Perturbing finite temperature multicomponent DFT 1D Kohn-Sham systems: Peierls gap & Kohn anomaly.

One of the greatest challenges when designing new technologies that make use of non-trivial quantum materials is the difficulty associated with predicting material-specific properties, such as critical temperature, gap parameter, etc. There is naturally a great amount of interest in these types of condensed matter systems because of their application to quantum sensing, quantum electronics, and quantum computation; however, they are exceedingly difficult to address from first principles because of the famous many-body problem. For this reason, a full electron-nuclear quantum calculation will likely remain completely out of reach for the foreseeable future.

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.

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.

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.

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.

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.

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.

Analysis of electron-positron wavefunctions in the nuclear-electronic orbital framework.

The nuclear-electronic orbital explicitly correlated Hartree-Fock (NEO-XCHF) approach is extended and applied to the positronic systems PsH, LiPs, and e(+)LiH. In this implementation, all electrons and positrons are treated quantum mechanically, and all nuclei are treated classically. This approach utilizes molecular orbital techniques with Gaussian basis sets for the electrons and positrons and includes electron-positron correlation with explicitly correlated Gaussian-type geminal functions.

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.

Alternative wavefunction ansatz for including explicit electron-proton correlation in the nuclear-electronic orbital approach.

The nuclear-electronic orbital (NEO) approach treats specified nuclei quantum mechanically on the same level as the electrons with molecular orbital techniques. The explicitly correlated Hartree-Fock (NEO-XCHF) approach was developed to incorporate electron-nucleus dynamical correlation directly into the variational optimization of the nuclear-electronic wavefunction. In the original version of this approach, the Hartree-Fock wavefunction is multiplied by (1+Ĝ), where Ĝ is a geminal operator expressed as a sum of Gaussian type geminal functions that depend on the electron-proton distance.

Properties of the exact universal functional in multicomponent density functional theory.

Multicomponent density functional theory has been developed to treat systems with more than one type of quantum particle, such as electrons and nuclei, in an external potential. The existence of the exact universal multicomponent density functional in terms of the one-particle densities for each type of quantum particle has been proven. In the present paper, a number of important mathematical properties of the exact universal multicomponent density functional are derived.

Calculation of the positron annihilation rate in PsH with the positronic extension of the explicitly correlated nuclear-electronic orbital method.

The nuclear-electronic orbital explicitly correlated Hartree-Fock (NEO-XCHF) method is modified and extended to study electron-positron quantum systems. The NEO-XCHF method is more computationally efficient than the explicitly correlated methods previously applied to positron systems because only the electron-positron dynamical correlation is treated explicitly in NEO-XCHF. As a result, the form of the wave function is much simpler with fewer parameters, and the variational optimization of the molecular orbital parameters is performed through an iterative scheme rather than a stochastic optimization.

Development of electron-proton density functionals for multicomponent density functional theory.

We present a strategy for the development of electron-proton density functionals in multicomponent density functional theory, treating electrons and selected nuclei quantum mechanically without the Born-Oppenheimer approximation. An electron-proton functional is derived using an explicitly correlated electron-proton pair density. This functional provides accurate hydrogen nuclear densities, thereby enabling reliable calculations of molecular properties.

Inclusion of explicit electron-proton correlation in the nuclear-electronic orbital approach using Gaussian-type geminal functions.

The nuclear-electronic orbital explicitly correlated Hartree-Fock (NEO-XCHF) approach for including electron-proton correlation in mixed nuclear-electronic wavefunctions is presented. A general ansatz for the nuclear-electronic wavefunction that includes explicit dependence on the nuclear-electronic distances with Gaussian-type geminal functions is proposed. Based on this ansatz, expressions are derived for the total energy and the electronic and nuclear Fock operators for multielectron systems.

Modeling positrons in molecular electronic structure calculations with the nuclear-electronic orbital method.

The nuclear-electronic orbital (NEO) method was modified and extended to positron systems for studying mixed positronic-electronic wavefunctions, replacing the mass of the proton with the mass of the positron. Within the modified NEO framework, the NEO-HF (Hartree-Fock) method provides the energy corresponding to the single-configuration mixed positronic-electronic wavefunction, minimized with respect to the molecular orbitals expressed as linear combinations of Gaussian basis functions. The electron-electron and electron-positron correlation can be treated in the NEO framework with second-order perturbation theory (NEO-MP2) or multiconfigurational methods such as the full configuration interaction (NEO-FCI) and complete active space self-consistent-field (NEO-CASSCF) methods.

Density functional theory treatment of electron correlation in the nuclear-electronic orbital approach.

This paper presents the nuclear-electronic orbital density functional theory [NEO-DFT(ee)] method for including electron-electron correlation and nuclear quantum effects self-consistently in quantum chemical calculations. The NEO approach is designed to treat a relatively small number of nuclei quantum mechanically, while the remaining nuclei are treated classically. In the NEO-DFT(ee) approach, the correlated electron density is used to obtain the nuclear molecular orbitals, and the resulting nuclear density is used to obtain the correlated electron density during an iterative procedure that continues until convergence of both the nuclear and electronic densities.

Explicit dynamical electron-proton correlation in the nuclear-electronic orbital framework.

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 NEO approach is designed for the quantum treatment of a relatively small number of nuclei, such as the hydrogen nuclei involved in key hydrogen bonding interactions or hydrogen transfer reactions.

Nuclear-electronic orbital nonorthogonal configuration interaction approach.

The nuclear-electronic orbital nonorthogonal configuration interaction (NEO-NOCI) approach is presented. In this framework, the hydrogen nuclei are treated quantum mechanically on the same level as the electrons, and a mixed nuclear-electronic time-independent Schrodinger equation is solved with molecular orbital techniques. For hydrogen transfer systems, the transferring hydrogen is represented by two basis function centers to allow delocalization of the nuclear wave function.

Investigation of isotope effects with the nuclear-electronic orbital approach.

This paper addresses fundamental issues that arise in the application of the nuclear-electronic orbital (NEO) approach to systems with equivalent quantum nuclei. Our analysis illustrates that Hartree-Fock nuclear wave functions do not provide physically reasonable descriptions of systems comprised of equivalent low-spin fermions or equivalent bosons. The physical basis for this breakdown is that the ionic terms dominate due to the localized nature of the nuclear orbitals.

Analysis of the nuclear-electronic orbital method for model hydrogen transfer systems.

Fundamental issues associated with the application of the nuclear-electronic orbital (NEO) approach to hydrogen transfer systems are addressed. In the NEO approach, specified nuclei are treated quantum mechanically on the same level as the electrons, and mixed nuclear-electronic wavefunctions are calculated with molecular orbital methods. The positions of the nuclear basis function centers are optimized variationally.

Electron-proton correlation for hydrogen tunneling systems.

Hydrogen tunneling is important for numerous chemical and biological processes. We study this phenomenon with a multiconfigurational nuclear-electronic orbital approach. Our results demonstrate that a single configuration nuclear-electronic wave function is inadequate to describe hydrogen tunneling systems because such wave functions do not include the essential electron-proton correlation.