Chad E. Hoyer

MOLCAS 8: New Capabilities for Multiconfigurational Quantum Chemical Calculations across the Periodic Table

In this report, we summarize and describe the recent unique updates and additions to the Molcas quantum chemistry program suite as contained in release version 8. These updates include natural and spin orbitals for studies of magnetic properties, local and linear scaling methods for the Douglas–Kroll–Hess transformation, the generalized active space concept in MCSCF methods, a combination of multiconfigurational wave functions with density functional theory in the MC‐PDFT method, additional methods for computation of magnetic properties, methods for diabatization, analytical gradients of state average complete active space SCF in association with density fitting, methods for constrained fragment optimization, large‐scale parallel multireference configuration interaction including analytic gradients via the interface to the Columbus package, and approximations of the CASPT2 method to be used for computations of large systems. In addition, the report includes the description of a computational machinery for nonlinear optical spectroscopy through an interface to the QM/MM package Cobramm. Further, a module to run molecular dynamics simulations is added, two surface hopping algorithms are included to enable nonadiabatic calculations, and the DQ method for diabatization is added. Finally, we report on the subject of improvements with respects to alternative file options and parallelization.

Diabatization based on the dipole and quadrupole: The DQ method

In this work, we present a method, called the DQ scheme (where D and Q stand for dipole and quadrupole, respectively), for transforming a set of adiabatic electronic states to diabatic states by using the dipole and quadrupole moments to determine the transformation coefficients. It is more broadly applicable than methods based only on the dipole moment; for example, it is not restricted to electron transfer reactions, and it works with any electronic structure method and for molecules with and without symmetry, and it is convenient in not requiring orbital transformations. We illustrate this method by prototype applications to two cases, LiH and phenol, for which we compare the results to those obtained by the fourfold-way diabatization scheme.

Multiconfiguration Pair-Density Functional Theory Is as Accurate as CASPT2 for Electronic Excitation.

A correct description of electronically excited states is critical to the interpretation of visible-ultraviolet spectra, photochemical reactions, and excited-state charge-transfer processes in chemical systems. We have recently proposed a theory called multiconfiguration pair-density functional theory (MC-PDFT), which is based on a combination of multiconfiguration wave function theory and a new kind of density functional called an on-top density functional. Here, we show that MC-PDFT with a first-generation on-top density functional performs as well as CASPT2 for an organic chemistry database including valence, Rydberg, and charge-transfer excitations. The results are very encouraging for practical applications.

Multiconfiguration Pair-Density Functional Theory Outperforms Kohn–Sham Density Functional Theory and Multireference Perturbation Theory for Ground-State and Excited-State Charge Transfer

The correct description of charge transfer in ground and excited states is very important for molecular interactions, photochemistry, electrochemistry, and charge transport, but it is very challenging for Kohn-Sham (KS) density functional theory (DFT). KS-DFT exchange-correlation functionals without nonlocal exchange fail to describe both ground- and excited-state charge transfer properly. We have recently proposed a theory called multiconfiguration pair-density functional theory (MC-PDFT), which is based on a combination of multiconfiguration wave function theory with a new type of density functional called an on-top density functional. Here we have used MC-PDFT to study challenging ground- and excited-state charge-transfer processes by using on-top density functionals obtained by translating KS exchange-correlation functionals. For ground-state charge transfer, MC-PDFT performs better than either the PBE exchange-correlation functional or CASPT2 wave function theory. For excited-state charge transfer, MC-PDFT (unlike KS-DFT) shows qualitatively correct behavior at long-range with great improvement in predicted excitation energies.

Controversial electronic structures and energies of Fe2, -resolved by RASPT2 calculations

The diatomic molecule Fe2 was investigated using restricted active space second-order perturbation theory (RASPT2). This molecule is very challenging to study computationally because predictions about the ground state and excited states depend sensitively on the choice of the quantum chemical method. For Fe2 we show that one needs to go beyond a full-valence active space in order to achieve even qualitative agreement with experiment for the dissociation energy, and we also obtain a smooth ground-state potential curve. In addition we report the first multireference study of Fe 2 (+), for which we predict an (8)Σu (-) ground state, which was not predicted by previous computational studies. By using an active space large enough to remove the most serious deficiencies of previous theoretical work and by explicitly investigating the interpretations of previous experimental results, this study elucidates previous difficulties and provides - for the first time - a qualitatively correct treatment of Fe2, Fe 2 (+), and Fe 2 (-). Moreover, this study represents a record in terms of the number or active electrons and active orbitals in the active space, namely 16 electrons in 28 orbitals. Conventional CASPT2 calculations can be performed with at most 16 electrons in 16 orbitals. We were able to overcome this limit by using the RASPT2 formalism.

Controversial electronic structures and energies of Fe2, Fe 2+, and Fe 2− resolved by RASPT2 calculations

The diatomic molecule Fe2 was investigated using restricted active space second-order perturbation theory (RASPT2). This molecule is very challenging to study computationally because predictions about the ground state and excited states depend sensitively on the choice of the quantum chemical method. For Fe2 we show that one needs to go beyond a full-valence active space in order to achieve even qualitative agreement with experiment for the dissociation energy, and we also obtain a smooth ground-state potential curve. In addition we report the first multireference study of Fe 2 (+), for which we predict an (8)Σu (-) ground state, which was not predicted by previous computational studies. By using an active space large enough to remove the most serious deficiencies of previous theoretical work and by explicitly investigating the interpretations of previous experimental results, this study elucidates previous difficulties and provides - for the first time - a qualitatively correct treatment of Fe2, Fe 2 (+), and Fe 2 (-). Moreover, this study represents a record in terms of the number or active electrons and active orbitals in the active space, namely 16 electrons in 28 orbitals. Conventional CASPT2 calculations can be performed with at most 16 electrons in 16 orbitals. We were able to overcome this limit by using the RASPT2 formalism.

The DQ and DQΦ electronic structure diabatization methods: Validation for general applications

We recently proposed the dipole-quadrupole (DQ) method for transforming adiabatic electronic states to diabatic states by using matrix elements of the dipole and quadrupole operators, and we applied the method to 3-state diabatizations of LiH and phenol. Here we extend the method to also include the electrostatic potential, and we call the resulting method the DQΦ method, which denotes the dipole-quadrupole-electrostatic-potential diabatization method. The electrostatic potential provides extra flexibility, and the goal of the present work is to test and illustrate the robustness of the methods for producing diabatic potential energy curves that tend to the adiabatic curves away from crossings and avoided crossings and are smooth in regions of crossings and avoided crossings. We illustrate the generality of the methods by an application to LiH with four states and by two-state diabatizations of HCl, (H2)2, O3, and the reaction Li + HF → LiF + H. We find that-if enough states are included-the DQ method does not have a significant dependence on the parameter weighting the quadrupole moment, and a geometry-independent value of 10 a0 (-2) is adequate in all cases tested. We also find that the addition of the electrostatic potential improves the diabatic potentials in some cases and provides an additional property useful for increasing the generality of the method for diabatization.

Multiconfiguration Pair-Density Functional Theory Spectral Calculations Are Stable to Adding Diffuse Basis Functions.

Time-dependent Kohn-Sham density functional theory (TD-KS-DFT) is useful for calculating electronic excitation spectra of large systems, but the low-energy spectra are often complicated by artificially lowered higher-energy states. This affects even the lowest energy excited states. Here, by calculating the lowest energy spin-conserving excited state for atoms from H to K and for formaldehyde, we show that this problem does not occur in multiconfiguration pair-density functional theory (MC-PDFT). We use the tPBE on-top density functional, which is a translation of the PBE exchange-correlation functional. We compare to a robust multireference method, namely, complete active space second-order perturbation theory (CASPT2), and to TD-KS-DFT with two popular exchange-correlation functionals, PBE and PBE0. We find for atoms that the mean unsigned error (MUE) of MC-PDFT with the tPBE functional improves from 0.42 to 0.40 eV with a double set of diffuse functions, whereas the MUEs for PBE and PBE0 drastically increase from 0.74 to 2.49 eV and from 0.45 to 1.47 eV, respectively.

Nonintuitive Diabatic Potential Energy Surfaces for Thioanisole.

Diabatization of potential energy surfaces is a technique that enables convenient molecular dynamics simulations of electronically nonadiabatic processes, but diabatization itself is nonunique and can be inconvenient; the best methods to achieve diabatization are still under study. Here, we present the diabatization of two electronic states of thioanisole in the S-CH3 bond stretching and C-C-S-C torsion two-dimensional nuclear coordinate space containing a conical intersection. We use two systematic methods: the (orbital-dependent) 4-fold way and the (orbital-free) Boys localization diabatization method. These very different methods yield strikingly similar diabatic potential energy surfaces that cross at geometries where the adiabatic surfaces are well separated and do not exhibit avoided crossings, and the contours of the diabatic gap and diabatic coupling are similar for the two methods. The validity of the diabatization is supported by comparing the nonadiabatic couplings calculated from the diabatic matrix elements to those calculated by direct differentiation of the adiabatic states.

Analytic Gradients for Complete Active Space Pair-Density Functional Theory

Analytic gradient routines are a desirable feature for quantum mechanical methods, allowing for efficient determination of equilibrium and transition state structures and several other molecular properties. In this work, we present analytical gradients for multiconfiguration pair-density functional theory (MC-PDFT) when used with a state-specific complete active space self-consistent field reference wave function. Our approach constructs a Lagrangian that is variational in all wave function parameters. We find that MC-PDFT locates equilibrium geometries for several small- to medium-sized organic molecules that are similar to those located by complete active space second-order perturbation theory but that are obtained with decreased computational cost.