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4.9.3 Multiple SCF Solutions for Non-Orthogonal CI

(July 14, 2022)

The solutions found through metadynamics often appear to be good approximations to diabatic surfaces, where the electronic structure does not significantly change with geometry. In situations where there are such multiple electronic states close in energy, an adiabatic state may be produced by diagonalizing a matrix of these states, i.e., through a configuration interaction (CI) procedure. As they are distinct solutions of the SCF equations, these states are non-orthogonal (i.e. one cannot be constructed as a single determinant made out of the orbitals of another), and so the CI is a little more complicated and corresponds to a non-orthogonal CI (NOCI). More information on NOCI can be found in Section 7.5.

Version 5.2 of Q-Chem introduces a new NOCI package, libnoci, for locating multiple SCF solutions and running NOCI calculations (see Section 7.5.2), including a new implementation of SCF metadynamics. The libnoci implementation of SCF metadynamics can be accessed using USE_LIBNOCI = TRUE in combination with NOCI_DETGEN = 3. In addition to the original SCF metadynamics features available in Q-Chem, this new implementation includes:

• An active space approach where orbital mixing and optimization occurs only in a user-defined subset of orbitals.

• Full support for restricted, unrestricted and generalized orbital types, along with complex (Hermitian) and holomorphic (non-Hermitian) orbitals; see Section 4.9.4.

Multiple Hartree-Fock states of particular relevance for NOCI are often related to varying orbital occupations in a dominant subset of molecular orbitals. For example, important multiple solutions may correspond to excited determinants whose orbitals have been individually relaxed at the SCF level, or symmetry-broken states formed from strong mixing in a dominant active space. libnoci allows multiple solutions to be identified by allowing orbital mixing and relaxation only in a subset of orbitals defined using the $active_orbitals input section By default, the multiple solutions located are then subsequently optimized in the full orbital space, although this can be skipped using SKIP_SCFMAN = TRUE. Finally, libnoci introduces easier control over reading initial guesses from previous calculations. Using the input NOCI_REFGEN = 1, all previous solutions are read from file (if available), while a particular subset can be chosen using SCF_READMINIMA. Example 4.27 Example of using the libnoci implementation of SCF metadynamics.$molecule
0 1
H    0.0000000   0.0000000   0.0000000
H    0.0000000   0.0000000   4.0000000
$end$rem
METHOD                     hf
UNRESTRICTED               true
BASIS                      sto-3g
SCF_CONVERGENCE            10
MAX_SCF_CYCLES             1000
MOM_START                  1
USE_LIBNOCI                true
NOCI_DETGEN                3
SCF_SAVEMINIMA             4
SCF_MINFIND_RANDOMMIXING   30000
SCF_MINFIND_MIXMETHOD      1
$end Active orbitals can be specified for SCF metadynamics in libnoci. Indices for $\beta$ orbitals are offset by the number of $\alpha$ MOs, i.e. the case selects $\alpha$ orbitals 1 and 2, and $\beta$ orbitals 1 and 2, with a total of 10 $\alpha$ molecular orbitals (including occupied and virtual).$active_orbitals
1 2 11 12
$end The initial guess coefficients can also be read in as follows:$scf_read
1 2 4 ...
\$end