Jie J. Bao

We improved the potential energy surfaces for 14 coupled ³A' states of O₃ by using parametrically managed diabatization by deep neural network (PM-DDNN) with three improvements: (1) We used a new functional form for the parametrically managed activation function, which ensures the continuity of the coordinates used in the parametric management. (2) We used higher weighting for low-lying states to achieve smoother potential energy surfaces. (3) The asymptotic behavior of the coupled potential energy surfaces was further refined by utilizing a better low-dimensional potential. As a result of these improvements, we obtained significantly smoother potentials that are better suited for dynamics calculations. For the new version of 14 coupled ³A' surfaces, the entire set of 532,560 adiabatic energies are fit with a mean unsigned error (MUE) of 45 meV, which is only 0.7% of the mean energy in the data set, which is 6.24 eV.

Multiconfiguration pair-density functional theory (MC-PDFT) was proposed a decade ago, but it is still in the early stage of density functional development. MC-PDFT uses functionals that are called on-top functionals; they depend on the density and the on-top pair density. Most MC-PDFT calculations to date have been unoptimized translations of generalized gradient approximations (GGAs) of Kohn–Sham density functional theory (KS-DFT). A hybrid MC-PDFT has also been developed, in which one includes a fraction of the complete active space self-consistent-field wave function energy in the total energy. Meta-GGA functionals, which use kinetic-energy densities in addition to GGA ingredients, have shown higher accuracy than GGAs in KS-DFT, yet the translation of meta-GGAs has not been previously proposed for MC-PDFT. In this paper, we propose a way to include kinetic energy density in a hybrid on-top functional for MC-PDFT, and we optimize the parameters of the resulting functional by training with a database developed as part of the present work that contains a wide variety of systems with diverse characters. The resulting hybrid meta functional is called the MC23 functional. We find that MC23 has improved performance as compared to KS-DFT functionals for both strongly and weakly correlated systems. We recommend MC23 for future MC-PDFT calculations.

Compressed multistate pair-density functional theory (CMS-PDFT) is a multistate version of multiconfiguration pair-density functional theory that can capture the correct topology of coupled potential energy surfaces (PESs) around conical intersections. In this work, we develop interstate coupling vectors (ISCs) for CMS-PDFT in the OpenMolcas and PySCF/mrh electronic structure packages. Yet, the main focus of this work is using ISCs to calculate minimum-energy conical intersections (MECIs) by CMS-PDFT. This is performed using the projected constrained optimization method in OpenMolcas, which uses ISCs to restrain the iterations to the conical intersection seam. We optimize the S₁/S₀ MECIs for ethylene, butadiene, and benzene and show that CMS-PDFT gives smooth PESs in the vicinities of the MECIs. Furthermore, the CMS-PDFT MECIs are in good agreement with the MECI calculated by the more expensive XMS-CASPT2 method.

The developments of the open-source OpenMolcas chemistry software environment since spring 2020 are described, with a focus on novel functionalities accessible in the stable branch of the package or via interfaces with other packages. These developments span a wide range of topics in computational chemistry and are presented in thematic sections: electronic structure theory, electronic spectroscopy simulations, analytic gradients and molecular structure optimizations, ab initio molecular dynamics, and other new features. This report offers an overview of the chemical phenomena and processes OpenMolcas can address, while showing that OpenMolcas is an attractive platform for state-of-the-art atomistic computer simulations.

In this article the recent developments of the open-source OpenMolcas chemistry software environment, since spring 2020, are described, with the main focus on novel functionalities that are accessible in the stable branch of the package and/or via interfaces with other packages. These community developments span a wide range of topics in computational chemistry, and are presented in thematic sections associated with electronic structure theory, electronic spectroscopy simulations, analytic gradients and molecular structure optimizations, ab initio molecular dynamics, and other new features. This report represents a useful summary of these developments, and it offers a solid overview of the chemical phenomena and processes that OpenMolcas can address, while showing that OpenMolcas is an attractive platform for state-of-the-art atomistic computer simulations.

Transition states for Diels-Alder reactions are strongly correlated, as evidenced by high-to-very-high M diagnostics, and therefore they require treatment by multireference methods. Multiconfiguration pair-density functional theory (MC-PDFT) combines a multiconfiguration wave function with a functional of the electron density and the on-top pair density to calculate the electronic energy for strongly correlated systems at a much lower cost than wave function methods that do not employ density functionals. Here we apply MC-PDFT to the Diels-Alder cycloaddition reaction of 1,3-butadiene with ethylene, where two kinds of reaction paths have been widely studied: concerted synchronous paths and diradical stepwise paths. The lowest-energy reaction path is now known to be a concerted synchronous one, and a method's ability to predict this is an important test. By comparison to the best available theoretical results in the literature, we test the accuracy of MC-PDFT with several choices of on-top functional for geometries and enthalpies of stable structures along both paths and for the transition state geometries. We also calculate the Arrhenius activation energies for both paths and compare these to experiment. We also compare to Kohn-Sham density functional theory (KS-DFT) with selected exchange-correlation functionals. CAS-PDFT gives consistently good energies and geometries for both the concerted and stepwise mechanisms, but none of the KS-DFT functionals gives accurate activation energies for both. The stepwise transition state is very strongly correlated, and MC-PDFT can treat it, but KS-DFT (which involves a single-configuration treatment) has larger errors. The results confirm that using a multiconfigurational reference function for strongly correlated transition states can significantly improve the reliability and that MC-PDFT can provide good accuracy at a much lower computational cost than competing multireference methods.

Photochemical reactions often involve states that are closely coupled due to near degeneracies, for example by proximity to conical intersections. Therefore, a multistate method is used to accurately describe these states; for example, ordinary perturbation theory is replaced by quasidegenerate perturbation theory. Multiconfiguration pair-density functional theory (MC-PDFT) provides an efficient way to approximate the full dynamical correlation energy of strongly correlated systems, and we recently proposed compressed multistate pair-density functional theory (CMS-PDFT) to treat closely coupled states. In the present paper, we report the implementation of analytic gradients for CMS-PDFT in both OpenMolcas and PySCF, and we illustrate the use of these gradients by applying the method to the excited states of formaldehyde and phenol. GRAPHICAL ABSTRACT

This feature article overviews recent work on active spaces, matrix product reference states, treatment of quasidegeneracy, hybrid theory, density-coherence functionals, machine-learned functionals, spin–orbit coupling, gradients, and dipole moments.

Zero-field splitting (ZFS) is a fundamental molecular property that is especially relevant for single-molecule magnets (SMMs), electron paramagnetic resonance spectra, and quantum computing. Developing a method that can accurately predict ZFS parameters can be very powerful for designing new SMMs. One of the challenges is to include external correlation in an inherently multiconfigurational open-shell species for the accurate prediction of magnetic properties. Previously available methods depend on expensive multireference perturbation theory calculations to include external correlation. In this paper, we present spin–orbit-inclusive multiconfiguration and multistate pair-density functional theory (MC-PDFT) calculations of ZFSs; these calculations have a cost comparable to complete-active-space self-consistent field (CASSCF) theory, but they include correlation external to the active space. We found that combining a multistate formulation of MC-PDFT, namely, compressed-state multistate pair-density functional theory, with orbitals optimized by weighted-state-averaged CASSCF, yields reasonably accurate ZFS results.

Multiconfiguration pair-density functional theory (MC-PDFT) is a multireference method that can be used to calculate excited states. However, MC-PDFT potential energy surfaces have the wrong topology at conical intersections because the last step of MC-PDFT is not a diagonalization of a model-space Hamiltonian matrix, as done in, for example, multistate second-order perturbation theory (MS-CASPT2). We have previously proposed methods that solve this problem by diagonalizing a model-space effective Hamiltonian matrix, where the diagonal elements are MC-PDFT energies for intermediate states, and the off-diagonal elements are evaluated by wave function theory. One previous method is called variational multistate PDFT (VMS-PDFT), whose intermediate states maximize the trace of the effective Hamiltonian, namely, the sum of the MC-PDFT energies of the model-space states; the VMS-PDFT is very robust but is more computationally expensive than another method, extended multistate PDFT (XMS-PDFT), in which the transformation to intermediate states is accomplished without needing any density functional evaluations. However, although VMS-PDFT was accurate in all cases tested, XMS-PDFT was accurate in only some of them. In the present paper, we propose a new method, called compressed-state multistate PDFT (CMS-PDFT), that is as efficient as XMS-PDFT and as accurate as VMS-PDFT. The new method maximizes the trace of the classical Coulomb energy of the intermediate states such that the electron densities of the intermediate states are compressed. We show that CMS-PDFT performs robustly even where XMS-PDFT fails.