9.8 Nonadiabatic Couplings and Optimization of Minimum-Energy Crossing Points 9.8.3 Minimum-Energy Crossing Points 9.8.5 State-Tracking Algorithm

9.8.4 Job Control and Examples

(September 1, 2024)

For MECP optimization, set MECP_OPT = TRUE in the $rem section, and note that the $derivative_coupling input section discussed in Section 9.8.2 is not necessary in this case.

MECP_OPT

MECP_OPT
       Determines whether we are doing MECP optimizations.
TYPE:
       LOGICAL
DEFAULT:
       FALSE
OPTIONS:
       TRUE Do MECP optimization. FALSE Do not do MECP optimization.
RECOMMENDATION:
       None.

MECP_METHODS

MECP_METHODS
       Determines which method to be used.
TYPE:
       STRING
DEFAULT:
       BRANCHING_PLANE
OPTIONS:
       BRANCHING_PLANE Use the branching-plane updating method. MECP_DIRECT Use the direct method. PENALTY_FUNCTION Use the penalty-constrained method.
RECOMMENDATION:
       The direct method is stable for small molecules or molecules with high symmetry. The branching-plane updating method is more efficient for larger molecules but does not work if the two states have different symmetries. If using the branching-plane updating method, GEOM_OPT_COORDS must be set to 0 in the $rem section, as this algorithm is available in Cartesian coordinates only. The penalty-constrained method converges slowly and is suggested only if other methods fail.

MECP_STATE1

MECP_STATE1
       Sets the first Born-Oppenheimer state for MECP optimization.
TYPE:
       INTEGER/INTEGER ARRAY
DEFAULT:
       None
OPTIONS:
       [ $i$ , $j$ ] Find the $j$ th excited state with the total spin $i$ ; $j=0$ means the SCF ground state.
RECOMMENDATION:
       $i$ is ignored for restricted calculations; for unrestricted calculations, $i$ can only be 0 or 1.

MECP_STATE2

MECP_STATE2
       Sets the second Born-Oppenheimer state for MECP optimization.
TYPE:
       INTEGER/INTEGER ARRAY
DEFAULT:
       None
OPTIONS:
       [ $i$ , $j$ ] Find the $j$ th excited state with the total spin $i$ ; $j=0$ means the SCF ground state.
RECOMMENDATION:
       $i$ is ignored for restricted calculations; for unrestricted calculations, $i$ can only be 0 or 1.

CIS_S2_THRESH

CIS_S2_THRESH
       Determines whether a state is a singlet or triplet in unrestricted calculations.
TYPE:
       INTEGER
DEFAULT:
       120
OPTIONS:
       $n$ Sets the $\langle\hat{S}^{2}\rangle$ threshold to $n/100$
RECOMMENDATION:
       For the default case, states with $\langle\hat{S}^{2}\rangle>1.2$ are treated as triplet states and other states are treated as singlets.

MECP_PROJ_HESS

MECP_PROJ_HESS
       Determines whether to project out the coupling vector from the Hessian when using branching plane updating method.
TYPE:
       LOGICAL
DEFAULT:
       TRUE
OPTIONS:
       TRUE FALSE
RECOMMENDATION:
       Use the default.

Example 9.26 MECP optimization of an intersection between the S ${}_{2}$ and S ${}_{3}$ states of NO ${}_{2}^{-}$ , using the direct method at the SOS-CIS(D0) level.

$molecule
   -1 1
   N1
   O2  N1  RNO
   O3  N1  RNO  O2  AONO

   RNO  = 1.50
   AONO = 100
$end

$rem
   JOBTYPE         = opt
   METHOD          = soscis(d0)
   BASIS           = aug-cc-pVDZ
   AUX_BASIS       = rimp2-aug-cc-pVDZ
   PURECART        = 1111
   CIS_N_ROOTS     = 4
   CIS_TRIPLETS    = false
   CIS_SINGLETS    = true
   MEM_STATIC      = 900
   MEM_TOTAL       = 1950
   MECP_OPT        = true
   MECP_STATE1     = [0,2]
   MECP_STATE2     = [0,3]
   MECP_METHODS    = mecp_direct
$end

Example 9.27 Optimization of the ethylidene MECP between S ${}_{0}$ and S ${}_{1}$ at the SF-TDDFT level using the branching-plane updating method.

$molecule
   0 3
   C   0.044626  -0.2419240   0.357157
   C   0.008905   0.6727548   1.460500
   H   0.928425  -0.1459163  -0.272095
   H  -0.831032  -0.1926895  -0.288529
   H  -0.009238   0.9611331   2.479936
   H   0.068314  -1.2533580   0.778847
$end

$rem
   JOBTYPE           opt
   METHOD            bhhlyp
   BASIS             6-31G(d,p)
   MECP_OPT          true
   MECP_METHODS      branching_plane
   MECP_PROJ_HESS    true  ! project out y vector from the hessian
   GEOM_OPT_COORDS   0     ! currently only works for Cartesian coordinate
   SPIN_FLIP         true
   UNRESTRICTED      true
   CIS_N_ROOTS       4
   MECP_STATE1       [0,1]
   MECP_STATE2       [0,2]
   CIS_S2_THRESH     120
$end

Example 9.28 Optimization of the twisted-pyramidalized ethylene MECP between S ${}_{0}$ and S ${}_{1}$ at the SF-TDDFT level using the penalty-constrained updating method.

$molecule
   0 3
   C  -0.015889   0.073532  -0.059559
   C   0.012427  -0.002468   1.315694
   H   0.857876   0.147014  -0.710529
   H  -0.936470  -0.011696  -0.626761
   H   0.764557   0.663381   1.762573
   H   0.740773  -0.869764   1.328583
$end

$rem
   JOBTYPE         opt
   MECP_OPT        true
   MECP_METHODS    penalty_function
   METHOD          bhhlyp
   SPIN_FLIP       true
   UNRESTRICTED    true
   BASIS           6-31G(d,p)
   CIS_N_ROOTS     4
   MECP_STATE1     [0,1]
   MECP_STATE2     [0,2]
   CIS_S2_THRESH   120
$end

Example 9.29 Optimization of the $\tilde{B}^{1}A_{2}$ and $\tilde{A}^{1}B_{2}$ states of N ${}_{3}^{+}$ at the EOM-EE-CCSD level using the direct method. See Section 7.10.27 for the specifics of performing MECP optimization with coupled cluster.

$molecule
   1 1
   N1
   N2 N1 rNN
   N3 N2 rNN N1 aNNN

   rNN  =  1.54
   aNNN = 50.0
$end

$rem
   JOBTYPE                opt
   MECP_OPT               true
   MECP_METHODS           mecp_direct
   METHOD                 eom-ccsd
   BASIS                  6-31g
   EE_SINGLETS            [0,2,0,2]
   XOPT_STATE_1           [0,2,2]
   XOPT_STATE_2           [0,4,1]
   CCMAN2                 false
   GEOM_OPT_TOL_GRADIENT  30
$end

Example 9.30 Optimization of the ethylidene MECP between S ${}_{0}$ and S ${}_{1}$ at the SF-TDDFT level with analytic derivative couplings.

$molecule
   0 3
   C   0.044626  -0.241924   0.357157
   C   0.008905   0.672754   1.460500
   H   0.928425  -0.145916  -0.272095
   H  -0.831032  -0.192689  -0.288529
   H  -0.009238   0.961133   2.479936
   H   0.068314  -1.253358   0.778847
$end

$rem
   JOBTYPE            opt
   MECP_OPT           true
   MECP_METHODS       branching_plane
   MECP_PROJ_HESS     true
   GEOM_OPT_COORDS    0
   MECP_STATE1        [0,1]
   MECP_STATE2        [0,2]
   UNRESTRICTED       true
   SPIN_FLIP          true
   CIS_N_ROOTS        4
   CALC_NAC           true
   CIS_DER_NUMSTATE   2
   MAX_CIS_CYCLES     50
   EXCHANGE           bhhlyp
   BASIS              6-31G(d,p)
   INTEGRAL_SYMMETRY  true
$end

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9.8.4 Job Control and Examples