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

7.10.27 Potential Energy Surface Crossing Minimization

(February 4, 2022)

EOM-CCSD can also be used as the excited-state method to find minimum energy crossing points (MECPs). See Section 9.8.3 for more general information about MECP calculations.

The potential energy surface crossing optimization procedure finds energy minima of crossing seams. On the seam, the potential surfaces are degenerate in the subspace perpendicular to the plane defined by two vectors: the gradient difference

𝐠=∂∂⁡𝐪⁢(E1-E2) (7.75)

and the derivative coupling

𝐡=⟨Ψ1|∂⁡𝐇∂⁡𝐪|Ψ2⟩ (7.76)

At this time Q-Chem is unable to locate crossing minima for states which have non-zero derivative coupling. Fortunately, this does not occur often. 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 EOM-CCSD methods must be employed for the ground and excited state calculations respectively.

Note:  MECP optimization is only available for methods with analytic gradients. Finite-difference evaluation of two gradients is not possible.

7.10.27.1 Job Control Options

Note:  When performing coupled-cluster-based MECP calculations, one must use the XOPT_STATE_1 and XOPT_STATE_2 keywords and not MECP_STATE1 and MECP_STATE2.

XOPT_STATE_1, XOPT_STATE_2

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 or IP_STATES,EA_STATES. spin = 1 Addresses states with high spin, see also EE_TRIPLETS. irrep Specifies the irreducible representation to which the state belongs; for example, in the C2⁢v point group, irreps are ordered 1, 2, 3, 4 for A1, A2, B1, and B2, respectively. 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 closed-shell RHF references. In the case of open-shell references all states are treated together, see also EE_STATES. For example, in spin-flip calculations use spin = 0 regardless of what is the actual multiplicity of the target state.

XOPT_SEAM_ONLY

XOPT_SEAM_ONLY
       Orders an intersection seam search only, no minimization is to be performed.
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 by setting this option to TRUE and using that geometry as a starting point for the minimization.

7.10.27.2 Examples

Example 7.105  Optimization of the intersection of Ã1B2 and B̃1A2 states of the N+3 ion at the EOM-EE-CCSD level.

$molecule
   1 1
   N1
   N2 N1 rnn
   N3 N2 rnn N1 annn

   rnn=1.46
   annn=70.0
$end

$rem
   JOBTYPE                opt
   METHOD                 eom-ccsd
   BASIS                  6-31g
   EE_SINGLETS            [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 N-N 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                 eom-ccsd
   BASIS                  6-31g
   EE_SINGLETS            [0,2,0,2]
   XOPT_STATE_1           [0,4,1]
   XOPT_STATE_2           [0,2,2]
   GEOM_OPT_TOL_GRADIENT  30
$end

View output

Example 7.106  Optimization of the intersection of Ã2A1 and B̃2B1 states of the NO2 molecule at the EOM-IP-CCSD level.

$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                 eom-ccsd
   N_FROZEN_CORE          0
   BASIS                  6-31g
   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
   CCMAN2                 false
$END

View output