# 7.10.24 Potential Energy Surface Crossing Minimization

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

 ${\rm\bf g}=\frac{\partial}{\partial{\rm\bf q}}(E_{1}-E_{2})$ (7.62)

and the derivative coupling

 ${\rm\bf h}=\left\langle\Psi_{1}\left|\frac{\partial{\rm\bf H}}{\partial{\rm\bf q% }}\right|\Psi_{2}\right\rangle$ (7.63)

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.

## 7.10.24.1 Job Control Options

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 $C_{2v}$ point group symmetry irrep = 1 for $A_{1}$, irrep = 2 for $A_{2}$, irrep = 3 for $B_{1}$, irrep = 4 for $B_{2}$. 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
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.

## 7.10.24.2 Examples

Example 7.90  Minimize the intersection of Ã${}^{1}$B${}_{2}$ and B̃${}^{1}$A${}_{2}$ states of the N${}_{3}^{+}$ ion using EOM-CCSD method.

$molecule 1 1 N1 N2 N1 rnn N3 N2 rnn N1 annn rnn=1.46 annn=70.0$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


Example 7.91  Minimize the intersection of Ã${}^{2}$A${}_{1}$ and B̃${}^{2}$B${}_{1}$ states of the NO${}_{2}$ molecule using EOM-IP-CCSD method.

$molecule -1 1 N1 O2 N1 rno O3 N1 rno O2 aono rno = 1.3040 aono = 106.7$end

$rem JOBTYPE opt Optimize the intersection seam UNRESTRICTED true METHOD eom-ccsd N_FROZEN_CORE 0 BASIS 6-31g IP_STATES [1,0,1,0] C2v point group symmetry EOM_FAKE_IPEA 1 XOPT_STATE_1 [0,1,1] 1A1 low spin state XOPT_STATE_2 [0,3,1] 1B1 low spin state GEOM_OPT_TOL_GRADIENT 30 Tighten gradient tolerance CCMAN2 false$END