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. 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.

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. The RXCHF method with a restricted basis set is applied to HCN and FHF(-) and is shown to agree quantitatively with results from RXCHF calculations with a full basis set. The number of many-particle integrals that must be calculated for these two molecules is reduced by over an order of magnitude with essentially no loss in accuracy, and the reduction factor will increase substantially for larger systems. Typically, the computational cost of RXCHF calculations with restricted basis sets will scale in terms of the number of basis functions centered on the quantum nucleus and the covalently bonded neighbor(s). In addition, the RXCHF method with an odd number of electrons that are not explicitly correlated to the nuclear orbital is implemented using a restricted open-shell formalism for these electrons. This method is applied to HCN(+), and the nuclear densities are in qualitative agreement with grid-based calculations. Future work will focus on the significance of nonadiabatic effects in molecular systems and the further enhancement of the NEO-RXCHF approach to accurately describe such effects.

Reduced explicitly correlated Hartree-Fock approach within the nuclear-electronic orbital framework: theoretical formulation.

The nuclear-electronic orbital (NEO) method treats electrons and select nuclei quantum mechanically on the same level to extend beyond the Born-Oppenheimer approximation. Electron-nucleus dynamical correlation has been found to be highly significant due to the attractive Coulomb interaction. The explicitly correlated Hartree-Fock (NEO-XCHF) approach includes explicit electron-nucleus correlation with Gaussian-type geminal functions during the variational optimization of the nuclear-electronic wavefunction. Although accurate for small model systems, the NEO-XCHF method is computationally impractical for larger chemical systems. In this paper, we develop the reduced explicitly correlated Hartree-Fock approach, denoted NEO-RXCHF, where only select electronic orbitals are explicitly correlated to the nuclear orbitals. By explicitly correlating only the relevant electronic orbitals to the nuclear orbitals, the NEO-RXCHF approach avoids problems that can arise when all electronic orbitals are explicitly correlated to the nuclear orbitals in the same manner. We examine three different NEO-RXCHF methods that differ in the treatment of the exchange between the geminal-coupled electronic orbitals and the other electronic orbitals: NEO-RXCHF-fe is fully antisymmetric with respect to exchange of all electronic coordinates and includes all electronic exchange terms; NEO-RXCHF-ne neglects the exchange between the geminal-coupled electronic orbitals and the other electronic orbitals; and NEO-RXCHF-ae includes approximate exchange terms between the geminal-coupled electronic orbitals and the other electronic orbitals. The latter two NEO-RXCHF methods offer substantial computational savings over the NEO-XCHF approach. The NEO-RXCHF approach is applicable to a wide range of chemical systems that exhibit non-Born-Oppenheimer effects between electrons and nuclei, as well as positron-containing molecular systems.

Reduced explicitly correlated Hartree-Fock approach within the nuclear-electronic orbital framework: applications to positronic molecular systems.

In the application of the nuclear-electronic orbital (NEO) method to positronic systems, all electrons and the positron are treated quantum mechanically on the same level. Explicit electron-positron correlation can be included using Gaussian-type geminal functions within the variational self-consistent-field procedure. In this paper, we apply the recently developed reduced explicitly correlated Hartree-Fock (RXCHF) approach to positronic molecular systems. In the application of RXCHF to positronic systems, only a single electronic orbital is explicitly correlated to the positronic orbital. We apply NEO-RXCHF to three systems: positron-lithium, lithium positride, and positron-lithium hydride. For all three of these systems, the RXCHF approach provides accurate two-photon annihilation rates, average contact densities, electronic and positronic single-particle densities, and electron-positron contact densities. Moreover, the RXCHF approach is significantly more accurate than the original XCHF approach, in which all electronic orbitals are explicitly correlated to the positronic orbital in the same manner, because the RXCHF wavefunction is optimized to produce a highly accurate description of the short-ranged electron-positron interaction that dictates the annihilation rates and other local properties. Furthermore, RXCHF methods that neglect or approximate the electronic exchange interactions between the geminal-coupled electronic orbital and the regular electronic orbitals lead to virtually identical annihilation rates and densities as the fully antisymmetric RXCHF method but offer substantial advantages in computational tractability. Thus, NEO-RXCHF is a promising, computationally practical approach for studying larger positron-containing systems.

A catalytically driven organometallic molecular motor.

We have observed by NMR spectroscopy that the diffusive movement of a ruthenium-based Grubbs' catalyst increases during ring-closing metathesis as a function of the substrate concentration. This is one of the smallest single molecule motors to exhibit catalytically driven motion.

Multicomponent density functional theory study of the interplay between electron-electron and electron-proton correlation.

The interplay between electron-electron and electron-proton correlation is investigated within the framework of the nuclear-electronic orbital density functional theory (NEO-DFT) approach, which treats electrons and select protons quantum mechanically on the same level. Recently two electron-proton correlation functionals were developed from the electron-proton pair densities obtained from explicitly correlated wavefunctions. In these previous derivations, the kinetic energy contribution arising from electron-proton correlation was neglected. In this paper, an electron-proton correlation functional that includes this kinetic energy contribution is derived using the adiabatic connection formula in multicomponent DFT. The performance of the NEO-DFT approach using all three electron-proton correlation functionals in conjunction with three well-established electronic exchange-correlation functionals is assessed. NEO-DFT calculations with these electron-proton correlation functionals capture the increase in the hydrogen vibrational stretching frequencies arising from the inclusion of electron-electron correlation in model systems. Electron-proton and electron-electron correlation are found to be uncoupled and predominantly additive effects to the total energy for the model systems studied. Thus, electron-proton correlation functionals and electronic exchange-correlation functionals can be developed independently and subsequently combined together without re-parameterization.

Proton-coupled electron transfer versus hydrogen atom transfer: generation of charge-localized diabatic states.

The distinction between proton-coupled electron transfer (PCET) and hydrogen atom transfer (HAT) mechanisms is important for the characterization of many chemical and biological processes. PCET and HAT mechanisms can be differentiated in terms of electronically nonadiabatic and adiabatic proton transfer, respectively. In this paper, quantitative diagnostics to evaluate the degree of electron-proton nonadiabaticity are presented. Moreover, the connection between the degree of electron-proton nonadiabaticity and the physical characteristics distinguishing PCET from HAT, namely, the extent of electronic charge redistribution, is clarified. In addition, a rigorous diabatization scheme for transforming the adiabatic electronic states into charge-localized diabatic states for PCET reactions is presented. These diabatic states are constructed to ensure that the first-order nonadiabatic couplings with respect to the one-dimensional transferring hydrogen coordinate vanish exactly. Application of these approaches to the phenoxyl-phenol and benzyl-toluene systems characterizes the former as PCET and the latter as HAT. The diabatic states generated for the phenoxyl-phenol system possess physically meaningful, localized electronic charge distributions that are relatively invariant along the hydrogen coordinate. These diabatic electronic states can be combined with the associated proton vibrational states to generate the reactant and product electron-proton vibronic states that form the basis of nonadiabatic PCET theories. Furthermore, these vibronic states and the corresponding vibronic couplings may be used to calculate rate constants and kinetic isotope effects of PCET reactions.

Derivation of an Electron-Proton Correlation Functional for Multicomponent Density Functional Theory within the Nuclear-Electronic Orbital Approach.

Multicomponent density functional theory enables the quantum mechanical treatment of electrons and selected hydrogen nuclei. An electron-proton correlation functional is derived from the electron-proton pair density associated with a recently proposed ansatz for the explicitly correlated nuclear-electronic wave function. This ansatz allows the retention of all terms in the pair density, and the resulting functional is expected to scale properly and to be computationally efficient. Applications to model systems illustrate that it provides accurate nuclear densities.

Diabatization Schemes for Generating Charge-Localized Electron-Proton Vibronic States in Proton-Coupled Electron Transfer Systems.

A scheme for the rigorous construction of charge-localized diabatic electron-proton vibronic states for proton-coupled electron transfer (PCET) reactions is presented. The diabatic electronic states are calculated using an adiabatic-to-diabatic transformation designed to ensure that the first-order nonadiabatic couplings with respect to a specified one-dimensional reaction coordinate vanish exactly. This scheme is applied to both symmetric and asymmetric PCET systems with several different one-dimensional reaction coordinates, including the hydrogen transfer coordinate, a normal mode coordinate, and the intrinsic reaction coordinate. This approach is also extended to describe the three-dimensional motion of the transferring hydrogen. The diabatic electronic states exhibit relatively invariant charge distributions along the reaction coordinate and are in excellent agreement with the analogous states obtained from the generalized Mulliken-Hush and Boys localization methods. Furthermore, these diabatic electronic states are combined with the associated proton vibrational wave functions to generate charge-localized electron-proton vibronic states that describe one- or three-dimensional hydrogen motion. These electron-proton vibronic states can be used to calculate the vibronic couplings, rate constants, and kinetic isotope effects of PCET reactions.

Hydrogen adsorption and diffusion in p-tert-butylcalix[4]arene: an experimental and molecular simulation study.

Experimental adsorption isotherms were measured and computer simulations were performed to determine the nature of the H(2) gas uptake in the low-density p-tert-butylcalix[4]arene (tBC) phase. (1)H NMR peak intensity measurements for pressures up to 175 bar were used to determine the H(2) adsorption isotherm. Weak surface adsorption (up to ≈2 mass % H(2) ) and stronger adsorption (not exceeding 0.25 mass % or one H(2) per calixarene bowl) inside the calixarene phase were detected. The latter type of adsorbed H(2) molecule has restricted motion and shows a reversible gas adsorption/desorption cycle. Pulsed field gradient (PFG) NMR pressurization/depressurization measurements were performed to study the diffusion of H(2) in the calixarene phases. Direct adsorption isotherms by exposure of the calixarene phase to pressures of H(2) gas to ≈60 bar are also presented, and show a maximum H(2) adsorption of 0.4 H(2) per calixarene bowl. Adsorption isotherms of H(2) in bulk tBC have been simulated using grand canonical Monte Carlo calculations in a rigid tBC framework, and yield adsorptions of ≈1 H(2) per calixarene bowl at saturation. Classical molecular dynamics simulations with a fully flexible calixarene molecular force field are used to determine the guest distribution and inclusion energy of the H(2) in the solid with different loadings.

Molecular dynamics simulations of equilibrium and transport properties of amino acid-based room temperature ionic liquids.

Molecular dynamics simulations are used to study liquid-state equilibrium and transport properties of the 1-ethyl-3-methylimidazolium salts of the 20 naturally occurring amino acids [emim][AA] that all form room temperature ionic liquids. These ionic liquids have been recently synthesized by Ohno and co-workers [J. Am. Chem. Soc. 2005, 127, 2398], but other than measured ionic conductivity at 25 degrees C, there is a dearth of quantitative measurements on the physiochemical properties of these liquids. The goal is to computationally study the density, polarity, transference number, and ionic conductivity of this family of solvents. We also study the spatial correlations among the imidazolium cation and amino acid anions in these liquids by computing atomic and charge radial distribution functions and preparing polarity maps. The microscopic dynamics behavior of these materials is determined by studying the mean square displacements (MSD) and velocity autocorrelation functions (VACF). The diffusion coefficients of the liquids are determined using the MSD and VACF, and the contributions of the anions and cations to the transport of charge in the ionic liquids are studied. Ionic liquids of this family that show strong anion-anion and anion-cation associations in the simulations are experimentally observed to show anomalously low electrical conductivities. Knowledge of the microscopic structures and dynamics of these liquids can allow for an intelligent choice of a solvent from this class that has required polarity and ionic conductivity.