Combining pair-density functional theory and variational two-electron reduced-density matrix methods

Complete active space self-consistent field (CASSCF) computations can be realized at polynomial cost via the variational optimization of the active-space two-electron reduced-density matrix (2-RDM). Like conventional approaches to CASSCF, variational 2-RDM (v2RDM)-driven CASSCF captures nondynamical electron correlation in the active space, but it lacks a description of the remaining dynamical correlation effects. Such effects can be modeled through a combination of v2RDM-CASSCF and on-top pair-density functional theory (PDFT). The resulting v2RDM-CASSCF-PDFT approach provides a computationally inexpensive framework for describing both static and dynamical correlation effects in multiconfigurational and strongly correlated systems. On-top pair-density functionals can be derived from familiar Kohn-Sham exchange-correlation (XC) density functionals through the translation of the v2RDM-CASSCF reference densities [Li Manni et al., J. Chem. Theory Comput. 10, 3669-3680 (2014)]. Translated and fully-translated on-top PDFT versions of several common XC functionals are applied to the potential energy curves of N2, H2O, and CN-, as well as to the singlet/triplet energy splittings in the linear polyacene series. Using v2RDM-CASSCF-PDFT and the translated PBE functional, the singlet/triplet energy splitting of an infinitely-long acene molecule is estimated to be 4.87 kcal/mol

Ab initio calculations to support accurate modelling of the rovibronic spectroscopy calculations of vanadium monoxide (VO)

Accurate knowledge of the rovibronic near-infrared and visible spectra of vanadium monoxide (VO) is very important for studies of cool stellar and hot planetary atmospheres. Here, the required ab initio dipole moment and spin-orbit coupling curves for VO are produced. This data forms the basis of a new VO line list considering 13 different electronic states and containing over 277 million transitions. Open shell transition, metal diatomics are challenging species to model through ab initio quantum mechanics due to the large number of low-lying electronic states, significant spin-orbit coupling and strong static and dynamic electron correlation. Multi-reference configuration interaction methodologies using orbitals from a complete active space self-consistent-field (CASSCF) calculation are the standard technique for these systems. We use different state-specific or minimal-state CASSCF orbitals for each electronic state to maximise the calculation accuracy. The off-diagonal dipole moment controls the intensity of electronic transitions. We test finite-field off-diagonal dipole moments, but found that (1) the accuracy of the excitation energies were not sufficient to allow accurate dipole moments to be evaluated and (2) computer time requirements for perpendicular transitions were prohibitive. The best off-diagonal dipole moments are calculated using wavefunctions with different CASSCF orbitals.Comment: Molecular Physics, 201

Can Density Matrix Embedding Theory with the Complete Activate Space Self-Consistent Field Solver Describe Single and Double Bond Breaking in Molecular Systems?

Density matrix embedding theory (DMET) [Phys. Rev. Lett.2012, 109, 186404] has been demonstrated as an efficient wave-function-based embedding method to treat extended systems. Despite its success in many quantum lattice models, the extension of DMET to real chemical systems has been tested only on selected cases. Herein, we introduce the use of the complete active space self-consistent field (CASSCF) method as a correlated impurity solver for DMET, leading to a method called CAS-DMET. We test its performance in describing the dissociation of a H-H single bond in a H10 ring model system and an N=N double bond in azomethane (CH3-N=N-CH3) and pentyldiazene (CH3(CH2)4-N=NH). We find that the performance of CAS-DMET is comparable to CASSCF with different active space choices when single-embedding DMET corresponding to only one embedding problem for the system is used. When multiple embedding problems are used for the system, the CAS-DMET is in a good agreement with CASSCF for the geometries around the equilibrium, but not in equal agreement at bond dissociation.Comment: 28 pages, 9 figures, TOC graphi

Tracking excited states in wave function optimization using density matrices and variational principles

We present a method for finding individual excited states' energy stationary points in complete active space self-consistent field theory that is compatible with standard optimization methods and highly effective at overcoming difficulties due to root flipping and near-degeneracies. Inspired by both the maximum overlap method and recent progress in excited state variational principles, our approach combines these ideas in order to track individual excited states throughout the orbital optimization process. In a series of tests involving root flipping, near-degeneracies, charge transfers, and double excitations, we show that this approach is more effective for state-specific optimization than either the naive selection of roots based on energy ordering or a more direct generalization of the maximum overlap method. Furthermore, we provide evidence that this state-specific approach improves the performance of complete active space perturbation theory. With a simple implementation, a low cost, and compatibility with large active space methods, the approach is designed to be useful in a wide range of excited state investigations.Comment: 13 pages, submitted to JCT

A general second order complete active space self-consistent-field solver for large-scale systems

We present a new second order complete active space self-consistent field implementation to converge wavefunctions for both large active spaces and large atomic orbital (AO) bases. Our algorithm decouples the active space wavefunction solver from the orbital optimization in the microiterations, and thus may be easily combined with various modern active space solvers. We also introduce efficient approximate orbital gradient and Hessian updates, and step size determination. We demonstrate its capabilities by calculating the low-lying states of the Fe(\Roman{2})-porphine complex with modest resources using a density matrix renormalization group solver in a CAS(22,27) active space and a 3000 AO basis

Orbital Optimization in the Density Matrix Renormalization Group, with applications to polyenes and \beta-carotene

In previous work we have shown that the Density Matrix Renormalization Group (DMRG) enables near-exact calculations in active spaces much larger than are possible with traditional Complete Active Space algorithms. Here, we implement orbital optimisation with the Density Matrix Renormalization Group to further allow the self-consistent improvement of the active orbitals, as is done in the Complete Active Space Self-Consistent Field (CASSCF) method. We use our resulting DMRGCASSCF method to study the low-lying excited states of the all-trans polyenes up to C24H26 as well as \beta-carotene, correlating with near-exact accuracy the optimised complete \pi-valence space with up to 24 active electrons and orbitals, and analyse our results in the light of the recent discovery from Resonance Raman experiments of new optically dark states in the spectrum.Comment: 16 pages, 8 figure

Recent advances in electronic structure theory and their influence on the accuracy of ab initio potential energy surfaces

Recent advances in electronic structure theory and the availability of high speed vector processors have substantially increased the accuracy of ab initio potential energy surfaces. The recently developed atomic natural orbital approach for basis set contraction has reduced both the basis set incompleteness and superposition errors in molecular calculations. Furthermore, full CI calculations can often be used to calibrate a CASSCF/MRCI approach that quantitatively accounts for the valence correlation energy. These computational advances also provide a vehicle for systematically improving the calculations and for estimating the residual error in the calculations. Calculations on selected diatomic and triatomic systems will be used to illustrate the accuracy that currently can be achieved for molecular systems. In particular, the F+H2 yields HF+H potential energy hypersurface is used to illustrate the impact of these computational advances on the calculation of potential energy surfaces

Orbital Optimization in the Active Space Decomposition Model

We report the derivation and implementation of orbital optimization algorithms for the active space decomposition (ASD) model, which are extensions of complete active space self-consistent field (CASSCF) and its occupation-restricted variants in the conventional multiconfiguration electronic-structure theory. Orbital rotations between active subspaces are included in the optimization, which allows us to unambiguously partition the active space into subspaces, enabling application of ASD to electron and exciton dynamics in covalently linked chromophores. One- and two-particle reduced density matrices, which are required for evaluation of orbital gradient and approximate Hessian elements, are computed from the intermediate tensors in the ASD energy evaluation. Numerical results on 4-(2-naphthylmethyl)-benzaldehyde and [3$_6$]cyclophane and model Hamiltonian analyses of triplet energy transfer processes in the Closs systems are presented. Furthermore model Hamiltonians for hole and electron transfer processes in anti-[2.2](1,4)pentacenophane are studied using an occupation-restricted variant