Hydrogen-Atom Electronic Basis Sets for Multicomponent Quantum Chemistry.

Multicomponent methods are a conceptually simple way to include nuclear quantum effects into quantum chemistry calculations. In multicomponent methods, the electronic molecular orbitals are described using the linear combination of atomic orbitals approximation. This requires the selection of a one-particle electronic basis set which, in practice, is commonly a correlation-consistent basis set.

(T) Correction for Multicomponent Coupled-Cluster Theory for a Single Quantum Proton.

(T) and [T] perturbative corrections are derived for multicomponent coupled-cluster theory with single and double excitations (CCSD). Benchmarking for systems with a single quantum proton shows that multicomponent CCSD methods that include perturbative corrections are more accurate than multicomponent CCSD for the calculation of proton affinities and absolute energies. An approximation is introduced that includes only (T) or [T] contributions from mixed electron-nuclear excitations.

Multicomponent MP4 and the inclusion of triple excitations in multicomponent many-body methods.

This study implements the full multicomponent third-order (MP3) and fourth-order (MP4) many-body perturbation theory methods for the first time. Previous multicomponent studies have only implemented a subset of the full contributions, and the present implementation is the first multicomponent many-body method to include any connected triples contribution to the electron-proton correlation energy. The multicomponent MP3 method is shown to be comparable in accuracy to the multicomponent coupled-cluster doubles method for the calculation of proton affinities, while the multicomponent MP4 method is of similar accuracy as the multicomponent coupled-cluster singles and doubles method.

Multicomponent heat-bath configuration interaction with the perturbative correction for the calculation of protonic excited states.

In this study, we extend the multicomponent heat-bath configuration interaction (HCI) method to excited states. Previous multicomponent HCI studies have been performed using only the variational stage of the HCI algorithm as they have largely focused on the calculation of protonic densities. Because this study focuses on energetic quantities, a second-order perturbative correction after the variational stage is essential.

Separation of electron-electron and electron-proton correlation in multicomponent orbital-optimized perturbation theory.

The multicomponent orbital-optimized second-order Møller-Plesset perturbation theory (OOMP2) method is the first multicomponent MP2 method that is able to calculate qualitatively accurate protonic densities, protonic affinities, and geometrical changes due to nuclear quantum effects in multicomponent systems. In this study, two approximations of the multicomponent OOMP2 method are introduced in an effort to demonstrate that, in orbital-optimized multicomponent methods, performing the orbital-optimization process with only electron-proton correlation is sufficient to obtain accurate protonic properties. Additionally, these approximations should reduce the computational expense of the multicomponent OOMP2 method.

Multicomponent CASSCF Revisited: Large Active Spaces Are Needed for Qualitatively Accurate Protonic Densities.

Multicomponent methods seek to treat select nuclei, typically protons, fully quantum mechanically and equivalent to the electrons of a chemical system. In such methods, it is well-known that due to the neglect of electron-proton correlation, a Hartree-Fock (HF) description of the electron-proton interaction catastrophically fails leading to qualitatively incorrect protonic properties. In single-component quantum chemistry, the qualitative failure of HF is normally indicative of the need for multireference methods such as complete active space self-consistent field (CASSCF).

Mixed Quantum-Classical Dynamics with Machine Learning-Based Potentials via Wigner Sampling.

Machine learning-based approaches for surface hopping (SH) offer the prospect of SH simulations with accuracy, but with a computational cost more similar to classical molecular dynamics simulations. However, such approaches in the adiabatic basis are difficult due to the need to fit a machine learning model to reproduce the nonadiabatic coupling, which rapidly changes in the vicinity of a conical intersection. Previous approaches have typically dealt with this difficulty by either computing the hopping probabilities using methods that do not require the explicit nonadiabatic coupling or by employing adaptive sampling.

Quantifying Multireference Character in Multicomponent Systems with Heat-Bath Configuration Interaction.

Multicomponent quantum chemical methods seek to include nuclear quantum effects of select nuclei in quantum chemistry calculations by not invoking the Born-Oppenheimer approximation for these nuclei. In multicomponent methods, the inclusion of electron-proton correlation is essential for obtaining even qualitatively accurate protonic densities. However, most of the recently developed multicomponent methods have either used or obtained molecular orbitals from a single-reference mean-field wave function that neglects all electron-proton correlation that is analogous to using Hartree-Fock orbitals in a single-component framework.

Vibrational adaptive sampling configuration interaction.

Selected configuration interaction plus perturbation theory approaches have long been used to solve both the electronic and vibrational Schrödinger equations. In the last few years, many new selection algorithms have been developed for these approaches and applied to solve the electronic Schrödinger equation, but these algorithms have seen little to no use for solving the vibrational Schrödinger equation. Herein, we adapt one of the recently developed approaches, the adaptive sampling configuration interaction (ASCI) method, to calculate the vibrational excitations of molecules.

Reproducing global potential energy surfaces with continuous-filter convolutional neural networks.

Neural networks fit to reproduce the potential energy surfaces of quantum chemistry methods offer a realization of analytic potential energy surfaces with the accuracy of ab initio methods at a computational cost similar to classical force field methods. One promising class of neural networks for this task is the SchNet architecture, which is based on the use of continuous-filter convolutional neural networks. Previous work has shown the ability of the SchNet architecture to reproduce density functional theory energies and forces for molecular configurations sampled during equilibrated molecular dynamics simulations.

Alternative forms and transferability of electron-proton correlation functionals in nuclear-electronic orbital density functional theory.

Multicomponent density functional theory (DFT) allows the consistent quantum mechanical treatment of both electrons and nuclei. Recently the epc17 electron-proton correlation functional was derived using a multicomponent extension of the Colle-Salvetti formalism and was implemented within the nuclear-electronic orbital (NEO) framework for treating electrons and specified protons quantum mechanically. Herein another electron-proton correlation functional, denoted epc18, is derived using a different form for the functional parameter interpreted as representing the correlation length for electron-proton interactions.

Development of a practical multicomponent density functional for electron-proton correlation to produce accurate proton densities.

Multicomponent density functional theory (DFT) enables the consistent quantum mechanical treatment of both electrons and protons. A major challenge has been the design of electron-proton correlation (epc) functionals that produce even qualitatively accurate proton densities. Herein an electron-proton correlation functional, epc17, is derived analogously to the Colle-Salvetti formalism for electron correlation and is implemented within the nuclear-electronic orbital (NEO) framework.

Multicomponent Density Functional Theory: Impact of Nuclear Quantum Effects on Proton Affinities and Geometries.

Nuclear quantum effects such as zero point energy play a critical role in computational chemistry and often are included as energetic corrections following geometry optimizations. The nuclear-electronic orbital (NEO) multicomponent density functional theory (DFT) method treats select nuclei, typically protons, quantum mechanically on the same level as the electrons. Electron-proton correlation is highly significant, and inadequate treatments lead to highly overlocalized nuclear densities.

Communication: Density functional theory embedding with the orthogonality constrained basis set expansion procedure.

Density functional theory (DFT) embedding approaches have generated considerable interest in the field of computational chemistry because they enable calculations on larger systems by treating subsystems at different levels of theory. To circumvent the calculation of the non-additive kinetic potential, various projector methods have been developed to ensure the orthogonality of molecular orbitals between subsystems. Herein the orthogonality constrained basis set expansion (OCBSE) procedure is implemented to enforce this subsystem orbital orthogonality without requiring a level shifting parameter.

Is the Accuracy of Density Functional Theory for Atomization Energies and Densities in Bonding Regions Correlated?

The development of approximate exchange-correlation functionals is critical for modern density functional theory. A recent analysis of atomic systems suggested that some modern functionals are straying from the path toward the exact functional because electron densities are becoming less accurate while energies are becoming more accurate since the year 2000. To investigate this trend for more chemically relevant systems, the electron densities in the bonding regions and the atomization energies are analyzed for a series of diatomic molecules with 90 different functionals.

Calculation of Positron Binding Energies and Electron-Positron Annihilation Rates for Atomic Systems with the Reduced Explicitly Correlated Hartree-Fock Method in the Nuclear-Electronic Orbital Framework.

Although the binding of a positron to a neutral atom has not been directly observed experimentally, high-level theoretical methods have predicted that a positron will bind to a neutral atom. In the present study, the binding energies of a positron to lithium, sodium, beryllium, and magnesium, as well as the electron-positron annihilation rates for these systems, are calculated using the reduced explicitly correlated Hartree-Fock (RXCHF) method within the nuclear-electronic orbital (NEO) framework. Due to the lack of explicit electron-positron correlation, NEO Hartree-Fock and full configuration interaction calculations with reasonable electronic and positronic basis sets do not predict positron binding to any of these atoms.

Multicomponent density functional theory embedding formulation.

Multicomponent density functional theory (DFT) methods have been developed to treat two types of particles, such as electrons and nuclei, quantum mechanically at the same level. In the nuclear-electronic orbital (NEO) approach, all electrons and select nuclei, typically key protons, are treated quantum mechanically. For multicomponent DFT methods developed within the NEO framework, electron-proton correlation functionals based on explicitly correlated wavefunctions have been designed and used in conjunction with well-established electronic exchange-correlation functionals.

The Melting Temperature of Liquid Water with the Effective Fragment Potential.

The direct simulation of the solid-liquid water interface with the effective fragment potential (EFP) via the constant enthalpy and pressure (NPH) ensemble was used to estimate the melting temperature (T(m)) of ice-I(h). Initial configurations and velocities, taken from equilibrated constant pressure and temperature (NPT) simulations at P = 1 atm and T = 305 K, 325 K and 399 K, respectively, yielded corresponding T(m) values of 378 ± 16 K, 382 ± 14 K and 384 ± 15 K. These estimates are consistently higher than experiment, albeit to the same degree as previously reported estimates using density functional theory (DFT)-based Born-Oppenheimer simulations with the Becke-Lee-Yang-Parr functional plus dispersion corrections (BLYP-D).

Analytic Gradient for Density Functional Theory Based on the Fragment Molecular Orbital Method.

The equations for the response terms for the fragment molecular orbital (FMO) method interfaced with the density functional theory (DFT) gradient are derived and implemented. Compared to the previous FMO-DFT gradient, which lacks response terms, the FMO-DFT analytic gradient has improved accuracy for a variety of functionals, when compared to numerical gradients. The FMO-DFT gradient agrees with the fully ab initio DFT gradient in which no fragmentation is performed, while reducing the nonlinear scaling associated with standard DFT.

Ab initio investigation of the aqueous solvation of the nitrate ion.

The surface affinity of the nitrate ion in aqueous clusters is investigated with a variety of theoretical methods. A sampling of structures in which the nitrate ion is solvated by 32 water molecules is optimized using second order Møller-Plesset perturbation theory (MP2). Four of these MP2 optimized structures are used as starting points for fully ab initio molecular dynamics simulations at the dispersion corrected restricted Hartree-Fock (RHF-D) level of theory.

Nuclear-electronic orbital reduced explicitly correlated Hartree-Fock approach: Restricted basis sets and open-shell systems.

The nuclear electronic orbital (NEO) reduced explicitly correlated Hartree-Fock (RXCHF) approach couples select electronic orbitals to the nuclear orbital via Gaussian-type geminal functions. This approach is extended to enable the use of a restricted basis set for the explicitly correlated electronic orbitals and an open-shell treatment for the other electronic orbitals. The working equations are derived and the implementation is discussed for both extensions.

Quantum treatment of protons with the reduced explicitly correlated Hartree-Fock approach.

The nuclear-electronic orbital (NEO) approach treats select nuclei quantum mechanically on the same level as the electrons and includes nonadiabatic effects between the electrons and the quantum nuclei. The practical implementation of this approach is challenging due to the significance of electron-nucleus dynamical correlation. Herein, we present a general extension of the previously developed reduced NEO explicitly correlated Hartree-Fock (RXCHF) approach, in which only select electronic orbitals are explicitly correlated to each quantum nuclear orbital via Gaussian-type geminal functions.

Surface affinity of the hydronium ion: the effective fragment potential and umbrella sampling.

The surface affinity of the hydronium ion in water is investigated with umbrella sampling and classical molecular dynamics simulations, in which the system is described with the effective fragment potential (EFP). The solvated hydronium ion is also explored using second order perturbation theory for the hydronium ion and the empirical TIP5P potential for the waters. Umbrella sampling is used to analyze the surface affinity of the hydronium ion, varying the number of solvent water molecules from 32 to 256.

Efficient and accurate fragmentation methods.

Conspectus Three novel fragmentation methods that are available in the electronic structure program GAMESS (general atomic and molecular electronic structure system) are discussed in this Account. The fragment molecular orbital (FMO) method can be combined with any electronic structure method to perform accurate calculations on large molecular species with no reliance on capping atoms or empirical parameters. The FMO method is highly scalable and can take advantage of massively parallel computer systems.

Fragment Molecular Orbital Molecular Dynamics with the Fully Analytic Energy Gradient.

Fragment molecular orbital molecular dynamics (FMO-MD) with periodic boundary conditions is performed on liquid water using the analytic energy gradient, the electrostatic potential point charge approximation, and the electrostatic dimer approximation. Compared to previous FMO-MD simulations of water that used an approximate energy gradient, inclusion of the response terms to provide a fully analytic energy gradient results in better energy conservation in the NVE ensemble for liquid water. An FMO-MD simulation that includes the fully analytic energy gradient and two body corrections (FMO2) gives improved energy conservation compared with a previously calculated FMO-MD simulation with an approximate energy gradient and including up to three body corrections (FMO3).