High-throughput ab initio reaction mechanism exploration in the cloud with automated multi-reference validation.

Quantum chemical calculations on atomistic systems have evolved into a standard approach to studying molecular matter. These calculations often involve a significant amount of manual input and expertise, although most of this effort could be automated, which would alleviate the need for expertise in software and hardware accessibility. Here, we present the AutoRXN workflow, an automated workflow for exploratory high-throughput electronic structure calculations of molecular systems, in which (i) density functional theory methods are exploited to deliver minimum and transition-state structures and corresponding energies and properties, (ii) coupled cluster calculations are then launched for optimized structures to provide more accurate energy and property estimates, and (iii) multi-reference diagnostics are evaluated to back check the coupled cluster results and subject them to automated multi-configurational calculations for potential multi-configurational cases. All calculations are carried out in a cloud environment and support massive computational campaigns. Key features of all components of the AutoRXN workflow are autonomy, stability, and minimum operator interference. We highlight the AutoRXN workflow with the example of an autonomous reaction mechanism exploration of the mode of action of a homogeneous catalyst for the asymmetric reduction of ketones.

Relativistic nonorthogonal configuration interaction: application to L2,3-edge X-ray spectroscopy.

In this article, we develop a relativistic exact-two-component nonorthogonal configuration interaction (X2C-NOCI) for computing L-edge X-ray spectra. This article to our knowledge is the first time NOCI has been used for relativistic wave functions. A set of molecular complexes, including SF6, SiCl4 and [FeCl6]3-, are used to demonstrate the accuracy and computational scaling of the X2C-NOCI method. Our results suggest that X2C-NOCI is able to satisfactorily capture the main features of the L2,3-edge X-ray absorption spectra. Excitations from the core require a large amount of orbital relaxation to yield reasonable energies and X2C-NOCI allows us to treat orbital optimization explicitly. However, the cost of computing the nonorthogonal coupling is higher than in conventional CI. Here, we propose an improved integral screening using overlap-scaled density combined with a continuous measure of the generalized Slater-Condon rules that allows us to estimate if an element is zero before attempting a two-electron integral contraction.

Quantum vibration perturbation approach with polyatomic probe in simulating infrared spectra.

The quantitative prediction of vibrational spectra of chromophore molecules in solution is challenging and numerous methods have been developed. In this work, we present a quantum vibration perturbation (QVP) approach, which is a procedure that combines molecular quantum vibration and molecular dynamics with perturbation theory. In this framework, an initial Newtonian molecular dynamics simulation is performed, followed by a substitution process to embed molecular quantum vibrational wave functions into the trajectory. The instantaneous vibrational frequency shift at each time step is calculated using the Rayleigh-Schrödinger perturbation theory, where the perturbation operator is the difference in the vibrational potential between the reference chromophore and the perturbed chromophore in the environment. Semi-classical statistical mechanics is employed to obtain the spectral lineshape function. We validated our method using HCOOH·nH2O (n = 1-2) clusters and HCOOH aqueous solution as examples. The QVP method can be employed for rapid prediction of the vibrational spectrum of a specific mode in solution.

Origin of thiocyanate spectral shifts in water and organic solvents.

Vibrational spectroscopy is a useful technique for probing chemical environments. The development of models that can reproduce the spectra of nitriles and azides is valuable because these probes are uniquely suited for investigating complex systems. Empirical vibrational spectroscopic maps are commonly employed to obtain the instantaneous vibrational frequencies during molecular dynamics simulations but often fail to adequately describe the behavior of these probes, especially in its transferability to a diverse range of environments. In this paper, we demonstrate several reasons for the difficulty in constructing a general-purpose vibrational map for methyl thiocyanate (MeSCN), a model for cyanylated biological probes. In particular, we found that electrostatics alone are not a sufficient metric to categorize the environments of different solvents, and the dominant features in intermolecular interactions in the energy landscape vary from solvent to solvent. Consequently, common vibrational mapping schemes do not cover all essential interaction terms adequately, especially in the treatment of van der Waals interactions. Quantum vibrational perturbation (QVP) theory, along with a combined quantum mechanical and molecular mechanical potential for solute-solvent interactions, is an alternative and efficient modeling technique, which is compared in this paper, to yield spectroscopic results in good agreement with experimental FTIR. QVP has been used to analyze the computational data, revealing the shortcomings of the vibrational maps for MeSCN in different solvents. The results indicate that insights from QVP analysis can be used to enhance the transferability of vibrational maps in future studies.

Variational Energy Decomposition Analysis of Charge-Transfer Interactions between Metals and Ligands in Carbonyl Complexes.

Variational energy decomposition analyses have been presented to quantify the σ-dative, ligand-to-metal forward charge transfer (CT) and the π-conjugative, metal-to-ligand backward charge delocalization on a series of isolelectronic transition-metal carbonyl complexes M(CO)6, including M = Ti2-, V-, Cr, Mn+, and Fe2+. Although the qualitative features of these energy terms are understood, well-defined quantitative studies have been scarce. Consistent with early findings, electrostatic and Pauli exchange effects play a key role in σ-donation, resulting in blue shifts in ligand vibrational frequency in the complex geometries. Excluding chemical bonding interactions between the CO ligand and the metal fragments in the energy decomposition analysis, we found that loosely bound electrostatic complexes can be formed at a longer metal-to-ligand distance due to the exponential decay of Pauli exchange. In all complexes, the overall binding stabilization can be attributed to CT effects, with opposing trends between σ-donation and π-back bonding that follows an order of Ti2- (4.4) > V1- (2.6) > Cr (1.5) > Mn1+ (1.1) > Fe2+ (0.5) in π-to-σ CT ratio. These electronic and energetic features are mirrored in the vibrational frequency shifts induced by different factors. The present investigation may help stimulate the use of energy decomposition techniques to understand the structure and activity of metallocatalysts using density functional theory.

Exact-two-component block-localized wave function: A simple scheme for the automatic computation of relativistic ΔSCF.

Block-localized wave function is a useful method for optimizing constrained determinants. In this article, we extend the generalized block-localized wave function technique to a relativistic two-component framework. Optimization of excited state determinants for two-component wave functions presents a unique challenge because the excited state manifold is often quite dense with degenerate states. Furthermore, we test the degree to which certain symmetries result naturally from the ΔSCF optimization such as time-reversal symmetry and symmetry with respect to the total angular momentum operator on a series of atomic systems. Variational optimizations may often break the symmetry in order to lower the overall energy, just as unrestricted Hartree-Fock breaks spin symmetry. Overall, we demonstrate that time-reversal symmetry is roughly maintained when using Hartree-Fock, but less so when using Kohn-Sham density functional theory. Additionally, maintaining total angular momentum symmetry appears to be system dependent and not guaranteed. Finally, we were able to trace the breaking of total angular momentum symmetry to the relaxation of core electrons.

Enhanced vibrational solvatochromism and spectral diffusion by electron rich substituents on small molecule silanes.

Fourier transform infrared and two-dimensional IR (2D-IR) spectroscopies were applied to two different silanes in three different solvents. The selected solutes exhibit different degrees of vibrational solvatochromism for the Si-H vibration. Density functional theory calculations confirm that this difference in sensitivity is the result of higher mode polarization with more electron withdrawing ligands. This mode sensitivity also affects the extent of spectral diffusion experienced by the silane vibration, offering a potential route to simultaneously optimize the sensitivity of vibrational probes in both steady-state and time-resolved measurements. Frequency-frequency correlation functions obtained by 2D-IR show that both solutes experience dynamics on similar time scales and are consistent with a picture in which weakly interacting solvents produce faster, more homogeneous fluctuations. Molecular dynamics simulations confirm that the frequency-frequency correlation function obtained by 2D-IR is sensitive to the presence of hydrogen bonding dynamics in the surrounding solvation shell.

Dynamic-then-Static Approach for Core Excitations of Open-Shell Molecules.

Delta self-consistent-field methods are widely used in studies of electronically excited states. However, the nonaufbau determinants are generally spin-contaminated. Here, we describe a general approach for spin-coupling interactions of open-shell molecules, making use of multistate density functional theory (MSDFT). In particular, the effective exchange integrals that determine spin coupling are obtained by enforcing the multiplet degeneracy of the S+1 state in the MS = S manifold. Consequently, they are consistent with the energy of the high-spin state that is adequately treated by Kohn-Sham density functional theory (DFT) and, thereby, free of double counting of correlation. The method was applied to core excitations of open-shell molecules and compared with those by spin-adapted time-dependent DFT. An excellent agreement with experiment was found employing the BLYP functional and aug-cc-pCVQZ basis set. Overall, MSDFT provides an effective combination of the strengths of DFT and wave function theory to achieve efficiency and accuracy.

Generalization of Block-Localized Wave Function for Constrained Optimization of Excited Determinants.

The block-localized wave function method is useful to provide insights on chemical bonding and intermolecular interactions through energy decomposition analysis. The method relies on block localization of molecular orbitals (MOs) by constraining the orbitals to basis functions within given blocks. Here, a generalized block-localized orbital (GBLO) method is described to allow both physically localized and delocalized MOs to be constrained in orbital-block definitions. Consequently, GBLO optimization can be conveniently tailored by imposing specific constraints. The GBLO method is illustrated by three examples: (1) constrained polarization response orbitals through dipole and quadrupole perturbation in a water dimer complex, (2) the ground and first excited-state potential energy curves of ethene about its C-C bond rotation, and (3) excitation energies of double electron excited states. Multistate density functional theory is used to determine the energies of the adiabatic ground and excited states using a minimal active space (MAS) comprising specifically charge-constrained and excited determinant configurations that are variationally optimized by the GBLO method. We find that the GBLO expansion that includes delocalized MOs in configurational blocks significantly reduces computational errors in comparison with physical block localization, and the computed ground- and excited-state energies are in good accordance with experiments and results obtained from multireference configuration interaction calculations.

Source code, input data, and sample output concerning the application of multistate density functional theory to the singdoublet and tripdoublet states of the ethylene cation.

This is the data and associated new software required to run multi-state density-functional theory (MSDDFT) calculations by the GAMESS programme. Also, data and software needed to drive GAMESS based on output from the Gaussian-16 package is included. Sample input and output files are included, as well as Perl scripts and Fortran source code. A separate execution of the scripts is required to create the input specifications for each state to be included in the MSDFT, then after GAMESS is run more software is included to calculate the final state energies. The associated basic theory and results are described in "Multistate density functional theory applied with 3 unpaired electrons in 3 orbitals: the singdoublet and tripdoublet states of the ethylene cation" [1].

Diabatic States at Construction (DAC) through Generalized Singular Value Decomposition.

A procedure, called generalized diabatic-at-construction (GDAC), is presented to transform adiabatic potential energy surfaces into a diabatic representation by generalized singular value decomposition. First, we use a set of localized, valence bond-like configuration state functions, called DAC, as the basis states. Then, the adiabatic ground and relevant excited states are determined using multistate density functional theory (MSDFT). GDAC differs in the opposite direction from traditional approaches based on adiabatic-to-diabatic transformation with certain property restraints. The method is illustrated with applications to a model first-order bond dissociation reaction of CH3OCH2Cl polarized by a solvent molecule, the ground- and first-excited-state potential energy surfaces near the minimum conical intersection for the ammonia dimer photodissociation, and the multiple avoided curve crossings in the dissociation of lithium hydride. The GDAC diabatization method may be useful for defining charge-localized states in studies of electron transfer and proton-coupled electron transfer reactions in proteins.

Spin-Multiplet Components and Energy Splittings by Multistate Density Functional Theory.

Kohn-Sham density functional theory has been tremendously successful in chemistry and physics. Yet, it is unable to describe the energy degeneracy of spin-multiplet components with any approximate functional. This work features two contributions. (1) We present a multistate density functional theory (MSDFT) to represent spin-multiplet components and to determine multiplet energies. MSDFT is a hybrid approach, taking advantage of both wave function theory and density functional theory. Thus, the wave functions, electron densities and energy density-functionals for ground and excited states and for different components are treated on the same footing. The method is illustrated on valence excitations of atoms and molecules. (2) Importantly, a key result is that for cases in which the high-spin components can be determined separately by Kohn-Sham density functional theory, the transition density functional in MSDFT (which describes electronic coupling) can be defined rigorously. The numerical results may be explored to design and optimize transition density functionals for configuration coupling in multiconfigurational DFT.

Diabatic-At-Construction Method for Diabatic and Adiabatic Ground and Excited States Based on Multistate Density Functional Theory.

We describe a diabatic-at-construction (DAC) strategy for defining diabatic states to determine the adiabatic ground and excited electronic states and their potential energy surfaces using the multistate density functional theory (MSDFT). The DAC approach differs in two fundamental ways from the adiabatic-to-diabatic (ATD) procedures that transform a set of preselected adiabatic electronic states to a new representation. (1) The DAC states are defined in the first computation step to form an active space, whose configuration interaction produces the adiabatic ground and excited states in the second step of MSDFT. Thus, they do not result from a similarity transformation of the adiabatic states as in the ATD procedure; they are the basis for producing the adiabatic states. The appropriateness and completeness of the DAC active space can be validated by comparison with experimental observables of the ground and excited states. (2) The DAC diabatic states are defined using the valence bond characters of the asymptotic dissociation limits of the adiabatic states of interest, and they are strictly maintained at all molecular geometries. Consequently, DAC diabatic states have specific and well-defined physical and chemical meanings that can be used for understanding the nature of the adiabatic states and their energetic components. Here we present results for the four lowest singlet states of LiH and compare them to a well-tested ATD diabatization method, namely the 3-fold way; the comparison reveals both similarities and differences between the ATD diabatic states and the orthogonalized DAC diabatic states. Furthermore, MSDFT can provide a quantitative description of the ground and excited states for LiH with multiple strongly and weakly avoided curve crossings spanning over 10 Å of interatomic separation.

Perturbation Approach for Computing Infrared Spectra of the Local Mode of Probe Molecules.

Linear and two-dimensional infrared (IR) spectroscopy of site-specific probe molecules provides an opportunity to gain a molecular-level understanding of the local hydrogen-bonding network, conformational dynamics, and long-range electrostatic interactions in condensed-phase and biological systems. A challenge in computation is to determine the time-dependent vibrational frequencies that incorporate explicitly both nuclear quantum effects of vibrational motions and an electronic structural representation of the potential energy surface. In this paper, a nuclear quantum vibrational perturbation (QVP) method is described for efficiently determining the instantaneous vibrational frequency of a chromophore in molecular dynamics simulations. Computational efficiency is achieved through the use of (a) discrete variable representation of the vibrational wave functions, (b) a perturbation theory to evaluate the vibrational energy shifts due to solvent dynamic fluctuations, and (c) a combined QM/MM potential for the systems. It was found that first-order perturbation is sufficiently accurate, enabling time-dependent vibrational frequencies to be obtained on the fly in molecular dynamics. The QVP method is illustrated in the mode-specific linear and 2D-IR spectra of the H-Cl stretching frequency in the HCl-water clusters and the carbonyl stretching vibration of acetone in aqueous solution. To further reduce computational cost, a hybrid strategy was proposed, and it was found that the computed vibrational spectral peak position and line shape are in agreement with experimental results. In addition, it was found that anharmonicity is significant in the H-Cl stretching mode, and hydrogen-bonding interactions further enhance anharmonic effects. The present QVP method complements other computational approaches, including path integral-based molecular dynamics, and represents a major improvement over the electrostatics-based spectroscopic mapping procedures.

Beyond Kohn-Sham Approximation: Hybrid Multistate Wave Function and Density Functional Theory.

A multistate density functional theory (MSDFT) is presented in which the energies and densities for the ground and excited states are treated on the same footing using multiconfigurational approaches. The method can be applied to systems with strong correlation and to correctly describe the dimensionality of the conical intersections between strongly coupled dissociative potential energy surfaces. A dynamic-then-static framework for treating electron correlation is developed to first incorporate dynamic correlation into contracted state functions through block-localized Kohn-Sham density functional theory (KSDFT), followed by diagonalization of the effective Hamiltonian to include static correlation. MSDFT can be regarded as a hybrid of wave function and density functional theory. The method is built on and makes use of the current approximate density functional developed in KSDFT, yet it retains its computational efficiency to treat strongly correlated systems that are problematic for KSDFT but too large for accurate WFT. The results presented in this work show that MSDFT can be applied to photochemical processes involving conical intersections.