7.8 Coupled-Cluster Excited-State and Open-Shell Methods

7.8.17 EOM-CC Optimization and Properties Job Control

CC_STATE_TO_OPT
       Specifies which state to optimize (or from which state compute EOM-EOM inter-state properties).
TYPE:
       INTEGER ARRAY
DEFAULT:
       None
OPTIONS:
       [i,j] optimize the jth state of the ith 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 C1 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 non-relaxed (expectation value) one-particle EOM-CCSD target state properties will be calculated. The properties currently include permanent dipole moment, the second moments X2, Y2, and Z2 of electron density, and the total R2=X2+Y2+Z2 (in atomic units). Incompatible with JOBTYPE=FORCE, OPT, FREQ.
TYPE:
       LOGICAL
DEFAULT:
       FALSE (no one-particle properties will be calculated)
OPTIONS:
       FALSE, TRUE
RECOMMENDATION:
       Additional equations (EOM-CCSD equations for the left eigenvectors) need to be solved for properties, approximately doubling the cost of calculation for each irrep. The cost of the one-particle properties calculation itself is low. The one-particle density of an EOM-CCSD target state can be analyzed with NBO or libwfa packages 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 EOM-CCSD target states will be calculated. By default, the transition dipole moment is calculated between the CCSD reference and the EOM-CCSD target states. In order to calculate transition dipole moment between a set of EOM-CCSD states and another EOM-CCSD state, the CC_STATE_TO_OPT must be specified for this state.
TYPE:
       INTEGER
DEFAULT:
       0 (no transition properties will be calculated)
OPTIONS:
       1 (calculate transition properties between all computed EOM state and the reference state) 2 (calculate transition properties between all pairs of EOM states)
RECOMMENDATION:
       Additional equations (for the left EOM-CCSD eigenvectors plus lambda CCSD equations in case if transition properties between the CCSD reference and EOM-CCSD 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.

Note:  When $trans_prop section is present in the input, it disables CC_TRANS_PROP rem.

CC_EOM_2PA
       Whether or not the transition moments and cross-sections for two-photon absorption will be calculated. By default, the transition moments are calculated between the CCSD reference and the EOM-CCSD target states. In order to calculate transition moments between a set of EOM-CCSD states and another EOM-CCSD state, the CC_STATE_TO_OPT must be specified for this state. If 2PA NTO analysis is requested, the CC_EOM_2PA value is redundant as long as CC_EOM_2PA >0.
TYPE:
       INTEGER
DEFAULT:
       0 (do not compute 2PA transition moments)
OPTIONS:
       1 Compute 2PA using the fastest algorithm (use σ~-intermediates for canonical and σ-intermediates for RI/CD response calculations). 2 Use σ-intermediates for 2PA response equation calculations. 3 Use σ~-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 the default algorithm. Setting CC_EOM_2PA >0 turns on CC_TRANS_PROP.

CALC_SOC
       Whether or not the spin-orbit couplings between CC/EOM/ADC/CIS/TDDFT electronic states will be calculated. In the CC/EOM-CC suite, by default the couplings are calculated between the CCSD reference and the EOM-CCSD target states. In order to calculate couplings between EOM states, CC_STATE_TO_OPT must specify the initial EOM state.
TYPE:
       INTEGER/LOGICAL
DEFAULT:
       FALSE (no spin-orbit couplings will be calculated)
OPTIONS:
       0/FALSE (no spin-orbit couplings will be calculated) 1/TRUE Activates SOC calculation. EOM-CC/EOM-MP2 only: spin-orbit couplings will be computed with the new code with L+/L- averaging 2 EOM-CC/EOM-MP2 only: spin-orbit couplings will be computed with the new code without L+/L- averaging 3 EOM-CC/EOM-MP2 only: spin-orbit couplings will be computed with the legacy code
RECOMMENDATION:
       CCMAN2 supports several variants of SOC calculation for EOM-CC/EOM-MP2 methods. One-electron and mean-field two-electron SOCs will be computed by default. To enable full two-electron SOCs, two-particle EOM properties must be turned on (see CC_EOM_PROP_TE).

CALC_NAC
       Whether or not non-adiabatic couplings will be calculated for the EOM-CC, CIS, and TDDFT wave functions.
TYPE:
       INTEGER
DEFAULT:
       0 (do not compute NAC)
OPTIONS:
       1 NYI for EOM-CC 2 Compute NACs using Szalay’s approach (this what needs to be specified for EOM-CC).
RECOMMENDATION:
       Additional response equations will be solved and gradients for all EOM states and for summed states will be computed, which increases the cost of calculations. Request only when needed and do not ask for too many EOM states.

CC_POL
       Specifies the approach for calculating the polarizability of the CCSD wave function.
TYPE:
       INTEGER
DEFAULT:
       0 (CCSD polarizability will not be calculated)
OPTIONS:
       1 (analytic-derivative or response-theory mixed symmetric-asymmetric approach) 2 (analytic-derivative or response-theory asymmetric approach) 3 (expectation-value approach with right response intermediates) 4 (expectation-value approach with left response intermediates)
RECOMMENDATION:
       CCSD polarizabilities are expensive since they require solving three/six (for static) or six/twelve (for dynamical) additional response equations. Do no request this property unless you need it.

EOM_POL
       Specifies the approach for calculating the polarizability of the EOM-CCSD wave function.
TYPE:
       INTEGER
DEFAULT:
       0 (EOM-CCSD polarizability will not be calculated)
OPTIONS:
       1 (analytic-derivative or response-theory mixed symmetric-asymmetric approach) 2 (analytic-derivative or response-theory asymmetric approach) 3 (expectation-value approach with right response intermediates) 4 (expectation-value approach with left response intermediates)
RECOMMENDATION:
       EOM-CCSD polarizabilities are expensive since they require solving three/nine (for static) or six/eighteen (for dynamical) additional response equations. Do no request this property unless you need it.

EOM_REF_PROP_TE
       Request for calculation of non-relaxed two-particle EOM-CC properties. The two-particle properties currently include S2. The one-particle properties also will be calculated, since the additional cost of the one-particle properties calculation is inferior compared to the cost of S2. The variable CC_EOM_PROP must be also set to TRUE. Alternatively, CC_CALC_SSQ can be used to request S2 calculation.
TYPE:
       LOGICAL
DEFAULT:
       FALSE (no two-particle properties will be calculated)
OPTIONS:
       FALSE, TRUE
RECOMMENDATION:
       The two-particle properties are computationally expensive since they require calculation and use of the two-particle density matrix (the cost is approximately the same as the cost of an analytic gradient calculation). Do not request the two-particle properties unless you really need them.

CC_FULLRESPONSE
       Fully relaxed properties (with or without orbital relaxation terms) will be computed. The variable CC_EOM_PROP must be also set to TRUE.
TYPE:
       INTEGER
DEFAULT:
       0 (no amplitude and orbital response will be calculated)
OPTIONS:
       1 (both amplitude and orbital response will be calculated) 2 (only amplitude response will be calculated)
RECOMMENDATION:
       Not available for non-UHF/RHF references. Only available for EOM/CI methods for which analytic gradients are available.

CC_SYMMETRY
       Controls the use of symmetry in coupled-cluster 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 A symmetry).
RECOMMENDATION:
       It is automatically turned off for any finite difference calculations, e.g. second derivatives.

STATE_ANALYSIS
       Activates excited state analyses using libwfa.
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 11.2.6.

7.8.17.1 Examples

Example 7.57  Geometry optimization for the excited open-shell singlet state, B21, of methylene followed by the calculations of the fully relaxed one-electron properties using EOM-EE-CCSD.

$molecule
   0 1
   C
   H  1 rCH
   H  1 rCH 2 aHCH

   rCH    = 1.083
   aHCH   = 145.
$end

$rem
   JOBTYPE                   OPT
   METHOD                    EOM-CCSD
   BASIS                     cc-pVTZ
   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
   METHOD               EOM-CCSD
   BASIS                cc-pVTZ
   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 7.58  Property and transition property calculation on the lowest singlet state of CH2 using EOM-SF-CCSD.

$molecule
   0 3
   C
   H  1 rch
   H  1 rch 2 ahch

  rch  = 1.1167
  ahch = 102.07
$end

$rem
   METHOD             eom-ccsd
   BASIS              cc-pvtz
   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 7.59  Geometry optimization with tight convergence for the 2A1 excited state of CH2Cl, followed by calculation of non-relaxed and fully relaxed permanent dipole moment and S2.

$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                     EOM-CCSD
   BASIS                      6-31G*  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
   METHOD             EOM-CCSD
   BASIS              6-31G*  Basis Set
   SCF_GUESS          READ
   EE_STATES          [0,0,0,1]
   EOM_NGUESS_SINGLES  2
   CC_EOM_PROP        1   calculate one-electron properties
   CC_EOM_PROP_TE     1   and two-electron properties (S^2)
$end

@@@

$molecule
   read
$end

$rem
   METHOD              EOM-CCSD
   BASIS               6-31G*  Basis Set
   SCF_GUESS           READ
   EE_STATES           [0,0,0,1]
   EOM_NGUESS_SINGLES  2
   CC_EOM_PROP         1  calculate one-electron properties
   CC_EOM_PROP_TE      1  and two-electron properties (S^2)CC_EXSTATES_PROP 1
   CC_FULLRESPONSE     1  same as above, but do fully relaxed properties
$end

Example 7.60  CCSD calculation on three A2 and one B2 state of formaldehyde. Transition properties will be calculated between the third A2 state and all other EOM states.

$molecule
   0  1
   O
   C  1  1.4
   H  2  1.0  1  120
   H  2  1.0  1  120  3 180
$end

$rem
   BASIS             6-31+G
   METHOD            EOM-CCSD
   EE_STATES         [0,3,0,1]
   CC_STATE_TO_OPT   [2,3]
   CC_TRANS_PROP     true
$end

Example 7.61  EOM-IP-CCSD geometry optimization of X B22 state of H2O+.

$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            eom-ccsd
   BASIS             6-311G
   IP_STATES         [0,0,0,1]
   CC_STATE_TO_OPT   [4,1]
$end

Example 7.62  CAP-EOM-EA-CCSD geometry optimization of the B12 anionic resonance state of formaldehyde. The applied basis is aug-cc-pVDZ augmented by 3s3p diffuse functions on heavy atoms.

$molecule
   0 1
   C       0.0000000000     0.0000000000     0.5721328608
   O       0.0000000000     0.0000000000    -0.7102635035
   H       0.9478180646     0.0000000000     1.1819748108
   H      -0.9478180646     0.0000000000     1.1819748108
$end

$rem
   JOBTYPE                    opt
   METHOD                     eom-ccsd
   BASIS                      gen
   N_FROZEN_CORE              0
   SCF_CONVERGENCE            9
   CC_CONVERGENCE             9
   EOM_DAVIDSON_CONVERGENCE   9
   EA_STATES                  [0,0,0,2]
   CC_STATE_TO_OPT            [4,1]
   XC_GRID                    000250000974
   COMPLEX_CCMAN              1
$end

$complex_ccman
   CS_HF 1
   CAP_TYPE 1
   CAP_ETA 60
   CAP_X 3850
   CAP_Y 2950
   CAP_Z 6100
$end

$basis
 H   0
 S   3  1.00
       13.0100000         0.196850000E-01
       1.96200000         0.137977000
      0.444600000         0.478148000
 S   1  1.00
      0.122000000          1.00000000
 P   1  1.00
      0.727000000          1.00000000
 S   1  1.00
      0.297400000E-01      1.00000000
 P   1  1.00
      0.141000000          1.00000000
 ****
 C   0
 S   8  1.00
       6665.00000         0.692000000E-03
       1000.00000         0.532900000E-02
       228.000000         0.270770000E-01
       64.7100000         0.101718000
       21.0600000         0.274740000
       7.49500000         0.448564000
       2.79700000         0.285074000
      0.521500000         0.152040000E-01
 S   8  1.00
       6665.00000        -0.146000000E-03
       1000.00000        -0.115400000E-02
       228.000000        -0.572500000E-02
       64.7100000        -0.233120000E-01
       21.0600000        -0.639550000E-01
       7.49500000        -0.149981000
       2.79700000        -0.127262000
      0.521500000         0.544529000
 S   1  1.00
      0.159600000          1.00000000
 P   3  1.00
       9.43900000         0.381090000E-01
       2.00200000         0.209480000
      0.545600000         0.508557000
 P   1  1.00
      0.151700000          1.00000000
 D   1  1.00
      0.550000000          1.00000000
 S   1  1.00
      0.469000000E-01     1.00000000
 P   1  1.00
      0.404100000E-01     1.00000000
 D   1  1.00
      0.151000000         1.00000000
 S   1  1.00
      0.234500000E-01      1.00000000
 S   1  1.00
      0.117250000E-01      1.00000000
 S   1  1.00
      0.058625000E-01      1.00000000
 P   1  1.00
      0.202050000E-01      1.00000000
 P   1  1.00
      0.101025000E-01      1.00000000
 P   1  1.00
      0.050512500E-01      1.00000000
 ****
 O   0
 S   8  1.00
       11720.0000         0.710000000E-03
       1759.00000         0.547000000E-02
       400.800000         0.278370000E-01
       113.700000         0.104800000
       37.0300000         0.283062000
       13.2700000         0.448719000
       5.02500000         0.270952000
       1.01300000         0.154580000E-01
 S   8  1.00
       11720.0000        -0.160000000E-03
       1759.00000        -0.126300000E-02
       400.800000        -0.626700000E-02
       113.700000        -0.257160000E-01
       37.0300000        -0.709240000E-01
       13.2700000        -0.165411000
       5.02500000        -0.116955000
       1.01300000         0.557368000
 S   1  1.00
      0.302300000          1.00000000
 P   3  1.00
       17.7000000         0.430180000E-01
       3.85400000         0.228913000
       1.04600000         0.508728000
 P   1  1.00
      0.275300000          1.00000000
 D   1  1.00
       1.18500000          1.00000000
 S   1  1.00
      0.789600000E-01      1.00000000
 P   1  1.00
      0.685600000E-01      1.00000000
 D   1  1.00
      0.332000000          1.00000000
 S   1  1.00
      0.394800000E-01      1.00000000
 S   1  1.00
      0.197400000E-01      1.00000000
 S   1  1.00
      0.098700000E-01      1.00000000
 P   1  1.00
      0.342800000E-01      1.00000000
 P   1  1.00
      0.171400000E-01      1.00000000
 P   1  1.00
      0.085700000E-01      1.00000000
 ****
$end

Example 7.63  Calculating resonant 2PA with degenerate photons.

$molecule
   0 1
   O
   H  1 0.959
   H  1 0.959 2 104.654
$end

$rem
   METHOD         eom-ccsd
   BASIS          aug-cc-pvtz
   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 7.64  Non-degenerate, 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         eom-ccsd
   BASIS          aug-cc-pvdz
   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
   n_2pa_points 11
   omega_1 500000 5000
$end

Example 7.65  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          eom-ccsd
   BASIS           aug-cc-pvtz
   EE_SINGLETS     [2,0,0,0] Two A_1 states
   CC_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 7.66  Mean-field spin–orbit calculation between two excited triplets for acetylene-O intermediate.

$molecule
0 1
  C        -0.0303943366   -0.3149506151   -0.0436827067
  H        -0.1031279784   -1.4353675705   -0.1647400816
  O         1.0178175761    0.2350702146    0.2517598501
  C        -1.3252768442    0.1905302054   -0.4205132671
  H        -2.0767072171    0.1461814657    0.3842573052
$end

$rem
    basis = cc-pvdz
    method = eom-ccsd
    sym_ignore = true
    sf_states = [2]
    cc_state_to_opt = [1,1]
    thresh = 14
    calc_soc = 1
    cc_trans_prop = 1
$end

Example 7.67  Mean-field spin–orbit calculation between the reference singlet and excited triplet states for acetylene-O intermediate.

$molecule
0 1
  C        -0.0303943366   -0.3149506151   -0.0436827067
  H        -0.1031279784   -1.4353675705   -0.1647400816
  O         1.0178175761    0.2350702146    0.2517598501
  C        -1.3252768442    0.1905302054   -0.4205132671
  H        -2.0767072171    0.1461814657    0.3842573052
$end

$rem
    basis = cc-pvdz
    method = eom-ccsd
    sym_ignore = true
    ee_triplets = [1]
    thresh = 14
    calc_soc = 1
    cc_trans_prop = 1
$end

Example 7.68  Computation of spin-orbit couplings between closed-shell singlet and MS=1 triplet state in NH using EOM-SF-CCSD.

$molecule
   0 3
   N
   H N 1.0450
$end

$rem
   METHOD          = eom-ccsd
   BASIS           = 6-31g
   SF_STATES       = [1,2,0,0]
   CC_TRANS_PROP   = true
   CALC_SOC        = 3         ! legacy code
   CC_STATE_TO_OPT = [1,1]
$end

Example 7.69  Computation of non-adiabatic couplings between EOM-EE states within triplet (first job) and singlet (second job) manifolds.

$molecule
   +1 1
   H          0.00000        0.00000        0.0
   He         0.00000        0.00000        3.0
$end

$rem
   JOBTYPE                  = FORCE
   BASIS                    = cc-pVDZ
   METHOD                   = EOM-CCSD
   INPUT_BOHR               = true
   EE_TRIPLETS              = [2]
   cc_eom_prop              = true
   SYM_IGNORE               = true  Do not reorient molecule and turn off symmetry
   CALC_NAC                 = 2     Invoke Szalay NAC
   eom_davidson_convergence = 9     tight davidson convergence
   scf_convergence          = 9     Hartree-Fock convergence threshold 1e-9
   cc_convergence           = 9
$end

@@@

$molecule
   read
$end

$rem
   JOBTYPE                  = FORCE
   BASIS                    = cc-pVDZ
   METHOD                   = EOM-CCSD
   INPUT_BOHR               = true
   EE_STATES                = [2]   singlets
   SYM_IGNORE               = true  Do not reorient molecule and turn off symmetry
   CALC_NAC                 = 2     Invoke Szalay NAC
   eom_davidson_convergence = 9     tight davidson convergence
   scf_convergence          = 9     Hartree-Fock convergence threshold 1e-9
   cc_convergence           = 9
$end

Example 7.70  Calculation of the static dipole polarizability of the CCSD wave function of Helium.

$molecule
   0 1
   He
$end

$rem
   METHOD            ccsd
   BASIS             cc-pvdz
   CC_REF_PROP       1
   CC_POL            2
   CC_DIIS_SIZE      15
   CC_FULLRESPONSE   1
$end