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. A recently developed electron-proton correlation functional, epc17, has been shown to provide accurate nuclear densities for molecular systems. Herein, the NEO-DFT/epc17 method is used to compute the proton affinities for a set of molecules and to examine the role of nuclear quantum effects on the equilibrium geometry of FHF. The agreement of the computed results with experimental and benchmark values demonstrates the promise of this approach for including nuclear quantum effects in calculations of proton affinities, pK's, optimized geometries, and reaction paths.

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 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. The NEO-DFT/epc17 method produces accurate proton densities efficiently and is promising for diverse applications.

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. For example, the method has been shown to scale nearly linearly on up to 131 000 processor cores for calculations on large water clusters. There have been many applications of the FMO method to large molecular clusters, to biomolecules (e.g., proteins), and to materials that are used as heterogeneous catalysts. The effective fragment potential (EFP) method is a model potential approach that is fully derived from first principles and has no empirically fitted parameters. Consequently, an EFP can be generated for any molecule by a simple preparatory GAMESS calculation. The EFP method provides accurate descriptions of all types of intermolecular interactions, including Coulombic interactions, polarization/induction, exchange repulsion, dispersion, and charge transfer. The EFP method has been applied successfully to the study of liquid water, π-stacking in substituted benzenes and in DNA base pairs, solvent effects on positive and negative ions, electronic spectra and dynamics, non-adiabatic phenomena in electronic excited states, and nonlinear excited state properties. The effective fragment molecular orbital (EFMO) method is a merger of the FMO and EFP methods, in which interfragment interactions are described by the EFP potential, rather than the less accurate electrostatic potential. The use of EFP in this manner facilitates the use of a smaller value for the distance cutoff (Rcut). Rcut determines the distance at which EFP interactions replace fully quantum mechanical calculations on fragment-fragment (dimer) interactions. The EFMO method is both more accurate and more computationally efficient than the most commonly used FMO implementation (FMO2), in which all dimers are explicitly included in the calculation. While the FMO2 method itself does not incorporate three-body interactions, such interactions are included in the EFMO method via the EFP self-consistent induction term. Several applications (ranging from clusters to proteins) of the three methods are discussed to demonstrate their efficacy. The EFMO method will be especially exciting once the analytic gradients have been completed, because this will allow geometry optimizations, the prediction of vibrational spectra, reaction path following, and molecular dynamics simulations using the method. Disciplines Chemistry CommentsReprinted (adapted) 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 molecu...

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. For hybrid generalized gradient approximation functionals developed since the year 2000, the errors in densities and atomization energies are decoupled; the accuracy of the energies remains relatively consistent while the accuracy of the densities varies significantly. Such decoupling is not observed for generalized gradient and meta-generalized gradient approximation functionals. Analysis of electron densities in bonding regions is found to be important for the evaluation of functionals for chemical systems.

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). Disciplines Chemistry CommentsReprinted (adapted) ABSTRACT: 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). INTRODUCTION1.1. Fragment Molecular Orbital Method. Much progress has been made recently in improving algorithms for ab initio calculations on large systems. 1,2 One strategy is to use a fragmentation approach, in which a large system of interest is divided into smaller subsystems, and ab initio calculations are performed on these smaller subsystems. 2 One of the most successful and extensively developed fragmentation methods is the fragment molecular orbital (FMO) method 3 proposed by Kitaura et al. in 1999. The FMO method has been implemented for most ab initio and density functional theory (DFT) methods. 4−8 Numerous approximations to the original FMO method have been implemented to improve the efficiency of the calculation. The two most important of these approximations are the electrostatic point charge (ESP-PC) approximation and the electrostatic dimer (ES-DIM) approximation. 9 The ESP-PC approximation calculates the FMO embedded electrostatic potential using point charges rather than two electron integrals, while the ES-DIM approximation calculates the dimer energy of two fragments using point charges rather than using ab initio methods.FMO gradients were developed soon after the introduction of the FMO method. 10 Improvements to the gradient followed that allowed the use of gradients with the ESP-PC approximation 11 and the ES-DIM approximation. 12 Because the dimer (or trimer) density is not iterated to self-consi...

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. We examine the consequences of using Hartree–Fock orbitals in multicomponent calculations by developing the multicomponent heat-bath configuration interaction (HCI) method. Multicomponent HCI is a multicomponent selected configuration interaction (CI) technique that enables an accurate approximation of a complete active space or truncated CI wave function for systems with large active spaces. The multicomponent HCI method is shown to reproduce the ground-state protonic density of the HeHHe+, HCN, and FHF– systems when compared to reference grid-based calculations. For all three systems, the coefficient of the leading configuration in the wave function expansion is less than 0.95, indicating that all systems have multireference character. This is highly noteworthy as none of the systems have multireference character in a single-component framework and suggests that multireference character appears inherent to or at least more commonly in a multicomponent framework than a single-component framework. Even when natural orbitals are used rather than Hartree–Fock orbitals for the multicomponent HCI calculations, aspects of the multireference character remain for FHF– and HCN. Consequences and implications of the multireference character of multicomponent quantum chemical systems are discussed.

Communication: A novel implementation to compute MP2 correlation energies without basis set superposition errors and complete basis set extrapolation

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. Approximations of the electronic exchange between the geminal-coupled electronic orbitals and the other electronic orbitals are also explored. This general approach enables computationally tractable yet accurate calculations on molecular systems with quantum protons. The RXCHF method is applied to the hydrogen cyanide (HCN) and FHF(-) systems, where the proton and all electrons are treated quantum mechanically. For the HCN system, only the two electronic orbitals associated with the CH covalent bond are geminal-coupled to the proton orbital. For the FHF(-) system, only the four electronic orbitals associated with the two FH covalent bonds are geminal-coupled to the proton orbital. For both systems, the RXCHF method produces qualitatively accurate nuclear densities, in contrast to mean field-based NEO approaches. The development and implementation of the RXCHF method provide the framework to perform calculations on systems such as proton-coupled electron transfer reactions, where electron-proton nonadiabatic effects are important.