Renormalized Singles with Correlation in <i>GW</i> Green’s Function Theory for Accurate Quasiparticle Energies

We apply the renormalized singles with the correlation (RSc) Green function in the GW approximation for accurate quasiparticle (QP) energies and orbitals. The RSc Green function includes singles contributions from the associated density functional approximation (DFA) and considers correlation contributions perturbatively. GRScWRSc uses the RSc Green function as the new starting point and in the formulation of the screened interaction. GRScW0 fixes the screened interaction at the DFA level. For the calculations of ionization potentials, GRScWRSc and GRScW0 significantly reduce the starting point dependence and provide accurate results with errors around 0.2  eV. For the calculations of core-level binding energies, GRScWRSc slightly overestimates the results because of underscreening, but GRScW0 with GGA functionals provides the optimal accuracy with errors of 0.40  eV. We also show that GRScWRSc predicts accurate dipole moments. GRScWRSc and GRScW0, are computationally favorable compared with any self-consistent GW methods. The RSc approach is promising for making GW and other Green function methods efficient and robust

Toward Building Protein Force Fields by Residue-Based Systematic Molecular Fragmentation and Neural Network

Accurate force fields are crucial for molecular dynamics investigation of complex biological systems. Building accurate protein force fields from quantum mechanical (QM) calculations is challenging due to the complexity of proteins and high computational costs of QM methods. In order to overcome these two difficulties, here we developed the residue-based systematic molecular fragmentation method to partition general proteins into only 20 types of amino acid dipeptides and one type of peptide bond at level 1. The total energy of proteins is the combination of the energies of these fragments. Each type of the fragments is then parametrized using neural network (NN) representation of the QM reference. Adopting NN representation can circumvent the limitation of the analytic form of classical molecular mechanics (MM) force fields. Using MM force fields as the baseline, our method adds NN representation of QM corrections at the length scale of amino acid dipeptides. We tested our force fields for both homogeneous and heterogeneous polypeptides. Energy and forces predicted by our force fields compare favorably with full QM calculations from tripeptides to decapeptides. Our development provides an efficient and accurate method of building protein force fields fully from ab initio QM calculations

Excitation Energies from the Single-Particle Green’s Function with the <i>GW</i> Approximation

Quasi-particle energies are important in predicting molecular ionization energies and bulk band structures. The state-of-the-art method for quasi-particle energy calculations, particularly for bulk systems, is the GW approximation. For excited state calculations, one needs to go beyond the GW approximation. The Bethe–Salpeter equation (BSE) is the commonly used approach for bulk-system excited state calculations beyond the GW approximation, which is accurate but computationally cumbersome. In this Article, we develop a new method to extract excitation energies directly from the quasi-particle energies based on the GW approximation. Starting from the (N – 1)-electron system, we are able to calculate molecular excitation energies with orbital energies at the GW level for HOMO excitations. Our calculations demonstrate that this method can accurately capture low-lying local excitations as well as charge transfer excitations in many molecular systems. Our method is shown to outperform the time-dependent density functional theory (TDDFT) and are comparable with higher level excited state calculations, including the equation-of-motion couple cluster (EOM-CC) theory and the BSE, but with less computational effort. This new approach provides an efficient alternative to the BSE method for accurate excited state calculations

Combining Renormalized Singles <i>GW</i> Methods with the Bethe–Salpeter Equation for Accurate Neutral Excitation Energies

We apply the renormalized singles (RS) Green’s function in the Bethe–Salpeter equation (BSE)/GW approach to predict accurate neutral excitation energies of molecular systems. The BSE calculations are performed on top of the GRSWRS method, which uses the RS Green’s function also for the computation of the screened Coulomb interaction W. We show that the BSE/GRSWRS approach significantly outperforms BSE/G0W0 for predicting excitation energies of valence, Rydberg, and charge-transfer (CT) excitations by benchmarking the Truhlar–Gagliardi set, Stein CT set, and an atomic Rydberg test set. For the Truhlar–Gagliardi test set, BSE/GRSWRS provides comparable accuracy to time-dependent density functional theory (TDDFT) and is slightly better than BSE starting from eigenvalue self-consistent GW (evGW). For the Stein CT test set, BSE/GRSWRS significantly outperforms BSE/G0W0 and TDDFT with the accuracy comparable to BSE/evGW. We also show that BSE/GRSWRS predicts Rydberg excitation energies of atomic systems well. Besides the excellent accuracy, BSE/GRSWRS largely eliminates the dependence on the choice of the density functional approximation. This work demonstrates that the BSE/GRSWRS approach is accurate and efficient for predicting excitation energies for a broad range of systems, which expands the applicability of the BSE/GW approach

Multireference Density Functional Theory for Describing Ground and Excited States with Renormalized Singles

We applied renormalized singles (RS) in the multireference density functional theory (DFT) to calculate accurate energies of ground and excited states. The multireference DFT approach determines the total energy of the N-electron system as the sum of the (N – 2)-electron energy from a density functional approximation (DFA) and the two-electron addition energies from the particle–particle Tamm–Dancoff approximation (ppTDA), naturally including multireference description. The ppTDA@RS-DFA approach uses the RS Hamiltonian capturing all singles contributions in calculating two-electron addition energies, and its total energy is optimized with the optimized effective potential method. It significantly improves the original ppTDA@DFA. For ground states, ppTDA@RS-DFA properly describes dissociation curves tested and the double bond rotation of ethylene. For excited states, ppTDA@RS-DFA provides accurate excitation energies and largely eliminates the DFA dependence. ppTDA@RS-DFA thus provides an efficient multireference approach to systems with static correlation

Solvation Free Energy Calculations with Quantum Mechanics/Molecular Mechanics and Machine Learning Models

For exploration of chemical and biological systems, the combined quantum mechanics and molecular mechanics (QM/MM) and machine learning (ML) models have been developed recently to achieve high accuracy and efficiency for molecular dynamics (MD) simulations. Despite its success on reaction free energy calculations, how to identify new configurations on insufficiently sampled regions during MD and how to update the current ML models with the growing database on the fly are both very important but still challenging. In this article, we apply the QM/MM ML method to solvation free energy calculations and address these two challenges. We employ three approaches to detect new data points and introduce the gradient boosting algorithm to reoptimize efficiently the ML model during ML-based MD sampling. The solvation free energy calculations on several typical organic molecules demonstrate that our developed method provides a systematic, robust, and efficient way to explore new chemistry using ML-based QM/MM MD simulations

Describing Chemical Reactivity with Frontier Molecular Orbitalets

Locality in physical space is critical in understanding chemical reactivity in the analysis of various phenomena and processes in chemistry, biology, and materials science, as exemplified in the concepts of reactive functional groups and active sites. Frontier molecular orbitals (FMOs) pinpoint the locality of chemical bonds that are chemically reactive because of the associated orbital energies and thus have achieved great success in describing chemical reactivity, mainly for small systems. For large systems, however, the delocalization nature of canonical molecular orbitals makes it difficult for FMOs to highlight the locality of the chemical reactivity. To obtain localized molecular orbitals that also reflect the frontier nature of the chemical processes, we develop the concept of frontier molecular orbitalets (FMOLs) for describing the reactivity of large systems. The concept of orbitalets was developed recently in the localized orbital scaling correction method, which aims for eliminating the delocalization error in common density functional approximations. Orbitalets are localized in both physical and energy spaces and thus contain both orbital locality and energy information. The FMOLs are thus the orbitalets with energies highest among occupied orbitalets and lowest among unoccupied ones. The applications of FMOLs to hexadeca-1,3,5,7,9,11,13,15-octaene in its equilibrium geometry, inter- and intra-molecular charge-transfer systems, and two transition states of a bifurcating reaction demonstrate that FMOLs can connect quantum mechanical treatments of chemical systems and chemical reactivities by locating the reactive region of large chemical systems. Therefore, FMOLs extend the role of FMOs for small systems and describe the chemical reactivity of large systems with energy and locality insight, with potentially broad applications