Orbital optimization in nonorthogonal multiconfigurational self-consistent field applied to the study of conical intersections and avoided crossings

Abstract

Nonorthogonal approaches to electronic structure methods have recently received renewed attention, with the hope that new forms of nonorthogonal wavefunction Ansätze may circumvent the computational bottleneck of orthogonal-based methods. The basis in which nonorthogonal configuration interaction is performed defines the compactness of the wavefunction description and hence the efficiency of the method. Within a molecular orbital approach, nonorthogonal configuration interaction is defined by a “different orbitals for different configurations” picture, with different methods being defined by their choice of determinant basis functions. However, identification of a suitable determinant basis is complicated, in practice, by (i) exponential scaling of the determinant space from which a suitable basis must be extracted, (ii) possible linear dependencies in the determinant basis, and (iii) inconsistent behavior in the determinant basis, such as disappearing or coalescing solutions, as a result of external perturbations, such as geometry change. An approach that avoids the aforementioned issues is to allow for basis determinant optimization starting from an arbitrarily constructed initial determinant set. In this work, we derive the equations required for performing such an optimization, extending previous work by accounting for changes in the orthogonality level (defined as the dimension of the orbital overlap kernel between two determinants) as a result of orbital perturbations. The performance of the resulting wavefunction for studying avoided crossings and conical intersections where strong correlation plays an important role is examined.

Multistate Density Functional Theory of Excited States

“…4−5 Å) along with a huge energy gap of about 1 eV. 43,44 In this Letter, we have provided rigorous mathematical proofs for (1) the existence of a Hamiltonian matrix functional of the multistate matrix density for the lowest N eigenstates, (2) the variational principle that leads to the exact energies and densities of all eigenstates, and (3) the N 2 -representation of the matrix density D(r) for computation. Whether or not the present theory may be considered as a pure density functional theory or a hybrid WFT and DFT, we hope that these fundamental principles will stimulate further work that goes beyond the ground state.…”

“…The work by Thompson on nonorthogonal multiconfigurational SCF in WFT is encouraging, and experience gained from that approach could be useful to MSDFT. 44 A few years ago, a postdoctoral associate implemented a variational version of MSDFT with preliminary results. We found the MSDFT-NOSI approach to be useful in practical applications, 22,23 allowing the construction of diabatic states from the basis state level (Figure 1).…”

“…Without dynamic correlation in nonorthogonal configuration interaction (NOCI) using the MSDFT orbitals in Figure b, or NOCI with optimized orbitals and complete active space self-consistent-field (CASSCF) calculations without dynamic correlation correction, the curve crossing point occurs at much shorter distances (ca. 4–5 Å) along with a huge energy gap of about 1 eV. , …”

“…It has not been fully implemented as an application tool. The work by Thompson on nonorthogonal multiconfigurational SCF in WFT is encouraging, and experience gained from that approach could be useful to MSDFT . A few years ago, a postdoctoral associate implemented a variational version of MSDFT with preliminary results.…”

GronOR: Scalable and Accelerated Nonorthogonal Configuration Interaction for Molecular Fragment Wave Functions

“…Expressed in an independently optimized and therefore in principle nonorthogonal orbital set, each diabatic state is ensured to be unbiased and to include full orbital relaxation. Our implementation of NOCI is one among the many that have been developed over the past decade. − The idea of expressing each electronic configuration in its own set of orbitals is not new, but only recently have computers become sufficiently powerful to efficiently perform such calculations.…”