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

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. Therefore, this study implements the second-order Epstein-Nesbet correction to the variational stage of multicomponent HCI for the first time. Additionally, this study introduces a new procedure for calculating reference excitation energies for multicomponent methods using the Fourier-grid Hamiltonian (FGH) method, which should allow the one-particle electronic basis set errors to be better isolated from errors arising from an incomplete description of electron-proton correlation. The excited-state multicomponent HCI method is benchmarked by computing protonic excitations of the HCN and FHF^- molecules and is shown to be of similar accuracy to previous excited-state multicomponent methods such as the multicomponent time-dependent density-functional theory and equation-of-motion coupled-cluster theory relative to the new FGH reference values.

Gaussian-Type Orbital Calculations for High Harmonic Generation in Vibrating Molecules: Benchmarks for H2. J Chem Theory Comput 2021;17:7353-7365. [PMID: 34747605 DOI: 10.1021/acs.jctc.1c00837]

The response of the hydrogen molecular ion, H₂⁺, to few-cycle laser pulses of different intensities is simulated. To treat the coupled electron-nuclear motion, we use adiabatic potentials computed with Gaussian-type basis sets together with a heuristic ionization model for the electron and a grid representation for the nuclei. Using this mixed-basis approach, the time-dependent Schrödinger equation is solved, either within the Born-Oppenheimer approximation or with nonadiabatic couplings included. The dipole response spectra are compared to all-grid-based solutions for the three-body problem, which we take as a reference to benchmark the Gaussian-type basis set approaches. Also, calculations employing the fixed-nuclei approximation are performed, to quantify effects due to nuclear motion. For low intensities and small ionization probabilities, we get excellent agreement of the dynamics using Gaussian-type basis sets with the all-grid solutions. Our investigations suggest that high harmonic generation (HHG) and high-frequency response, in general, can be reliably modeled using Gaussian-type basis sets for the electrons for not too high harmonics. Further, nuclear motion destroys electronic coherences in the response spectra even on the time scale of about 30 fs and affects HHG intensities, which reflect the electron dynamics occurring on the attosecond time scale. For the present system, non-Born-Oppenheimer effects are small. The Gaussian-based, nonadiabatically coupled, time-dependent multisurface approach to treat quantum electron-nuclear motion beyond the non-Born-Oppenheimer approximation can be easily extended to approximate wavefunction methods, such as time-dependent configuration interaction singles (TD-CIS), for systems where no benchmarks are available.

Domain-based local pair natural orbital methods within the correlation consistent composite approach

Ab initio composite approaches have been utilized to model and predict main group thermochemistry within 1 kcal mol^-1 , on average, from well-established reliable experiments, primarily for molecules with less than 30 atoms. For molecules of increasing size and complexity, such as biomolecular complexes, composite methodologies have been limited in their application. Therefore, the domain-based local pair natural orbital (DLPNO) methods have been implemented within the correlation consistent composite approach (ccCA) framework, namely DLPNO-ccCA, to reduce the computational cost (disk space, CPU (central processing unit) time, memory) and predict energetic properties such as enthalpies of formation, noncovalent interactions, and conformation energies for organic biomolecular complexes including one of the largest molecules examined via composite strategies, within 1 kcal mol^-1 , after calibration with 119 molecules and a set of linear alkanes. © 2019 Wiley Periodicals, Inc.

Multicomponent coupled cluster singles and doubles and Brueckner doubles methods: Proton densities and energies

The nuclear-electronic orbital (NEO) framework enables computationally practical coupled cluster calculations of multicomponent molecular systems, in which all electrons and specified nuclei, typically protons, are treated quantum mechanically. In addition to energies, computing accurate proton densities is essential for the calculation of reliable molecular properties, including vibrationally averaged geometries and vibrational frequencies. Herein, the Lagrangian formalism for the multicomponent coupled cluster with single and double excitations (NEO-CCSD) method is derived and implemented. The multicomponent coupled cluster with double excitations method using optimized Brueckner orbitals, denoted as NEO-BCCD, is also developed. Both of these methods are used to compute the proton densities for two molecular systems. The results illustrate that orbital relaxation effects, which can be included either indirectly with the NEO-CCSD method or directly with the NEO-BCCD method, are critical for computing even qualitatively accurate proton densities. Both methods are also able to provide accurate proton affinities and vibrationally averaged optimized geometries. This Lagrangian formalism will enable the calculation of other properties such as analytical nuclear gradients and Hessians with NEO coupled cluster methods. Moreover, the accuracy of these methods may be improved systematically by the inclusion of higher-order excitations. Thus, this work provides the foundation for a wide range of future methodological developments and applications within the NEO framework.

Developing effective electronic-only coupled-cluster and Møller-Plesset perturbation theories for the muonic molecules

Recently we have proposed an effective Hartree-Fock (EHF) theory for the electrons of the muonic molecules that is formally equivalent to the HF theory within the context of the nuclear-electronic orbital theory [Phys. Chem. Chem. Phys., 2018, 20, 4466]. In the present report we extend the muon-specific effective electronic structure theory beyond the EHF level by introducing the effective second order Møller-Plesset perturbation theory (EMP2) and the effective coupled-cluster theory at single and double excitation levels (ECCSD) as well as an improved version including perturbative triple excitations (ECCSD(T)). These theories incorporate electron-electron correlation into the effective paradigm and through their computational implementation, a diverse set of small muonic species is considered as a benchmark at these post-EHF levels. A comparative computational study on this set demonstrates that the muonic bond length is in general non-negligibly longer than corresponding hydrogenic analogs. Next, the developed post-EHF theories are applied for the muoniated N-heterocyclic carbene/silylene/germylene and the muoniated triazolium cation revealing the relative stability of the sticking sites of the muon in each species. The computational results, in line with previously reported experimental data demonstrate that the muon generally prefers to attach to the divalent atom with carbeneic nature. A detailed comparison of these muonic adducts with the corresponding hydrogenic adducts reveals subtle differences that have already been overlooked.

Multicomponent Time-Dependent Density Functional Theory: Proton and Electron Excitation Energies

The quantum mechanical treatment of both electrons and protons in the calculation of excited state properties is critical for describing nonadiabatic processes such as photoinduced proton-coupled electron transfer. Multicomponent density functional theory enables the consistent quantum mechanical treatment of more than one type of particle and has been implemented previously for studying ground state molecular properties within the nuclear-electronic orbital (NEO) framework, where all electrons and specified protons are treated quantum mechanically. To enable the study of excited state molecular properties, herein the linear response multicomponent time-dependent density functional theory (TDDFT) is derived and implemented within the NEO framework. Initial applications to FHF^- and HCN illustrate that NEO-TDDFT provides accurate proton and electron excitation energies within a single calculation. As its computational cost is similar to that of conventional electronic TDDFT, the NEO-TDDFT approach is promising for diverse applications, particularly nonadiabatic proton transfer reactions, which may exhibit mixed electron-proton vibronic excitations.

Toward a muon-specific electronic structure theory: effective electronic Hartree-Fock equations for muonic molecules

An effective set of Hartree-Fock (HF) equations are derived for electrons of muonic systems, i.e., molecules containing a positively charged muon, conceiving the muon as a quantum oscillator, which are completely equivalent to the usual two-component HF equations used to derive stationary states of the muonic molecules. In these effective equations, a non-Coulombic potential is added to the orthodox coulomb and exchange potential energy terms, which describes the interaction of the muon and the electrons effectively and is optimized during the self-consistent field cycles. While in the two-component HF equations a muon is treated as a quantum particle, in the effective HF equations it is absorbed into the effective potential and practically transformed into an effective potential field experienced by electrons. The explicit form of the effective potential depends on the nature of muon's vibrations and is derivable from the basis set used to expand the muonic spatial orbital. The resulting effective Hartree-Fock equations are implemented computationally and used successfully, as a proof of concept, in a series of muonic molecules containing all atoms from the second and third rows of the Periodic Table. To solve the algebraic version of the equations muon-specific Gaussian basis sets are designed for both muon and surrounding electrons and it is demonstrated that the optimized exponents are quite distinct from those derived for the hydrogen isotopes. The developed effective HF theory is quite general and in principle can be used for any muonic system while it is the starting point for a general effective electronic structure theory that incorporates various types of quantum correlations into the muonic systems beyond the HF equations.

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. 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_a's, optimized geometries, and reaction paths.

Incorporating nuclear vibrational energies into the "atom in molecules" analysis: An analytical study

The quantum theory of atoms in molecules (QTAIM) is based on the clamped nucleus paradigm and solely working with the electronic wavefunctions, so does not include nuclear vibrations in the AIM analysis. On the other hand, the recently extended version of the QTAIM, called the multi-component QTAIM (MC-QTAIM), incorporates both electrons and quantum nuclei, i.e., those nuclei treated as quantum waves instead of clamped point charges, into the AIM analysis using non-adiabatic wavefunctions. Thus, the MC-QTAIM is the natural framework to incorporate the role of nuclear vibrations into the AIM analysis. In this study, within the context of the MC-QTAIM, the formalism of including nuclear vibrational energy in the atomic basin energy is developed in detail and its contribution is derived analytically using the recently proposed non-adiabatic Hartree product nuclear wavefunction. It is demonstrated that within the context of this wavefunction, the quantum nuclei may be conceived pseudo-adiabatically as quantum oscillators and both isotropic harmonic and anisotropic anharmonic oscillator models are used to compute the zero-point nuclear vibrational energy contribution to the basin energies explicitly. Inspired by the results gained within the context of the MC-QTAIM analysis, a heuristic approach is proposed within the context of the QTAIM to include nuclear vibrational energy in the basin energy from the vibrational wavefunction derived adiabatically. The explicit calculation of the basin contribution of the zero-point vibrational energy using the uncoupled harmonic oscillator model leads to results consistent with those derived from the MC-QTAIM.

Unusual H/D isotope effect in isomerization and keto–enol tautomerism reactions of pyruvic acid: nuclear quantum effect restricts some rotational isomerization reactions

H/D isotope effects on isomerization and keto–enol tautomerism reactions of the pyruvic acid molecule have been investigated using the multicomponent B3LYP methods, which can take account of the nuclear quantum effect of protons and deuterons.