 1.188579 0.000000 C 0.220600 1.220808 0.000000 O 2.298632 0.108788 0.000000 H 2.681798 0.773704 0.000000 H 0.823779 2.130309 0.000000 H 1.650336 2.170478 0.000000 H 2.939976 0.044987 0.000000 H 1.722580 2.123864 0.000000 H 0.768011 2.158602 0.000000 $end $rem jobtype SP single point METHOD EOMCCSD BASIS 631+G(d,p) cc_memory 3000 ccman2 memory mem_static 250 CC_T_CONV 4 Tamplitudes convergence threshold CC_E_CONV 6 Energy convergence threshold ee_states [0,1] Calculate 1 A" states EOM_DAVIDSON_CONVERGENCE 5 Convergence threshold for the Davidson procedure EOM_DAVIDSON_THRESHOLD 5 Threshold for inclusion of new vectors to the subspace eom_user_guess true Use user guess from $eom_user_guess section $end $eom_user_guess 24 Transition from the occupied orbital number 24(3 A") 2 to the virtual orbital number 2 (23 A') $end
Example 6.140 Complexscaled EOMEE calculation for He. All roots of Ag symmetry are computed (full diagonalization)
$molecule 0 1 HE 0 0 0.0 $END $rem complex_ccman 1 engage complex_ccman jobtype SP single point METHOD EOMCCSD BASIS gen use general basis PURECART 1111 EE_SINGLETS [2000,0,0,0,0,0,0,0] compute all excitation energies of Ag symmetry EOM_DAVIDSON_CONV 5 EOM_DAVIDSON_THRESH 5 EOM_NGUESS_SINGLES 2000 Number of guess singles EOM_NGUESS_DOUBLES 2000 Number of guess doubles cc_memory 5000 mem_total 3000 $end $complex_ccman CS_HF 1 Use complex HF CS_ALPHA 1000 Set alpha equal 1 CS_THETA 300 Set theta (angle) equals 0.3 (radian) $end $basis He 0 S 4 1.000000 2.34000000E+02 2.58700000E03 3.51600000E+01 1.95330000E02 7.98900000E+00 9.09980000E02 2.21200000E+00 2.72050000E01 S 1 1.000000 6.66900000E01 1.00000000E+00 S 1 1.000000 2.08900000E01 1.00000000E+00 P 1 1.000000 3.04400000E+00 1.00000000E+00 P 1 1.000000 7.58000000E01 1.00000000E+00 D 1 1.000000 1.96500000E+00 1.00000000E+00 S 1 1.000000 5.13800000E02 1.00000000E+00 P 1 1.000000 1.99300000E01 1.00000000E+00 D 1 1.000000 4.59200000E01 1.00000000E+00 S 1 1.000000 2.44564000E02 1.00000000E+00 S 1 1.000000 1.2282000E02 1.00000000E+00 S 1 1.000000 6.1141000E03 1.00000000E+00 P 1 1.0 8.130000e02 1.0 P 1 1.0 4.065000e02 1.0 P 1 1.0 2.032500e02 1.0 D 1 1.0 2.34375e01 1.0 D 1 1.0 1.17187e01 1.0 D 1 1.0 5.85937e02 1.0 **** $end
Example 6.141 CAPaugmented EOMEACCSD calculation for N2. augccpVTZ basis augmented by the 3s3p3d diffuse functions placed in the COM. 2 EA states are computed for CAP strength eta=0.002
$molecule 0 1 N 0.0 0.0 0.54875676501 N 0.0 0.0 0.54875676501 Gh 0.0 0.0 0.0 $end $rem complex_ccman 1 engage complex_ccman jobtype SP single point METHOD EOMCCSD BASIS gen use general basis EA_STATES [0,0,2,0,0,0,0,0] compute electron attachment energies cc_memory 5000 ccman2 memory mem_total 2000 CC_EOM_PROP true compute excited state properties $end $complex_ccman CS_HF 1 Use complex HF CAP_ETA 200 Set strength of CAP potential 0.002 CAP_X 2760 Set length of the box along x dimension CAP_Y 2760 Set length of the box along y dimension CAP_Z 4880 Set length of the box along z dimension CAP_TYPE 1 Use cuboid CAP $end $basis N 0 augccpvtz **** Gh 0 S 1 1.000000 2.88000000E02 1.00000000E+00 S 1 1.000000 1.44000000E02 1.00000000E+00 S 1 1.000000 0.72000000E02 1.00000000E+00 P 1 1.000000 2.45000000E02 1.00000000E+00 P 1 1.000000 1.22000000E02 1.00000000E+00 P 1 1.000000 0.61000000E02 1.00000000E+00 D 1 1.000000 0.755000000E01 1.00000000E+00 D 1 1.000000 0.377500000E01 1.00000000E+00 D 1 1.000000 0.188750000E01 1.00000000E+00 **** $end
In cases of problematic openshell references, e.g., strongly spincontaminated doublet, triplet or quartet states, one may choose to use DFT orbitals. This can be achieved by first doing DFT calculation and then reading the orbitals and turning HartreeFock off. A more convenient way is just to specify EXCHANGE, e.g., if EXCHANGE=B3LYP, B3LYP orbitals will be computed and used in the CCMAN/CCMAN2 module.
Analytic gradients are available for the CCSD and all EOMCCSD methods for both closed and openshell references (UHF and RHF only), including frozen core/virtual functionality [362] (see also Section 5.12).
Application limit: same as for the singlepoint CCSD or EOMCCSD calculations.
Limitations: Gradients for ROHF and nonHF (e.g., B3LYP) orbitals are not yet available.
For the CCSD and EOMCCSD wavefunctions, QChem currently can calculate permanent and transition dipole moments, oscillator strengths, (as well as XX, YY and ZZ components separately, which is useful for assigning different Rydberg states, e.g., vs. , etc.), and the values. Interface of the CCSD and EOMCCSD codes with the NBO 5.0 package is also available. Furthermore, excited state analyses can be requested for EOMCCSD excited states. Similar functionality is available for some EOMOD and CI models.
The coupledcluster package in QChem can calculate properties of target EOM states including transition dipoles, twophoton absorption transition moments (and corss sections), and geometry optimizations. The target state of interest is selected by CC_STATE_TO_OPT $rem, which specifies the symmetry and the number of the EOM state.
Analysis of the EOMCC wavefunctions can also be performed; see Section 10.2.7.
Users must be aware of the point group symmetry of the system being studied and also the symmetry of the excited (target) state of interest. It is possible to turn off the use of symmetry using the CC_SYMMETRY. If set to FALSE the molecule will be treated as having symmetry and all states will be of symmetry.
Calculation of transition moments and cross sections for twophoton absorption for EOMEECCSD wave functions is available in QChem (CCMAN2 only). Both CCSDEOM and EOMEOM transitions can be computed. The formalism is described in Ref. [373]. This feature is available both for canonical and RI/CD implementations. Relevant keywords are CC_EOM_2PA (turns on the calculation), CC_STATE_TO_OPT (used for EOMEOM transitions); additional customization can be performed using the $2pa section.
The $2pa section is used to specify the range of frequencypairs satisfying the resonance condition. If $2pa section is absent in the input, the transition moments are computed for 2 degenerate photons with total energy matching the excitation energy of each target EOM state (for CCSDEOM) or each EOMEOM energy difference (for EOMEOM transitions):
$2pa Nondegenerate resonant 2PA N_2PA_POINTS 6 Number of frequency pairs OMEGA_1 500000 10000 Scans 500 cm$^{1}$ to 550 cm$^{1}$ in steps of 10 cm$^{1}$ $end
N_2PA_POINTS is the number of frequency pairs across the spectrum. The first value associated with OMEGA_1 is the frequency in cm at the start of the spectrum and the second value is the step size in cm. The frequency of the second photon at each step is determined within the code as the excitation energy minus OMEGA_1.
Calculations of spinorbit couplings (SOCs) for EOMCC wavefunctions is available[374] in CCMAN2. We employ a perturbative approach in which SOCs are computed as matrix elements of the respective part of the BreitPauli Hamiltonian using zeroorder nonrelativistic wave functions. Both the full twoelectron treatment and the meanfield approximation (a partial account of the twoelectron contributions) are available for the EOMEE/SF/IP/EA wavefunctions, as well as between the CCSD reference and EOMEE/SF. To enable SOC calculation, transition properties between EOM states must be enabled via CC_TRANS_PROP, and SOC requested using CC_CALC_SOC. By default, oneelectron and meanfield twoelectron couplings will be computed. Full twoelectron coupling calculation is activated by setting CC_EOM_PROP_TE.
As with other EOM transition properties, the initial EOM state is set by CC_STATE_TO_OPT, and couplings are computed between that state and all other EOM states. In the absense of CC_STATE_TO_OPT, SOCs are computed between the reference state and all EOMEE or EOMSF states.
CC_STATE_TO_OPT
Specifies which state to optimize (or from which state compute EOMEOM interstate properties).
TYPE:
INTEGER ARRAY
DEFAULT:
None
OPTIONS:
[,]
optimize the th state of the th irrep.
RECOMMENDATION:
None
Note: The state number should be smaller or equal to the number of excited states calculated in the corresponding irrep.
Note: If analytic gradients are not available, the finite difference calculations will be performed and the symmetry will be turned off. In this case, CC_STATE_TO_OPT should be specified assuming C symmetry, i.e., as [1,N] where N is the number of state to optimize (the states are numbered from 1).
CC_EOM_PROP
Whether or not the nonrelaxed (expectation value) oneparticle EOMCCSD target state properties will be calculated. The properties currently include permanent dipole moment, the second moments , , and of electron density, and the total (in atomic units). Incompatible with JOBTYPE=FORCE, OPT, FREQ.
TYPE:
LOGICAL
DEFAULT:
FALSE (no oneparticle properties will be calculated)
OPTIONS:
FALSE, TRUE
RECOMMENDATION:
Additional equations (EOMCCSD equations for the left eigenvectors) need to be solved for properties, approximately doubling the cost of calculation for each irrep. Sometimes the equations for left and right eigenvectors converge to different sets of target states. In this case, the simultaneous iterations of left and right vectors will diverge, and the properties for several or all the target states may be incorrect! The problem can be solved by varying the number of requested states, specified with XX_STATES, or the number of guess vectors (EOM_NGUESS_SINGLES). The cost of the oneparticle properties calculation itself is low. The oneparticle density of an EOMCCSD target state can be analyzed with NBO package by specifying the state with CC_STATE_TO_OPT and requesting NBO=TRUE and CC_EOM_PROP=TRUE.
CC_TRANS_PROP
Whether or not the transition dipole moment (in atomic units) and oscillator strength for the EOMCCSD target states will be calculated. By default, the transition dipole moment is calculated between the CCSD reference and the EOMCCSD target states. In order to calculate transition dipole moment between a set of EOMCCSD states and another EOMCCSD state, the CC_STATE_TO_OPT must be specified for this state.
TYPE:
LOGICAL
DEFAULT:
FALSE (no transition dipole and oscillator strength will be calculated)
OPTIONS:
FALSE, TRUE
RECOMMENDATION:
Additional equations (for the left EOMCCSD eigenvectors plus lambda CCSD equations in case if transition properties between the CCSD reference and EOMCCSD target states are requested) need to be solved for transition properties, approximately doubling the computational cost. The cost of the transition properties calculation itself is low.
CC_EOM_2PA
Whether or not the transition moments and cross sections for twophoton absorption will be calculated. By default, the transition moments are calculated between the CCSD reference and the EOMCCSD target states. In order to calculate transition moments between a set of EOMCCSD states and another EOMCCSD state, the CC_STATE_TO_OPT must be specified for this state.
TYPE:
INTEGER
DEFAULT:
0 (do not compute 2PA transition moments)
OPTIONS:
1
Compute 2PA using the fastest algorithm (use intermediates for canonical
and intermediates for RI/CD response calculations).
2
Use intermediates for 2PA response equation calculations.
3
Use intermediates for 2PA response equation calculations.
RECOMMENDATION:
Additional response equations (6 for each target state) will be solved, which increases the cost of calculations. The cost of 2PA moments is about 10 times that of energy calculation. Use default algorithm. Setting CC_EOM_2PA0 turns on CC_TRANS_PROP.
CC_CALC_SOC
Whether or not the spinorbit couplings between CC/EOM electronic states will be calculated. By default, the couplings are calculated between the CCSD reference and the EOMCCSD target states. In order to calculate couplings between EOM states, CC_STATE_TO_OPT must specify the initial EOM state.
TYPE:
LOGICAL
DEFAULT:
FALSE (no spinorbit couplings will be calculated)
OPTIONS:
FALSE, TRUE
RECOMMENDATION:
Oneelectron and meanfield twoelectron SOCs will be computed by default. To enable full twoelectron SOCs, twoparticle EOM properties must be turned on (see CC_EOM_PROP_TE).
EOM_REF_PROP_TE
Request for calculation of nonrelaxed twoparticle EOMCC properties. The twoparticle properties currently include . The oneparticle properties also will be calculated, since the additional cost of the oneparticle properties calculation is inferior compared to the cost of . The variable CC_EOM_PROP must be also set to TRUE. Alternatively, CC_CALC_SSQ can be used to request calculation.
TYPE:
LOGICAL
DEFAULT:
FALSE
(no twoparticle properties will be calculated)
OPTIONS:
FALSE, TRUE
RECOMMENDATION:
The twoparticle properties are computationally expensive since they require calculation and use of the twoparticle density matrix (the cost is approximately the same as the cost of an analytic gradient calculation). Do not request the twoparticle properties unless you really need them.
CC_FULLRESPONSE
Fully relaxed properties (including orbital relaxation terms) will be computed. The variable CC_EOM_PROP must be also set to TRUE.
TYPE:
LOGICAL
DEFAULT:
FALSE
(no orbital response will be calculated)
OPTIONS:
FALSE, TRUE
RECOMMENDATION:
Not available for nonUHF/RHF references. Only available for EOM/CI methods for which analytic gradients are available.
CC_SYMMETRY
Controls the use of symmetry in coupledcluster calculations
TYPE:
LOGICAL
DEFAULT:
TRUE
OPTIONS:
TRUE
Use the point group symmetry of the molecule
FALSE
Do not use point group symmetry (all states will be of symmetry).
RECOMMENDATION:
It is automatically turned off for any finite difference calculations, e.g. second derivatives.
STATE_ANALYSIS
Activates excited state analyses.
TYPE:
LOGICAL
DEFAULT:
FALSE (no excited state analyses)
OPTIONS:
TRUE, FALSE
RECOMMENDATION:
Set to TRUE if excited state analysis is required, but also if plots of densities or orbitals are needed. For details see section 10.2.7.
Example 6.142 Geometry optimization for the excited openshell singlet state, , of methylene followed by the calculations of the fully relaxed oneelectron properties using EOMEECCSD
$molecule 0 1 C H 1 rCH H 1 rCH 2 aHCH rCH = 1.083 aHCH = 145. $end $rem jobtype OPT METHOD EOMCCSD BASIS ccpVTZ SCF_GUESS CORE SCF_CONVERGENCE 9 EE_SINGLETS [0,0,0,1] EOM_NGUESS_SINGLES 2 cc_state_to_opt [4,1] EOM_DAVIDSON_CONVERGENCE 9 use tighter convergence for EOM amplitudes $end @@@ $molecule READ $end $rem jobtype SP METHOD EOMCCSD BASIS ccpVTZ SCF_GUESS READ EE_SINGLETS [0,0,0,1] EOM_NGUESS_SINGLES 2 CC_EOM_PROP 1 calculate properties for EOM states CC_FULLRESPONSE 1 use fully relaxed properties $end
Example 6.143 Property and transition property calculation on the lowest singlet state of CH using EOMSFCCSD
$molecule 0 3 C H 1 rch H 1 rch 2 ahch rch = 1.1167 ahch = 102.07 $end $rem METHOD eomccsd BASIS ccpvtz SCF_GUESS core SCF_CONVERGENCE 9 SF_STATES [2,0,0,3] Get three 1^B2 and two 1^A1 SF states CC_EOM_PROP 1 CC_TRANS_PROP 1 CC_STATE_TO_OPT [4,1] First EOM state in the 4th irrep $end
Example 6.144 Geometry optimization with tight convergence for the A excited state of CHCl, followed by calculation of nonrelaxed and fully relaxed permanent dipole moment and .
$molecule 0 2 H C 1 CH CL 2 CCL 1 CCLH H 2 CH 3 CCLH 1 DIH CH=1.096247 CCL=2.158212 CCLH=122.0 DIH=180.0 $end $rem JOBTYPE OPT METHOD EOMCCSD BASIS 631G* Basis Set SCF_GUESS SAD EOM_DAVIDSON_CONVERGENCE 9 EOM amplitude convergence CC_T_CONV 9 CCSD amplitudes convergence EE_STATES [0,0,0,1] cc_state_to_opt [4,1] EOM_NGUESS_SINGLES 2 GEOM_OPT_TOL_GRADIENT 2 GEOM_OPT_TOL_DISPLACEMENT 2 GEOM_OPT_TOL_ENERGY 2 $end @@@ $molecule READ $end $rem JOBTYPE SP METHOD EOMCCSD BASIS 631G* Basis Set SCF_GUESS READ EE_STATES [0,0,0,1] CC_NGUESS_SINGLES 2 CC_EOM_PROP 1 calculate oneelectron properties CC_EOM_PROP_TE 1 and twoelectron properties (S^2) $end @@@ $molecule READ $end $rem JOBTYPE SP METHOD EOMCCSD BASIS 631G* Basis Set SCF_GUESS READ EE_STATES [0,0,0,1] EOM_NGUESS_SINGLES 2 CC_EOM_PROP 1 calculate oneelectron properties CC_EOM_PROP_TE 1 and twoelectron properties (S^2)CC_EXSTATES_PROP 1 CC_FULLRESPONSE 1 same as above, but do fully relaxed properties $end
Example 6.145 CCSD calculation on three and one state of formaldehyde. Transition properties will be calculated between the third state and all other EOM states
$molecule 0 1 O C 1 1.4 H 2 1.0 1 120 H 3 1.0 1 120 $end $rem BASIS 631+G METHOD EOMCCSD EE_STATES [0,3,0,1] CC_STATE_TO_OPT [2,3] CC_TRANS_PROP true $end
Example 6.146 EOMIPCCSD geometry optimization of X state of .
$molecule 0 1 H 0.774767 0.000000 0.458565 O 0.000000 0.000000 0.114641 H 0.774767 0.000000 0.458565 $end $rem jobtype opt method eomccsd basis 6311G ip_states [0,0,0,1] cc_state_to_opt [4,1] $end
Example 6.147 Calculating resonant 2PA with degenerate photons.
$molecule 0 1 O H 1 0.959 H 1 0.959 2 104.654 $end $rem method eomccsd basis augccpvtz ee_singlets [1,0,0,0] 1A_1 state CC_TRANS_PROP 1 Compute transition properties CC_EOM_2PA 1 Calculate 2PA cross sections using the fastest algorithm $end
Example 6.148 Nondegenerate, resonant 2PA scan over a range of frequency pairs.
$molecule 0 1 O H 1 0.959 H 1 0.959 2 104.654 $end $rem method eomccsd basis augccpvtz ee_singlets [2,0,0,0] Two A_1 states CC_TRANS_PROP 1 Calculate transition properties CC_EOM_2PA 1 Calculate 2PA cross sections using the fastest algorithm $end $2pa Nondegenerate resonant 2PA n_2pa_points 11 Number of frequency pairs omega_1 500000 5000 Scans 500 cm$^{1}$ to 550 cm$^{1}$ in steps of 5 cm$^{1}$ $end
Example 6.149 Resonant 2PA with degenerate photons between two excited states.
$molecule 0 1 O H 1 0.959 H 1 0.959 2 104.654 $end $rem method eomccsd basis augccpvtz ee_singlets [2,0,0,0] Two A_1 states STATE_TO_OPT [1,1] "Reference" state for transition properties is 1A_1 state CC_TRANS_PROP 1 Compute transition properties CC_EOM_2PA 1 Calculate 2PA cross sections using the fastest algorithm $end
Example 6.150 Computation of spinorbit couplings between closedshell singlet and triplet state in NH using EOMSFCCSD
$molecule 0 3 N H N 1.0450 $end $rem jobtype = sp method = eomccsd basis = 631g sf_states = [1,2,0,0] cc_trans_prop = true cc_calc_soc = true cc_state_to_opt = [1,1] $end
In the EOMCC(2,3) approach [375], the transformed Hamiltonian is diagonalized in the basis of the reference, singly, doubly, and triply excited determinants, i.e., the excitation operator is truncated at triple excitations. The excitation operator , however, is truncated at double excitation level, and its amplitudes are found from the CCSD equations, just like for EOMCCSD [or EOMCC(2,2)] method.
The accuracy of the EOMCC(2,3) method closely follows that of full EOMCCSDT [which can be also called EOMCC(3,3)], whereas computational cost of the former model is less.
The inclusion of triple excitations is necessary for achieving chemical accuracy (1 kcal/mol) for ground state properties. It is even more so for excited states. In particular, triple excitations are crucial for doubly excited states [375], excited states of some radicals and SF calculations (diradicals, triradicals, bondbreaking) when a reference openshell state is heavily spincontaminated. Accuracy of EOMCCSD and EOMCC(2,3) is compared in Table 6.7.15.
System 
EOMCCSD 
EOMCC(2,3) 
Singlyexcited electronic states 
0.1–0.2 eV 
0.01 eV 
Doublyexcited electronic states 
1 eV 
0.1–0.2 eV 
Severe spincontamination of the reference 
0.5 eV 
0.1 eV 
Breaking single bond (EOMSF) 
0.1–0.2 eV 
0.01 eV 
Breaking double bond (EOM2SF) 
1 eV 
0.1–0.2 eV 
The applicability of the EOMEE/SFCC(2,3) models to larger systems can be extended by using their activespace variants, in which triple excitations are restricted to semiinternal ones.
Since the computational scaling of EOMCC(2,3) method is , these calculations can be performed only for relatively small systems. Moderate size molecules (10 heavy atoms) can be tackled by either using the active space implementation or tiny basis sets. To achieve high accuracy for these systems, energy additivity schemes can be used. For example, one can extrapolate EOMCCSDT/large basis set values by combining large basis set EOMCCSD calculations with small basis set EOMCCSDT ones.
Running the full EOMCC(2,3) calculations is straightforward, however, the calculations are expensive with the bottlenecks being storage of the data on a hard drive and the CPU time. Calculations with around 80 basis functions are possible for a molecule consisting of four first row atoms (NO dimer). The number of basis functions can be larger for smaller systems.
Note: In EE calculations, one needs to always solve for at least one lowspin root in the first symmetry irrep in order to obtain the correlated EOM energy of the reference. The triples correction to the total reference energy must be used to evaluate EOM(2,3) excitation energies.
Note: EOMCC(2,3) works for EOMEE, EOMSF, and EOMIP/EA. In EOMIP, “triples” correspond to excitations, and the computational scaling of EOMIPCC(2,3) is less.
Active space calculations are less demanding with respect to the size of a hard drive. The main bottlenecks here are the memory usage and the CPU time. Both arise due to the increased number of orbital blocks in the active space calculations. In the current implementation, each block can contain from 0 up to 16 orbitals of the same symmetry irrep, occupancy, and spinsymmetry. For example, for a typical molecule of C symmetry, in a small/moderate basis set (e.g., TMM in 631G*), the number of blocks for each index is:
occupied:
virtuals:
(usually there are more than 16 and virtual orbitals).
In EOMCCSD, the total number of blocks is . In EOMCC(2,3) the number of blocks in the EOM part is . In active space EOMCC(2,3), additional fragmentation of blocks occurs to distinguish between the restricted and active orbitals. For example, if the active space includes occupied and virtual orbitals of all symmetry irreps (this will be a very large active space), the number of occupied and virtual blocks for each index is 16 and 20, respectively, and the total number of blocks increases to . Not all of the blocks contain real information, some blocks are zero because of the spatial or spinsymmetry requirements. For the C symmetry group, the number of nonzero blocks is about 10–12 times less than the total number of blocks, i.e., . This is the number of nonzero blocks in one vector. Davidson diagonalization procedure requires (2*MAX_VECTORS + 2*NROOTS) vectors, where MAX_VECTORS is the maximum number of vectors in the subspace, and NROOTS is the number of the roots to solve for. Taking NROOTS=2 and MAX_VECTORS=20, we obtain 44 vectors with the total number of nonzero blocks being .
In CCMAN implementation, each block is a logical unit of information. Along with real data, which are kept on a hard drive at all the times except of their direct usage, each nonzero block contains an auxiliary information about its size, structure, relative position with respect to other blocks, location on a hard drive, and so on. The auxiliary information about blocks is always kept in memory. Currently, the approximate size of this auxiliary information is about 400 bytes per block. It means, that in order to keep information about one vector ( blocks), 1.2 GB of memory is required! The information about 44 vectors amounts 53 GB. Moreover, the huge number of blocks significantly slows down the code.
To make the calculations of active space EOMCC(2,3) feasible, we need to reduce the total number of blocks. One way to do this is to reduce the symmetry of the molecule to lower or C symmetry group (of course, this will result in more expensive calculation). For example, lowering the symmetry group from C to C would results in reducing the total number of blocks in active space EOMCC(2,3) calculations in about times, and the number of nonzero blocks in about 30 times (the relative portion of nonzero blocks in C symmetry group is smaller compared to that in C).
Alternatively, one may keep the MAX_VECTORS and NROOTS parameters of Davidson’s diagonalization procedure as small as possible (this mainly concerns the MAX_VECTORS parameter). For example, specifying MAX_VECTORS = 12 instead of 20 would require 30% less memory.
One more trick concerns specifying the active space. In a desperate situation of a severe lack of memory, should the two previous options fail, one can try to modify (increase) the active space in such a way that the fragmentation of active and restricted orbitals would be less. For example, if there is one restricted occupied orbital and one active occupied orbital, adding the restricted to the active space will reduce the number of blocks, by the price of increasing the number of FLOPS. In principle, adding extra orbital to the active space should increase the accuracy of calculations, however, a special care should be taken about the (near) degenerate pairs of orbitals, which should be handled in the same way, i.e., both active or both restricted.
EOMCC(2,3) is invoked by METHOD=EOMCC(2,3). The following options are available:
EOM_PRECONV_SD
Solves the EOMCCSD equations, prints energies, then uses EOMCCSD vectors as initial vectors in EOMCC(2,3). Very convenient for calculations using energy additivity schemes.
TYPE:
INTEGER
DEFAULT:
0
OPTIONS:
Do SD iterations
RECOMMENDATION:
Turning this option on is recommended
CC_REST_AMPL
Forces the integrals, , and amplitudes to be determined in the full space even though the CC_REST_OCC and CC_REST_VIR keywords are used.
TYPE:
INTEGER
DEFAULT:
1
OPTIONS:
0
Do apply restrictions
1
Do not apply restrictions
RECOMMENDATION:
None
CC_REST_TRIPLES
Restricts amplitudes to the active space, i.e., one electron should be removed from the active occupied orbital and one electron should be added to the active virtual orbital.
TYPE:
INTEGER
DEFAULT:
1
OPTIONS:
1
Applies the restrictions
RECOMMENDATION:
None
CC_REST_OCC
Sets the number of restricted occupied orbitals including frozen occupied orbitals.
TYPE:
INTEGER
DEFAULT:
0
OPTIONS:
Restrict occupied orbitals.
RECOMMENDATION:
None
CC_REST_VIR
Sets the number of restricted virtual orbitals including frozen virtual orbitals.
TYPE:
INTEGER
DEFAULT:
0
OPTIONS:
Restrict virtual orbitals.
RECOMMENDATION:
None
To select the active space, orbitals can be reordered by specifying the new order in the $reorder_mosection. The section consists of two rows of numbers ( and sets), starting from , and ending with , where is the number of the last orbital specified.
Example 6.151 Example $reorder_mosection with orbitals 16 and 17 swapped for both and electrons
$reorder_mo
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 17 16
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 17 16
$end
Example 6.152 EOMSF(2,3) calculations of methylene.
$molecule 0 3 C H 1 CH H 1 CH 2 HCH CH = 1.07 HCH = 111.0 $end $rem method eomcc(2,3) basis 631G sf_states [2,0,0,2] n_frozen_core 1 n_frozen_virtual 1 eom_preconv_sd 20 Get EOMCCSD energies first (max_iter=20). $end
Example 6.153 This is activespace EOMSF(2,3) calculations for methane with an elongated CC bond. HF MOs should be reordered as specified in the $reorder_mosection such that active space for triples consists of sigma and sigma* orbitals.
$molecule 0 3 C H 1 CH H 1 CHX 2 HCH H 1 CH 2 HCH 3 A120 H 1 CH 2 HCH 4 A120 CH=1.086 HCH=109.4712206 A120=120. CHX=1.8 $end $rem jobtype sp method eomcc(2,3) basis 631G* sf_states [1,0] n_frozen_core 1 eom_preconv_sd 20 does eomccsd first, max_iter=20 cc_rest_triples 1 triples are restricted to the active space only cc_rest_ampl 0 ccsd and eom singles and doubles are fullspace cc_rest_occ 4 specifies active space cc_rest_vir 17 specifies active space print_orbitals 10 (number of virtuals to print) $end $reorder_mo 1 2 5 4 3 1 2 3 4 5 $end
Example 6.154 EOMIPCC(2,3) calculation of three lowest electronic states of water cation.
$molecule 0 1 H 0.774767 0.000000 0.458565 O 0.000000 0.000000 0.114641 H 0.774767 0.000000 0.458565 $end $rem jobtype sp method eomcc(2,3) basis 6311G ip_states [1,0,1,1] $end
The effect of triple excitations to EOMCCSD energies can be included via perturbation theory in an economical computational scheme. Using EOMCCSD wavefunctions as zeroorder wavefunctions, the second order triples correction to the th EOMEE or SF state is:
(6.37) 
where and denote occupied orbitals, and and are virtual orbital indices. is the EOMCCSD excitation energy of the th state. The quantities and are:
(6.38)  
where, the and are left and right eigenvectors for th state. Two different choices of the denominator, , define the (dT) and (fT) variants of the correction. In (fT), is just HartreeFock orbital energy differences. A more accurate (but not fully orbital invariant) (dT) correction employs the complete three body diagonal of , , as a denominator. For the reference (e.g., a groundstate CCSD wavefunction), the (fT) and (dT) corrections are identical to the CCSD(2) and CRCCSD(T) corrections of Piecuch and coworkers [376].
The EOMSFCCSD(dT) and EOMSFCCSD(fT) methods yield a systematic improvement over EOMSFCCSD bringing the errors below 1 kcal/mol. For theoretical background and detailed benchmarks, see Ref. Manohar:2008.
Similar corrections are available for EOMIPCCSD [378], where triples correspond to excitations.
Triples corrections are requested by using METHOD or EOM_CORR:
METHOD
Specifies the calculation method.
TYPE:
STRING
DEFAULT:
No default value
OPTIONS:
EOMCCSD(DT)
EOMCCSD(dT), available for EE, SF, and IP
EOMCCSD(FT)
EOMCCSD(fT), available for EE, SF, and IP
EOMCCSD(ST)
EOMCCSD(sT), available for IP
RECOMMENDATION:
None
EOM_CORR
Specifies the correlation level.
TYPE:
STRING
DEFAULT:
None
No correction will be computed
OPTIONS:
SD(DT)
EOMCCSD(dT), available for EE, SF, and IP
SD(FT)
EOMCCSD(fT), available for EE, SF, and IP
SD(ST)
EOMCCSD(sT), available for IP
RECOMMENDATION:
None
Example 6.155 EOMEECCSD(fT) calculation of CH
$molecule 1 1 C H C CH CH = 2.137130 $end $rem input_bohr true jobtype sp method eomccsd(ft) basis general ee_states [1,0,1,1] eom_davidson_max_iter 60 increase number of Davidson iterations $end $basis H 0 S 3 1.00 19.24060000 0.3282800000E01 2.899200000 0.2312080000 0.6534000000 0.8172380000 S 1 1.00 0.1776000000 1.000000000 S 1 1.00 0.0250000000 1.000000000 P 1 1.00 1.00000000 1.00000000 **** C 0 S 6 1.00 4232.610000 0.2029000000E02 634.8820000 0.1553500000E01 146.0970000 0.7541100000E01 42.49740000 0.2571210000 14.18920000 0.5965550000 1.966600000 0.2425170000 S 1 1.00 5.147700000 1.000000000 S 1 1.00 0.4962000000 1.000000000 S 1 1.00 0.1533000000 1.000000000 S 1 1.00 0.0150000000 1.000000000 P 4 1.00 18.15570000 0.1853400000E01 3.986400000 0.1154420000 1.142900000 0.3862060000 0.3594000000 0.6400890000 P 1 1.00 0.1146000000 1.000000000 P 1 1.00 0.0110000000 1.000000000 D 1 1.00 0.750000000 1.00000000 **** $end
Example 6.156 EOMSFCCSD(dT) calculations of methylene
$molecule 0 3 C H 1 CH H 1 CH 2 HCH CH = 1.07 HCH = 111.0 $end $rem method eomccsd(dt) basis 631G sf_states [2,0,0,2] n_frozen_core 1 n_frozen_virtual 1 $end
Example 6.157 EOMIPCCSD(dT) calculations of Mg
$molecule 0 1 Mg 0.000000 0.000000 0.000000 $end $rem jobtype sp method eomccsd(dt) basis 631g ip_states [1,0,0,0,0,1,1,1] $end
Potential energy surface crossing optimization procedure finds energy minima on crossing seams. On the seam, the potential surfaces are degenerated in the subspace perpendicular to the plane defined by two vectors: the gradient difference
(6.39) 
and the derivative coupling
(6.40) 
At this time QChem is unable to locate crossing minima for states which have nonzero derivative coupling. Fortunately, often this is not the case. Minima on the seams of conical intersections of states of different multiplicity can be found as their derivative coupling is zero. Minima on the seams of intersections of states of different point group symmetry can be located as well.
To run a PES crossing minimization, CCSD and EOMCCSD methods must be employed for the ground and excited state calculations respectively.
XOPT_STATE_1, XOPT_STATE_2
Specify two electronic states the intersection of which will be searched.
TYPE:
[INTEGER, INTEGER, INTEGER]
DEFAULT:
No default value (the option must be specified to run this calculation)
OPTIONS:
[spin, irrep, state]
spin = 0
Addresses states with low spin,
see also EE_SINGLETS.
spin = 1
Addresses states with high spin,
see also EE_TRIPLETS.
irrep
Specifies the irreducible representation to which
the state belongs, for point group symmetry
irrep = 1 for , irrep = 2 for ,
irrep = 3 for , irrep = 4 for .
state
Specifies the state number within the irreducible
representation, state = 1 means the lowest excited
state, state = 2 is the second excited state, etc..
0, 0, 1
Ground state.
RECOMMENDATION:
Only intersections of states with different spin or symmetry can be calculated at this time.
Note: The spin can only be specified when using closedshell RHF references. In the case of openshell references all states are treated together, see also EE_STATES.
XOPT_SEAM_ONLY
Orders an intersection seam search only, no minimization is to perform.
TYPE:
LOGICAL
DEFAULT:
FALSE
OPTIONS:
TRUE
Find a point on the intersection seam and stop.
FALSE
Perform a minimization of the intersection seam.
RECOMMENDATION:
In systems with a large number of degrees of freedom it might be useful to locate the seam first setting this option to TRUE and use that geometry as a starting point for the minimization.
Example 6.158 Minimize the intersection of ÃA and B states of the NO molecule using EOMIPCCSD method
$molecule 1 1 N1 O2 N1 rno O3 N1 rno O2 aono rno = 1.3040 aono = 106.7 $end $rem JOBTYPE opt Optimize the intersection seam UNRESTRICTED true METHOD eomccsd BASIS 631g IP_STATES [1,0,1,0] C2v point group symmetry EOM_FAKE_IPEA 1 XOPT_STATE_1 [0,1,1] 1A1 low spin state XOPT_STATE_2 [0,3,1] 1B1 low spin state GEOM_OPT_TOL_GRADIENT 30 Tighten gradient tolerance $END
Example 6.159 Minimize the intersection of ÃB and A states of the N ion using EOMCCSD method
$molecule 1 1 N1 N2 N1 rnn N3 N2 rnn N1 annn rnn=1.46 annn=70.0 $end $rem JOBTYPE opt METHOD eomccsd BASIS 631g EE_SINGLES [0,2,0,2] C2v point group symmetry XOPT_STATE_1 [0,4,1] 1B2 low spin state XOPT_STATE_2 [0,2,2] 2A2 low spin state XOPT_SEAM_ONLY true Find the seam only GEOM_OPT_TOL_GRADIENT 100 $end $opt CONSTRAINT Set constraints on the NN bond lengths stre 1 2 1.46 stre 2 3 1.46 ENDCONSTRAINT $end @@@ $molecule READ $end $rem JOBTYPE opt Optimize the intersection seam METHOD eomccsd BASIS 631g EE_SINGLETS [0,2,0,2] XOPT_STATE_1 [0,4,1] XOPT_STATE_2 [0,2,2] GEOM_OPT_TOL_GRADIENT 30 $end
Dyson orbitals can be used to compute total photodetachment/photoionization cross sections, as well as angular distribution of photoelectrons. A Dyson orbital is the overlap between the Nelectron molecular wavefunction and the N1/N+1 electron wavefunction of the corresponding cation/anion:
(6.41)  
(6.42) 
For the HartreeFock wavefunctions and within Koopmans’ approximation, these are just the canonical HF orbitals. For correlated wavefunctions, Dyson orbitals are linear combinations of the reference molecular orbitals:
(6.43)  
(6.44)  
(6.45) 
The calculation of Dyson orbitals is straightforward within the EOMIP/EACCSD methods, where cation/anion and initial molecule states are defined with respect to the same MO basis. Since the left and right CC vectors are not the same, one can define correspondingly two Dyson orbitals (leftright and rightleft):
(6.46)  
(6.47) 
The norm of these orbitals is proportional to the oneelectron character of the transition.
Dyson orbitals also offer qualitative insight visualizing the difference between molecular and ionized/attached states. In ionization/photodetachment processes, these orbitals can be also interpreted as the wavefunction of the leaving electron. For additional details, see Refs. Oana:2007,Oana:2009.
The calculation of Dyson orbitals is implemented for the ground (reference) and excited states ionization/electron attachment. To obtain the ground state Dyson orbitals one needs to run an EOMIP/EACCSD calculation, request transition properties calculation by setting CC_TRANS_PROP=TRUE and CC_DO_DYSON = TRUE. The Dyson orbitals decomposition in the MO basis is printed in the output, for all transitions between the reference and all IP/EA states. At the end of the file, also the coefficients of the Dyson orbitals in the AO basis are available.
Two implementations of Dyson orbitals are currently available: (i) the original implementation in CCMAN; and (ii) new implementation in CCMAN2. The CCMAN implementation is using a diffuse orbital trick (i.e., EOM_FAKE_IPEA will be automatically set to TRUE in these calculations). Note: this implementation has a bug affecting the values of norms of Dyson orbitals (the shapes are correct); thus, using this code is strongly discouraged. CCMAN2 currently includes only EOMIP and EOMEA Dyson orbitals (EOMEE and SF is not yet available). Also, plotting Dyson orbitals in CCMAN2 is not yet available. The CCMAN2 implementation can utilize userspecified EOM guess (using EOM_USER_GUESS keyword and $eom_user_guess section), which is recommended for highly excited states (such as coreionized states).
CC_DO_DYSON
Whether the referencestate Dyson orbitals will be calculated for EOMIP/EACCSD calculations.
TYPE:
LOGICAL
DEFAULT:
FALSE (the option must be specified to run this calculation)
OPTIONS:
TRUE/FALSE
RECOMMENDATION:
none
For calculating Dyson orbitals between excited states from the reference configuration and IP/EA states, CC_TRANS_PROP=TRUE and CC_DO_DYSON_EE = TRUE have to be added to the usual EOMIP/EACCSD calculation. The IP_STATES keyword is used to specify the target ionized states. The attached states are specified by EA_STATES. The EASF states are specified by EOM_EA_BETA. The excited (or spinflipped) states are specified by EE_STATES and SF_STATES The Dyson orbital decomposition in MO and AO bases is printed for each EEIP/EA pair of states in the order: EE1  IP/EA1, EE1  IP/EA2, , EE2  IP/EA1, EE2  IP/EA2, , and so on. This feature is only available in CCMAN.
CC_DO_DYSON_EE
Whether excitedstate or spinflip state Dyson orbitals will be calculated for EOMIP/EACCSD calculations.
TYPE:
LOGICAL
DEFAULT:
FALSE (the option must be specified to run this calculation)
OPTIONS:
TRUE/FALSE
RECOMMENDATION:
none
Dyson orbitals can be also plotted using IANLTY = 200 and the $plots utility (CCMAN only). Only the sizes of the box need to be specified, followed by a line of zeros:
$plots comment 10 2 2 10 2 2 10 2 2 0 0 0 0 $plots
All Dyson orbitals on the xyz Cartesian grid will be written in the resulting plot.mo file. For RHF(UHF) reference, the columns order in plot.mo is:
In addition, setting the MAKE_CUBE_FILES keyword to TRUE will create cube files for Dyson orbitals which can be viewed with VMD or other programs (see Section 10.6.4 for details). Other means of visualization (e.g., with MOLDEN_FORMAT=TRUE or GUI=2) are currently not available.
Example 6.160 Plotting grdex and exgrd state Dyson orbitals for ionization of the oxygen molecule. The target states of the cation are A and B. Works for CCMAN only.
$molecule 0 3 O 0.000 0.000 0.000 O 1.222 0.000 0.000 $end $rem jobtype sp basis 631G* method eomccsd ip_states [1,0,0,0,0,0,1,0] Target EOMIP states cc_trans_prop true request transition OPDMs to be calculated cc_do_dyson true calculate Dyson orbitals IANLTY 200 $end $plots plots excited states densities and trans densities 10 2 2 10 2 2 10 2 2 0 0 0 0 $plots
Example 6.161 Plotting exex state Dyson orbitals between the 1st excited state of the HO radical and the the 1st A and A excited states of HO. Works for CCMAN only.
$molecule 1 1 H 0.000 0.000 0.000 O 1.000 0.000 0.000 $end $rem jobtype SP method eomccsd BASIS 631G* ip_states [1,0,0,0] states of HO radical ee_states [1,1,0,0] excited states of HO CC_TRANS_PROP true calculate transition properties CC_DO_DYSON_EE true calculate Dyson orbitals for ionization from ex. states IANLTY 200 $end $plots plot excited states densities and trans densities 10 2 2 10 2 2 10 2 2 0 0 0 0 $plots
Example 6.162 Dyson orbitals for ionization of CO molecule; A and B ionized states requested.
$molecule 0 1 O C O 1.131 $end $rem jobtype SP single point correlation CCSD basis ccpVDZ purecart 111 5d, will be required for ezDyson ip_states [1,0,1,0] (A1,A2,B1,B2) ccman2 true cc_do_dyson true cc_trans_prop true necessary for Dyson orbitals job print_general_basis true will be required for ezDyson $end
Example 6.163 Dyson orbitals for ionization of HO; core (A) state requested — ionization from O(1s).
$molecule 0 1 O H1 O 0.955 H2 O 0.955 H1 104.5 $end $rem jobtype SP single point correlation CCSD basis ccpVTZ purecart 111 5d, will be required for ezDyson ip_states [1,0,0,0] (A1,A2,B1,B2) eom_user_guess 1 on, further defined in $eom_user_guess ccman2 true cc_do_dyson true cc_trans_prop true necessary for Dyson orbitals job print_general_basis true will be required for ezDyson $end $eom_user_guess 1 $end
Example 6.164 Dyson orbitals for ionization of NO molecule using EOMEA and a closedshell cation reference; A and B states requested.
$molecule +1 1 N 0.00000 0.00000 0.00000 O 0.00000 0.00000 1.02286 $end $rem jobtype SP single point correlation CCSD basis augccpVTZ purecart 111 5d, will be required for ezDyson ea_states [1,0,0,1] (A1,A2,B1,B2) ccman2 true cc_do_dyson true cc_trans_prop true necessary for Dyson orbitals job print_general_basis true will be required for ezDyson $end
Example 6.165 Dyson orbitals for ionization of triplet O and O at slightly stretched (relative to the equibrium O geometry); B states are requested.
$comment EOMIPCCSD/6311+G* and EOMEACCSD/6311+G* levels of theory, UHF reference. Start from O2: 1) detach electron  ionizion of neutral (alpha IP). 2) attach electron, use EOMEA w.f. as initial state  ionization of anion (beta EA). $end $molecule 0 3 O 0.00000 0.00000 0.00000 O 0.00000 0.00000 1.30000 $end $rem jobtype SP single point correlation CCSD basis 6311(3+)G* purecart 2222 6d, will be required for ezDyson eom_ip_alpha [0,0,0,1,0,0,0,0] (Ag,B1g,B2g,B3g,Au,B1u,B2u,B3u) eom_ea_beta [0,0,0,1,0,0,0,0] (Ag,B1g,B2g,B3g,Au,B1u,B2u,B3u) ccman2 true cc_do_dyson true cc_trans_prop true necessary for Dyson orbitals job print_general_basis true will be required for ezDyson $end
Analysis of the leading wavefunction amplitudes is always necessary for determining the character of the state (e.g., HOMOLUMO excitation, openshell diradical, etc.). The CCMAN module print out leading EOM/CI amplitudes using its internal orbital numbering scheme, which is printed in the beginning. The typical CCMAN EOMCCSD output looks like:
Root 1 Convd yes Tot Ene= 113.722767530 hartree (Ex Ene 7.9548 eV), U1^2=0.858795, U2^2=0.141205 Res=4.4E07 Right U1: Value i > a 0.5358 7( B2 ) B > 17( B2 ) B 0.5358 7( B2 ) A > 17( B2 ) A 0.2278 7( B2 ) B > 18( B2 ) B 0.2278 7( B2 ) A > 18( B2 ) A
This means that this state is derived by excitation from occupied orbital #7 (which has symmetry) to virtual orbital #17 (which is also of symmetry). The two leading amplitudes correspond to and excitation (the spin part is denoted by or ). The orbital numbering for this job is defined by the following map:
The orbitals are ordered and numbered as follows: Alpha orbitals: Number Energy Type Symmetry ANLMAN number Total number: 0 20.613 AOCC A1 1A1 1 1 11.367 AOCC A1 2A1 2 2 1.324 AOCC A1 3A1 3 3 0.944 AOCC A1 4A1 4 4 0.600 AOCC A1 5A1 5 5 0.720 AOCC B1 1B1 6 6 0.473 AOCC B1 2B1 7 7 0.473 AOCC B2 1B2 8 0 0.071 AVIRT A1 6A1 9 1 0.100 AVIRT A1 7A1 10 2 0.290 AVIRT A1 8A1 11 3 0.327 AVIRT A1 9A1 12 4 0.367 AVIRT A1 10A1 13 5 0.454 AVIRT A1 11A1 14 6 0.808 AVIRT A1 12A1 15 7 1.196 AVIRT A1 13A1 16 8 1.295 AVIRT A1 14A1 17 9 1.562 AVIRT A1 15A1 18 10 2.003 AVIRT A1 16A1 19 11 0.100 AVIRT B1 3B1 20 12 0.319 AVIRT B1 4B1 21 13 0.395 AVIRT B1 5B1 22 14 0.881 AVIRT B1 6B1 23 15 1.291 AVIRT B1 7B1 24 16 1.550 AVIRT B1 8B1 25 17 0.040 AVIRT B2 2B2 26 18 0.137 AVIRT B2 3B2 27 19 0.330 AVIRT B2 4B2 28 20 0.853 AVIRT B2 5B2 29 21 1.491 AVIRT B2 6B2 30
The first column is CCMAN’s internal numbering (e.g., 7 and 17 from the example above). This is followed by the orbital energy, orbital type (frozen, restricted, active, occupied, virtual), and orbital symmetry. Note that the orbitals are blocked by symmetries and then ordered by energy within each symmetry block, (i.e., first all occupied , then all , etc.), and numbered starting from 0. The occupied and virtual orbitals are numbered separately, and frozen orbitals are excluded from CCMAN numbering. The two last columns give numbering in terms of the final ANLMAN printout (starting from 1), e.g., our occupied orbital #7 will be numbered as 1 in the final printout. The last column gives the absolute orbital number (all occupied and all virtuals together, starting from 1), which is often used by external visualization routines.
CCMAN2 numbers orbitals by their energy within each irrep keeping the same numbering for occupied and virtual orbitals. This numbering is exactly the same as in the final printout of the SCF wavefunction analysis. Orbital energies are printed next to the respective amplitudes. For example, a typical CCMAN2 EOMCCSD output will look like that:
EOMEECCSD transition 2/A1 Total energy = 75.87450159 a.u. Excitation energy = 11.2971 eV. R1^2 = 0.9396 R2^2 = 0.0604 Res^2 = 9.51e08 Amplitude Orbitals with energies 0.6486 1 (B2) A > 2 (B2) A 0.5101 0.1729 0.6486 1 (B2) B > 2 (B2) B 0.5101 0.1729 0.1268 3 (A1) A > 4 (A1) A 0.5863 0.0404 0.1268 3 (A1) B > 4 (A1) B 0.5863 0.0404
which means that for this state, the leading EOM amplitude corresponds to the transition from the first b orbital (orbital energy ) to the second b orbital (orbital energy 0.1729).