Dynamical electron -proton correlation in the nuclear -electronic orbital framework

The nuclear-electronic orbital (NEO) approach is a method for including nuclear quantum effects directly into electronic structure calculations. In the NEO approach, specified nuclei are treated quantum mechanically on the same level as the electrons, and mixed nuclear-electronic wavefunctions are calculated using molecular orbital methods. The influence of dynamical electron-proton correlation within the NEO framework is the focus of this dissertation.;A formulation of nuclear-electronic orbital many-body perturbation theory (NEO-MP2) for treating electron-proton correlation is presented. Second-order Rayleigh-Schrodinger perturbation theory based on the NEO-HF (Hartree-Fock) reference Hamiltonian is used to construct corrections for electron-electron and electron-proton correlation.;Fundamental issues associated with the application of the NEO approach to hydrogen transfer systems are addressed. Within the NEO framework, the transferring hydrogen atom can be represented by two basis function centers to allow delocalization of the proton vibrational wavefunction. The NEO approach is applied to the [He-H-He]+ and [He-H-He]++ model systems. Analyses of basis center optimization with the NEO-MP2 method demonstrates that electron-proton correlation impacts the delocalized nature of nuclear wavefunctions. Technical issues pertaining to flexibility of the basis set to describe both single and double well proton potential energy surfaces, linear dependency of the hydrogen basis functions, multiple minima in the basis function center optimization, convergence of the number of hydrogen basis function centers, and basis set superposition error are also presented. The accuracy of the NEO approach is tested by comparison to grid calculations for these model systems.;The structural impact of nuclear quantum effects is investigated for a set of bihalides, [XHX]-, X = F, Cl, Br, and hydrogen fluoride clusters, (HF)2--8. Structures are calculated with the vibrational self-consistent-field (VSCF) method, the second-order vibrational perturbation theory method (VPT2), path integral Car-Parrinello molecular dynamics (PICPMD), and the nuclear-electronic orbital (NEO) approach. In the VSCF, VPT2, and PICPMD methods, the vibrationally-averaged geometries are calculated for the Born-Oppenheimer electronic potential energy surface. Electron-electron and electron-proton dynamical correlation effects are included in the NEO approach using NEO-MP2. The nuclear quantum effects are found to alter the distances between the heavy atoms by 0.02--0.05 A, which is of similar magnitude as electron correlation effects. For the bihalides, inclusion of the nuclear quantum effects with the NEO-MP2 or the VSCF method increases the X--X distance. The bihalide X--X distances are similar for both methods and are consistent with two-dimensional grid calculations and experimental values, thereby validating the use of the computationally efficient NEO-MP2 method for these types of systems.;For the hydrogen fluoride clusters, inclusion of nuclear quantum effects decreases the F--F distance with the NEO-MP2 method. The nuclear quantum effects included with the PICPMD and VPT2 methods result in increased F--F distances for the (HF)2--4 clusters and decreased F--F distances for the (HF)5--6 clusters. The VPT2 F--F distances for the hydrogen fluoride dimer and the deuterated form are consistent with the experimentally determined values. The NEO-MP2 F--F distance is in excellent agreement with the distance obtained experimentally for a model that removes the large amplitude bending motions. The NEO-MP2 method does not include the large amplitude bending motions properly because it does not recover enough dynamical electron-proton correlation.;A method that includes explicit electron-proton correlation directly into the nuclear-electronic orbital self-consistent-field framework is presented. This nuclear-electronic orbital explicitly correlated Hartree-Fock (NEO-XCHF) scheme is formulated using Gaussian basis functions for the electrons and the quantum nuclei in conjunction with Gaussian-type geminal functions. The description of the nuclear wavefunction is significantly improved by the inclusion of explicit electron-proton correlation. The NEO-XCHF method leads to hydrogen vibrational stretch frequencies that are in excellent agreement with those calculated from grid-based methods.;The results presented indicate that dynamical electron-proton correlation significantly impacts the qualitative characteristics of nuclear wavefunctions. Moreover, dynamical electron-proton correlation is essential for treating systems containing low frequency, large amplitude atomic motions such as hydrogen bonded clusters. Methods based on orbital expansions for recovering dynamical electron-proton correlation suffer from slow convergence reminiscent of that found for precise treatments of electron-electron correlation. Therefore, an explicit treatment of electron-proton correlation is required.