7.11 Correlated Excited State Methods: The ADC(n) Family

7.11.11 ADC Job Control

(June 30, 2021)

For an ADC calculation it is important to ensure that there are sufficient resources available for the necessary integral calculations and transformations. These resources are controlled using the $rem variables MEM_STATIC and MEM_TOTAL. The memory used by ADC is currently 95% of the difference MEM_TOTAL - MEM_STATIC.

An ADC calculation is requested by setting the $rem variable METHOD to the respective ADC variant. Furthermore, the number of excited states to be calculated has to be specified using one of the $rem variables EE_STATES, EE_SINGLETS or EE_TRIPLETS. The former variable should be used for open-shell or unrestricted closed-shell calculations, while the latter two variables are intended for restricted closed-shell calculations. Even though not recommended, it is possible to use EE_STATES in a restricted calculation which translates into EE_SINGLETS, if neither EE_SINGLETS nor EE_TRIPLETS is set. Similarly, the use EE_SINGLETS in an unrestricted calculation will translate into EE_STATES, if the latter is not set as well. For IP- and EA-ADC calculations, the IP_STATES, EOM_IP_ALPHA, EOM_IP_BETA, EA_STATES, EOM_EA_ALPHA and EOM_EA_BETA are available to control the number and type of ionized or electron-attached states to calculate. IP_STATES and EA_STATES should be used in case of restricted calculations, while the EOM_[IP/EA]_[ALPHA/BETA] keywords control the number of α- and β-ionized and -electron-attached states to calculate in case of unrestricted or open-shell calculations.

All $rem variables to set the number of excited, ionized or electron-attached states accept either an integer number or a vector of integer numbers. A single number specifies that the same number of excited states are calculated for every irreducible representation the point group of the molecular system possesses (molecules without symmetry are treated as C1 symmetric). In contrast, a vector of numbers determines the number of states for each irreducible representation explicitly. Thus, the length of the vector always has to match the number of irreducible representations. Hereby, the excited states are labeled according to the irreducible representation of the electronic transition which might be different from the irreducible representation of the excited state wave function. Users can choose to calculate any molecule as C1 symmetric by setting CC_SYMMETRY = FALSE.

METHOD
       Controls the order in perturbation theory of ADC.
TYPE:
       STRING
DEFAULT:
       None
OPTIONS:
       ADC(1) Perform ADC(1) calculation. ADC(2) Perform ADC(2)-s, IP-ADC(2)-s or EA-ADC(2)-s calculation. ADC(2)-x Perform ADC(2)-x calculation. ADC(3) Perform ADC(3), IP-ADC(3) or EA-ADC(3) calculation. SOS-ADC(2) Perform spin-opposite scaled ADC(2)-s calculation. SOS-ADC(2)-x Perform spin-opposite scaled ADC(2)-x calculation. CVS-ADC(1) Perform ADC(1) calculation of core excitations. CVS-ADC(2) Perform ADC(2)-s calculation of core excitations. CVS-ADC(2)-x Perform ADC(2)-x calculation of core excitations.
RECOMMENDATION:
       None

EE_STATES
       Controls the number of excited states to calculate.
TYPE:
       INTEGER/ARRAY
DEFAULT:
       0 Do not perform an ADC calculation
OPTIONS:
       n>0 Number of states to calculate for each irrep or [n1,n2,] Compute n1 states for the first irrep, n2 states for the second irrep, …
RECOMMENDATION:
       Use this variable to define the number of excited states in case of unrestricted or open-shell calculations. In restricted calculations it can also be used, if neither EE_SINGLETS nor EE_TRIPLETS is given. Then, it has the same effect as setting EE_SINGLETS.

EE_SINGLETS
       Controls the number of singlet excited states to calculate.
TYPE:
       INTEGER/ARRAY
DEFAULT:
       0 Do not perform an ADC calculation of singlet excited states
OPTIONS:
       n>0 Number of singlet states to calculate for each irrep or [n1,n2,] Compute n1 states for the first irrep, n2 states for the second irrep, …
RECOMMENDATION:
       Use this variable to define the number of excited states in case of restricted calculations of singlet states. In unrestricted calculations it can also be used, if EE_STATES not set. Then, it has the same effect as setting EE_STATES.

EE_TRIPLETS
       Controls the number of triplet excited states to calculate.
TYPE:
       INTEGER/INTEGER ARRAY
DEFAULT:
       0 Do not perform an ADC calculation of triplet excited states
OPTIONS:
       n>0 Number of triplet states to calculate for each irrep or [n1,n2,] Compute n1 states for the first irrep, n2 states for the second irrep, …
RECOMMENDATION:
       Use this variable to define the number of excited states in case of restricted calculations of triplet states.

IP_STATES
       Controls the number of ionized states to calculate.
TYPE:
       INTEGER/INTEGER ARRAY
DEFAULT:
       0 Do not perform an IP-ADC calculation
OPTIONS:
       n>0 Number of states to calculate for each irrep or [n1,n2,] Compute n1 states for the first irrep, n2 states for the second irrep, …
RECOMMENDATION:
       Use this variable to define the number of ionized states in case of restricted calculations.

EOM_IP_ALPHA
       Controls the number of α-ionized states to calculate.
TYPE:
       INTEGER/INTEGER ARRAY
DEFAULT:
       0 Do not compute α-ionized states
OPTIONS:
       n>0 Number of α-ionized states to calculate for each irrep or [n1,n2,] Compute n1 α-ionized states for the first irrep, n2 α-ionized states for the second irrep, …
RECOMMENDATION:
       Use this variable to define the number of α-ionized states in case of unrestricted or open-shell calculations.

EOM_IP_BETA
       Controls the number of β-ionized states to calculate.
TYPE:
       INTEGER/INTEGER ARRAY
DEFAULT:
       0 Do not compute β-ionized states
OPTIONS:
       n>0 Number of β-ionized states to calculate for each irrep or [n1,n2,] Compute n1 β-ionized states for the first irrep, n2 β-ionized states for the second irrep, …
RECOMMENDATION:
       Use this variable to define the number of β-ionized states in case of unrestricted or open-shell calculations.

EA_STATES
       Controls the number of electron-attached states to calculate.
TYPE:
       INTEGER/INTEGER ARRAY
DEFAULT:
       0 Do not perform an EA-ADC calculation
OPTIONS:
       n>0 Number of states to calculate for each irrep or [n1,n2,] Compute n1 states for the first irrep, n2 states for the second irrep, …
RECOMMENDATION:
       Use this variable to define the number of electron-attached states in case of restricted calculations.

EOM_EA_ALPHA
       Controls the number of α-electron-attached states to calculate.
TYPE:
       INTEGER/INTEGER ARRAY
DEFAULT:
       0 Do not compute α-electron-attached states
OPTIONS:
       n>0 Number of α-electron-attached states to calculate for each irrep or [n1,n2,] Compute n1 α-electron-attached states for the first irrep, n2 α-electron-attached states for the second irrep, …
RECOMMENDATION:
       Use this variable to define the number of α-electron-attached states in case of unrestricted or open-shell calculations.

EOM_EA_BETA
       Controls the number of β-electron-attached states to calculate.
TYPE:
       INTEGER/INTEGER ARRAY
DEFAULT:
       0 Do not compute β-electron-attached states
OPTIONS:
       n>0 Number of β-electron-attached states to calculate for each irrep or [n1,n2,] Compute n1 β-electron-attached states for the first irrep, n2 β-electron-attached states for the second irrep, …
RECOMMENDATION:
       Use this variable to define the number of β-electron-attached states in case of unrestricted or open-shell calculations.

CC_SYMMETRY
       Activates point-group symmetry in the ADC calculation.
TYPE:
       LOGICAL
DEFAULT:
       TRUE If the system possesses any point-group symmetry.
OPTIONS:
       TRUE Employ point-group symmetry FALSE Do not use point-group symmetry
RECOMMENDATION:
       None

ADC_DENSITY_ORDER
       Controls the order of the ground state density used for the computation of third-order ADC matrix elements (non-CVS methods only).
TYPE:
       INTEGER
DEFAULT:
       2 Use strict third-order ADC(3) schemes.
OPTIONS:
       3 Use a third-order ground state density computed from the IP-ADC(3) effective transition moments and the corresponding fourth order static self-energy according to the Σ(4) scheme 4 Use an improved third-order ground state density and the corresponding improved fourth-order static self-energy computed according to the self-consistent Σ(4+) procedure
RECOMMENDATION:
       In case of IP-ADC(3) calculations, employing the Σ(4+) scheme provides more accurate ionization potentials and ionized state dipole moments.

ADC_DENSITY_MAXITER
       When setting ADC_DENSITY_ORDER = 4, this keyword controls the maximum number of DIIS iterations carried out in the Σ(4+) procedure.
TYPE:
       INTEGER
DEFAULT:
       1000
OPTIONS:
       n User-defined integer.
RECOMMENDATION:
       Use the default value.

ADC_DIRECT
       For third-order ADC methods, this keyword controls if some large intermediate tensor contractions should be carried out in advance and the result saved in memory for later use or if these quantities should be evaluated directly whenever they are encountered.
TYPE:
       LOGICAL
DEFAULT:
       FALSE
OPTIONS:
       TRUE Directly evaluate some N6-scaling tensor contractions. This will reduce the memory requirement by 10 %. FALSE Precompute all possible N6-scaling intermediates. This will speed up ADC(3) calculations considerably (by a factor of 3 in case of ADC(3) for N-electron excitations and somewhat less for IP- and EA-ADC(3)).
RECOMMENDATION:
       Use the default value unless memory is the bottleneck.

ADC_STRICT_ISR
       Controls how second-order ground state contributions are treated in the calculation of second- and third-order IP- and EA-ADC state properties using the second-order ISR formalism.
TYPE:
       LOGICAL
DEFAULT:
       FALSE
OPTIONS:
       TRUE Scale the second-order part of the ground state contribution to one-electron properties of ionized/electron-attached states by the one-hole/one-particle character of the respective states as implied by the strict ISR derivation. FALSE Use the full second-order ground state contribution for each ionized/electron-attached state property.
RECOMMENDATION:
       Use the default value. Both options are, however, valid second-order treatments of ionized/electron-attached state properties and should yield very similar results for states with predominant one-hole/one-particle chaaracter.

ADC_DO_DYSON
       Controls if Dyson orbitals are output in case of IP- and EA-ADC calculations. This keyword only takes effect when used together with STATE_ANALYSIS = TRUE. See Section. 10.2.6 for further details.
TYPE:
       LOGICAL
DEFAULT:
       FALSE
OPTIONS:
       TRUE Output Dyson orbitals as cube files. FALSE Do not output Dyson orbitals.
RECOMMENDATION:
       Set to TRUE if visualization of ionization/electron-attachment processes is desired.

ADC_CAP
       Controls the type of CAP/ADC calculation to be performed.
TYPE:
       INTEGER
DEFAULT:
       0 Do not perform a CAP/ADC calculation.
OPTIONS:
       1 Perform a subspace-projected CAP/ADC calculation.
RECOMMENDATION:
       Set to 1 for the computation of CAP/ADC subspace projections.

CAP_X
       For ADC methods, in combination with a smoothed Voronoi-CAP (CAP_TYPE = 2) or a spherical CAP (CAP_TYPE = 0), this keyword controls the lower limit for a series of CAP onsets, where the upper limit is given by CAP_X_END. The parameter value in a.u. is obtained by multiplying the given integer by 10-3. In this case, the onset value defines the region around the molecule with zero CAP strength. In combination with a cuboid CAP (CAP_TYPE = 1) or in general for other electronic structure methods (see 7.10.8 for further details), this keyword controls the CAP onset in x direction.
TYPE:
       INTEGER
DEFAULT:
       0
OPTIONS:
       n>0 User-defined integer.
RECOMMENDATION:
       Usually, values of 2000 to 4000 (corresponding to onset values between 2.0 and 4.0 a.u.) give reasonable results.

CAP_X_STEP
       Controls the step size for a series of CAP onsets between CAP_X and CAP_X_END. The parameter value in a.u. is obtained by multiplying the given integer by 10-3. Currently only used in ADC methods.
TYPE:
       INTEGER
DEFAULT:
       500 corresponding to 0.5 a.u.
OPTIONS:
       n>0 User-defined integer.
RECOMMENDATION:
       None.

CAP_X_END
       Controls the upper onset limit for a series of CAP onsets, where the lower limit is given by CAP_X. The parameter value in a.u. is obtained by multiplying the given integer by 10-3. Currently only used in ADC methods.
TYPE:
       INTEGER
DEFAULT:
       CAP_X Do not compute a series of CAP onsets but only use a single CAP with an onset value of CAP_X.
OPTIONS:
       n>CAP_X User-defined integer.
RECOMMENDATION:
       Use this keyword if CAP onset series are desired.

ADC_PROP_ES
       Controls the calculation of excited, ionized or electron-attached state properties (currently only dipole moments and r^2 expectation values).
TYPE:
       LOGICAL
DEFAULT:
       FALSE
OPTIONS:
       TRUE Calculate excited, ionized or electron-attached state properties. FALSE Do not compute state properties.
RECOMMENDATION:
       Set to TRUE, if properties are required.

ADC_PROP_ES2ES
       Controls the calculation of transition properties between excited, ionized or electron-attached states (currently only transition dipole moments and oscillator strengths). For ADC for N-electron excitations, this keyword also controls the computation of two-photon absorption cross-sections of excited states using the sum-over-states expression.
TYPE:
       LOGICAL
DEFAULT:
       FALSE
OPTIONS:
       TRUE Calculate state-to-state transition properties. FALSE Do not compute transition properties between excited, ionized or electron-attached states.
RECOMMENDATION:
       Set to TRUE, if state-to-state properties (ADC, IP-ADC, EA-ADC) or sum-over-states two-photon absorption cross-sections (only ADC) are required.

ADC_PROP_TPA
       Controls the calculation of two-photon absorption cross-sections of excited states using matrix inversion techniques.
TYPE:
       LOGICAL
DEFAULT:
       FALSE
OPTIONS:
       TRUE Calculate two-photon absorption cross-sections. FALSE Do not compute two-photon absorption cross-sections.
RECOMMENDATION:
       Set to TRUE, if to obtain two-photon absorption cross-sections.

STATE_ANALYSIS
       Controls the analysis and export of excited, ionized or electron-attached state densities and orbitals (see 10.2.6 for details).
TYPE:
       LOGICAL
DEFAULT:
       FALSE
OPTIONS:
       TRUE Perform excited state analyses. FALSE No excited state analyses or export will be performed.
RECOMMENDATION:
       Set to TRUE, if detailed analysis of the excited, ionized or electron-attached states is required or if density or orbital plots are needed.

ADC_C_T
       Set the spin-opposite scaling parameter cT for an SOS-ADC(2) calculation. The parameter value is obtained by multiplying the given integer by 10-3.
TYPE:
       INTEGER
DEFAULT:
       1300 Optimized value cT=1.3.
OPTIONS:
       n Corresponding to n10-3
RECOMMENDATION:
       Use the default.

ADC_C_C
       Set the spin-opposite scaling parameter cc for the ADC(2) calculation. The parameter value is obtained by multiplying the given integer by 10-3.
TYPE:
       INTEGER
DEFAULT:
       1170 Optimized value cc=1.17 for ADC(2)-s or 1000 cc=1.0 for ADC(2)-x
OPTIONS:
       n Corresponding to n10-3
RECOMMENDATION:
       Use the default.

ADC_C_X
       Set the spin-opposite scaling parameter cx for the ADC(2)-x calculation. The parameter value is obtained by multiplying the given integer by 10-3.
TYPE:
       INTEGER
DEFAULT:
       1300 Optimized value cx=0.9 for ADC(2)-x.
OPTIONS:
       n Corresponding to n10-3
RECOMMENDATION:
       Use the default.

ADC_NGUESS_SINGLES
       Controls the number of excited state guess vectors which are single excitations, one-hole ionizations and one-particle electron-attachments in case of ADC, IP-ADC and EA-ADC, respectively. If the number of requested excited states exceeds the total number of guess vectors (singles and doubles), this parameter is automatically adjusted, so that the number of guess vectors matches the number of requested excited states.
TYPE:
       INTEGER
DEFAULT:
       Equals to the number of excited states requested.
OPTIONS:
       n User-defined integer.
RECOMMENDATION:
       Increase if there are convergence problems.

ADC_NGUESS_DOUBLES
       Controls the number of excited state guess vectors which are double excitations, two-hole-one-particle ionizations and one-hole-two-particle electron-attachments in case of ADC, IP-ADC and EA-ADC, respectively.
TYPE:
       INTEGER
DEFAULT:
       0
OPTIONS:
       n User-defined integer.
RECOMMENDATION:
      

ADC_DO_DIIS
       Activates the use of the DIIS algorithm for the calculation of ADC(2) excited states.
TYPE:
       LOGICAL
DEFAULT:
       FALSE
OPTIONS:
       TRUE Use DIIS algorithm. FALSE Do diagonalization using Davidson algorithm.
RECOMMENDATION:
       None.

ADC_DIIS_START
       Controls the iteration step at which DIIS is turned on.
TYPE:
       INTEGER
DEFAULT:
       1
OPTIONS:
       n User-defined integer.
RECOMMENDATION:
       Set to a large number to switch off DIIS steps.

ADC_DIIS_SIZE
       Controls the size of the DIIS subspace.
TYPE:
       INTEGER
DEFAULT:
       7
OPTIONS:
       n User-defined integer
RECOMMENDATION:
       None

ADC_DIIS_MAXITER
       Controls the maximum number of DIIS iterations.
TYPE:
       INTEGER
DEFAULT:
       50
OPTIONS:
       n User-defined integer.
RECOMMENDATION:
       Increase in case of slow convergence.

ADC_DIIS_ECONV
       Controls the convergence criterion for the excited state energy during DIIS.
TYPE:
       INTEGER
DEFAULT:
       6 Corresponding to 10-6
OPTIONS:
       n Corresponding to 10-n
RECOMMENDATION:
       None

ADC_DIIS_RCONV
       Convergence criterion for the residual vector norm of the excited state during DIIS.
TYPE:
       INTEGER
DEFAULT:
       6 Corresponding to 10-6
OPTIONS:
       n Corresponding to 10-n
RECOMMENDATION:
       None

ADC_DAVIDSON_MAXSUBSPACE
       Controls the maximum subspace size for the Davidson procedure.
TYPE:
       INTEGER
DEFAULT:
       5× the number of excited states to be calculated.
OPTIONS:
       n User-defined integer.
RECOMMENDATION:
       Should be at least 2–4× the number of excited states to calculate. The larger the value the more disk space is required.

ADC_DAVIDSON_MAXITER
       Controls the maximum number of iterations of the Davidson procedure.
TYPE:
       INTEGER
DEFAULT:
       60
OPTIONS:
       n Number of iterations
RECOMMENDATION:
       Use the default unless convergence problems are encountered.

ADC_DAVIDSON_CONV
       Controls the convergence criterion of the Davidson procedure.
TYPE:
       INTEGER
DEFAULT:
       6 Corresponding to 10-6
OPTIONS:
       n12 Corresponding to 10-n.
RECOMMENDATION:
       Use the default unless higher accuracy is required or convergence problems are encountered.

ADC_DAVIDSON_THRESH
       Controls the threshold for the norm of expansion vectors to be added during the Davidson procedure.
TYPE:
       INTEGER
DEFAULT:
       Twice the value of ADC_DAVIDSON_CONV, but at maximum 10-14.
OPTIONS:
       n14 Corresponding to 10-n
RECOMMENDATION:
       Use the default unless convergence problems are encountered. The threshold value 10-n should always be smaller than the convergence criterion ADC_DAVIDSON_CONV.

ADC_PRINT
       Controls the amount of printing during an ADC calculation.
TYPE:
       INTEGER
DEFAULT:
       1 Basic status information and results are printed.
OPTIONS:
       0 Quiet: almost only results are printed. 1 Normal: basic status information and results are printed. 2 Debug: more status information, extended information on timings.
RECOMMENDATION:
       Use the default.

ADC_CVS
       Activates the use of the CVS approximation for the calculation of CVS-ADC core-excited states.
TYPE:
       LOGICAL
DEFAULT:
       FALSE
OPTIONS:
       TRUE Activates the CVS approximation. FALSE Do not compute core-excited states using the CVS approximation.
RECOMMENDATION:
       Set to TRUE, if to obtain core-excited states for the simulation of X-ray absorption spectra. In the case of TRUE, the $rem variable CC_REST_OCC has to be defined as well.

CC_REST_OCC
       Sets the number of restricted occupied orbitals including active core occupied orbitals.
TYPE:
       INTEGER
DEFAULT:
       0
OPTIONS:
       n Restrict n energetically lowest occupied orbitals to correspond to the active core space.
RECOMMENDATION:
       Example: cytosine with the molecular formula C4H5N3O includes one oxygen atom. To calculate O 1s core-excited states, n has to be set to 1, because the 1s orbital of oxygen is the energetically lowest. To obtain the N 1s core excitations, the integer n has to be set to 4, because the 1s orbital of the oxygen atom is included as well, since it is energetically below the three 1s orbitals of the nitrogen atoms. Accordingly, to simulate the C 1s spectrum of cytosine, n must be set to 8.

SF_STATES
       Controls the number of excited spin-flip states to calculate.
TYPE:
       INTEGER
DEFAULT:
       0 Do not perform a SF-ADC calculation
OPTIONS:
       n>0 Number of states to calculate for each irrep or [n1,n2,] Compute n1 states for the first irrep, n2 states for the second irrep, …
RECOMMENDATION:
       Use this variable to define the number of excited states in the case of a spin-flip calculation. SF-ADC is available for ADC(2)-s, ADC(2)-x and ADC(3).

Keywords for SS-PCM control in $pcm:

EQSOLV
       Main switch of the self-consistent SS-PCM procedure.
INPUT SECTION: $pcm
TYPE:
       INTEGER
DEFAULT:
       0
OPTIONS:
       0 No self-consistent SS-PCM. 1 Single SS-PCM calculation (SCF+ADC) with the solvent field found on disk. n>1 Do a maximum of n automatic solvent-field iterations.
RECOMMENDATION:
       We recommend to use 15 steps max. Typical convergence is 3-5 steps. In difficult cases 6-12. If the solvent-field iteration do not converge in 15 steps, something is wrong. Also make sure that a solvent field has been stored on disk by a previous job.

EQSTATE
       Specifies the state for which the solvent field is to be optimized.
INPUT SECTION: $pcm
TYPE:
       INTEGER
DEFAULT:
       0
OPTIONS:
       0 MP2 ground state (for PTED approach) 1 energetically lowest excited state 2 2nd lowest excited state
RECOMMENDATION:
       Given that only one class of excited states is calculated, the state will be selected according to its energetic position shown in the “Exited-State Summary” of the output file. A maximum of 99 states is stored and can be selected.

EQS_CONV
       Controls the convergence of the solvent-field iterations by setting the convergence criteria (a mixture of SCF energy and charge-vector). SCF energy criterion computes as 10-value Eh.
INPUT SECTION: $pcm
TYPE:
       INTEGER
DEFAULT:
       SCF_CONVERGENCE-4=4
OPTIONS:
       3 May be sufficient for emission energies 4 Assured converged total energies (2.7 meV) 5 Really tight
RECOMMENDATION:
       Use the default.

EQS_REF
       Allows to specify which state is to be treated as the reference state in the ADC part of the calculation. Does in contrast to EQSTATE not affect which solvent field is loaded in the SCF step. Only has to be used when singlets are computed in the solvent field of a triplet reference. Note that (converged) singlets states are always counted before triplets, and thus to select T1 in a calculation with EE_SINGLETS = 2 this has to be set to 3.
INPUT SECTION: $pcm
TYPE:
       INTEGER
DEFAULT:
       Same as EQSTATE
OPTIONS:
       1 First excited state 2 Second excited state
RECOMMENDATION:
       Only needed when computing singlet states in the solvent field of a triplet reference.