A generalized any particle propagator theory: Assessment of nuclear quantum effects on electron propagator calculations

In this work we propose an extended propagator theory for electrons and other types of quantum particles. This new approach has been implemented in the LOWDIN package and applied to sample calculations of atomic and small molecular systems to determine its accuracy and performance. As a first application of the method we have studied the nuclear quantum effects on electron ionization energies. We have observed that ionization energies of atoms are similar to those obtained with the electron propagator approach. However, for molecular systems containing hydrogen atoms there are improvements in the quality of the results with the inclusion of nuclear quantum effects. An energy term analysis has allowed us to conclude that nuclear quantum effects are important for zero order energies whereas propagator results correct the electron and electron-nuclear correlation terms. Results presented for a series of n-alkanes have revealed the potential of this method for the accurate calculation of ionization energies of a wide variety of molecular systems containing hydrogen nuclei. The proposed methodology will also be applicable to exotic molecular systems containing positrons or muons.     

Opposing Electronic and Nuclear Quantum Effects on Hydrogen Bonds in H2O and D2O

The effect of extending the O−H bond length(s) in water on the hydrogen-bonding strength has been investigated using static ab initio molecular orbital calculations. The “polar flattening” effect that causes a slight σ-hole to form on hydrogen atoms is strengthened when the bond is stretched, so that the σ-hole becomes more positive and hydrogen bonding stronger. In opposition to this electronic effect, path-integral ab initio molecular-dynamics simulations show that the nuclear quantum effect weakens the hydrogen bond in the water dimer. Thus, static electronic effects strengthen the hydrogen bond in H₂O relative to D₂O, whereas nuclear quantum effects weaken it. These quantum fluctuations are stronger for the water dimer than in bulk water.     

Structure of isolated and solvated peroxyl radicals

We have investigated the structure of HO₂ and a series of alkyl peroxyl radicals ROO using a variety of quantum mechanical methods. We first compute the geometries, vibrational frequencies, electronic charge distributions, and spin densities for the series of radicals considered in the gas phase. Significant differences with respect to previous calculations have been pointed out in a few cases. In particular, we show the fundamental importance of electronic correlation when computing net atomic charges and spin densities, which have generally been estimated in the litterature by means of Hartree–Fock SCF electronic densities. Solvation effects on the geometry and electronic structure have been estimated by carrying out self-consistent reaction field computations in a polarizable continuum environment with relative dielectric permittivity equal to that of liquid water. Large electronic polarization is predicted in such conditions. This may be important in order to understand reactive properties of the radicals in different media. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1039–1048, 1999     

Theoretical study on isotope and temperature effect in hydronium ion using ab initio path integral simulation

We have applied the ab initio path integral molecular dynamics simulation to study hydronium ion and its isotopes, which are the simplest systems for hydrated proton and deuteron. In this simulation, all the rotational and vibrational degrees of freedom are treated fully quantum mechanically, while the potential energies of the respective atomic configurations are calculated "on the fly" using ab initio quantum chemical approach. With the careful treatment of the ab initio electronic structure calculation by relevant choices in electron correlation level and basis set, this scheme is theoretically quite rigorous except for Born-Oppenheimer approximation. This accurate calculation allows a close insight into the structural shifts for the isotopes of hydronium ion by taking account of both quantum mechanical and thermal effects. In fact, the calculation is shown to be successful to quantitatively extract the geometrical isotope effect with respect to the Walden inversion. It is also shown that this leads to the isotope effect on the electronic structure as well as the thermochemical properties.     

Theory and computation of nuclear magnetic resonance parameters

The art of quantum chemical electronic structure calculation has over the last 15 years reached a point where systematic computational studies of magnetic response properties have become a routine procedure for molecular systems. One of their most prominent areas of application are the spectral parameters of nuclear magnetic resonance (NMR) spectroscopy, due to the immense importance of this experimental method in many scientific disciplines. This article attempts to give an overview on the theory and state-of-the-art of the practical computations in the field, in terms of the size of systems that can be treated, the accuracy that can be expected, and the various factors that would influence the agreement of even the most accurate imaginable electronic structure calculation with experiment. These factors include relativistic effects, thermal effects, as well as solvation/environmental influences, where my group has been active. The dependence of the NMR spectra on external magnetic and optical fields is also briefly touched on.     

LOWDIN: The any particle molecular orbital code

LOWDIN is a computational program that implements the Any Particle Molecular Orbital (APMO) method. The current version of the code encompasses Hartree–Fock, second‐order Møller–Plesset, configuration interaction, density functional, and generalized propagator theories. LOWDIN input file offers a unique flexibility, allowing users to exploit all the programs' capabilities to study systems containing any type and number of quantum species. This review provides a basic introduction to LOWDIN's key computational details and capabilities. © 2013 Wiley Periodicals, Inc.     

Non-adiabatic quantum molecular dynamics: basic formalism and case study

A general formalism is presented that treats selfconsistently and simultaneously classical atomic motion and quantum electronic excitations in dynamical processes of atomic many-body systems (non-adiabatic quantum molecular dynamics). On the basis of time-dependent density functional theory, coupled highly non-linear equations of motion are derived for arbitrary basis sets for the time-dependent Kohn-Sham orbitals. Possible approximations to make the approach practical for large atomic cluster systems are discussed. As a first application of the still exact equations of motion, non-adiabatic effects in the scattering of H⁺+H, as a case study, are investigated.     

Combined QM/MM and path integral simulations of kinetic isotope effects in the proton transfer reaction between nitroethane and acetate ion in water

An integrated Feynman path integral-free energy perturbation and umbrella sampling (PI-FEP/UM) method has been used to investigate the kinetic isotope effects (KIEs) in the proton transfer reaction between nitroethane and acetate ion in water. In the present study, both nuclear and electronic quantum effects are explicitly treated for the reacting system. The nuclear quantum effects are represented by bisection sampling centroid path integral simulations, while the potential energy surface is described by a combined quantum mechanical and molecular mechanical (QM/MM) potential. The accuracy essential for computing KIEs is achieved by a FEP technique that transforms the mass of a light isotope into a heavy one, which is equivalent to the perturbation of the coordinates for the path integral quasiparticle in the bisection sampling scheme. The PI-FEP/UM method is applied to the proton abstraction of nitroethane by acetate ion in water through molecular dynamics simulations. The rule of the geometric mean and the Swain-Schaad exponents for various isotopic substitutions at the primary and secondary sites have been examined. The computed total deuterium KIEs are in accord with experiments. It is found that the mixed isotopic Swain-Schaad exponents are very close to the semiclassical limits, suggesting that tunneling effects do not significantly affect this property for the reaction between nitroethane and acetate ion in aqueous solution.     

若干有机共轭分子二阶非线性光学系数和结构的关系

利用CNDO/S-CI程序计算了四类结构近似的有机共轭分子的二阶非线性光学系数,系统地研究了分子结构、共轭链链长、取代基的电子性质、取代位置等对有机共轭大分子二阶非线性光学性质的影响。研究结果表明,四类化合物的二阶非线性光学性质与其分子结构有着密切的关系。     

Quantum wavepacket ab initio molecular dynamics for extended systems

In this paper, we introduce a symmetry-adapted quantum nuclear propagation technique that utilizes distributed approximating functionals for quantum wavepacket dynamics in extended condensed-phase systems. The approach is developed with a goal for implementation in quantum-classical methods such as the recently developed quantum wavepacket ab intio molecular dynamics (QWAIMD) to facilitate the study of extended systems. The method has been numerically benchmarked for extended electronic systems as well as protonic conducting systems that benefit from quantum nuclear treatment. Vibrational properties are computed for the case of the protonic systems through use of a novel velocity-flux correlation function. The treatment is found to be numerically accurate and efficient.     

Continuum treatment of electronic polarization effect

A continuum treatment of electronic polarization has been explored for in molecular mechanics simulations in implicit solvents. The dielectric constant for molecule interior is the only parameter in the continuum polarizable model. A value of 4 is found to yield optimal agreement with high-level ab initio quantum mechanical calculations for the tested molecular systems. Interestingly, its performance is not sensitive to the definition of molecular volume, in which the continuum electronic polarization is defined. In this model, quantum mechanical electrostatic field in different dielectric environments from vacuum, low-dielectric organic solvent, and water can be used simultaneously in atomic charge fitting to achieve consistent treatment of electrostatic interactions. The tests show that a single set of atomic charges can be used consistently in different dielectric environments and different molecular conformations, and the atomic charges transfer well from training monomers to tested dimers. The preliminary study gives us the hope of developing a continuum polarizable force field for more consistent simulations of proteins and nucleic acids in implicit solvents.     

Quantum wavepacket ab initio molecular dynamics: an approach for computing dynamically averaged vibrational spectra including critical nuclear quantum effects

We have introduced a computational methodology to study vibrational spectroscopy in clusters inclusive of critical nuclear quantum effects. This approach is based on the recently developed quantum wavepacket ab initio molecular dynamics method that combines quantum wavepacket dynamics with ab initio molecular dynamics. The computational efficiency of the dynamical procedure is drastically improved (by several orders of magnitude) through the utilization of wavelet-based techniques combined with the previously introduced time-dependent deterministic sampling procedure measure to achieve stable, picosecond length, quantum-classical dynamics of electrons and nuclei in clusters. The dynamical information is employed to construct a novel cumulative flux/velocity correlation function, where the wavepacket flux from the quantized particle is combined with classical nuclear velocities to obtain the vibrational density of states. The approach is demonstrated by computing the vibrational density of states of [Cl-H-Cl]-, inclusive of critical quantum nuclear effects, and our results are in good agreement with experiment. A general hierarchical procedure is also provided, based on electronic structure harmonic frequencies, classical ab initio molecular dynamics, computation of nuclear quantum-mechanical eigenstates, and employing quantum wavepacket ab initio dynamics to understand vibrational spectroscopy in hydrogen-bonded clusters that display large degrees of anharmonicities.     

Recent development of self-interaction-free time-dependent density-functional theory for nonperturbative treatment of atomic and molecular multiphoton processes in intense laser fields

In this paper, we present a short account of some recent developments of self-interaction-free density-functional theory (DFT) and time-dependent density-functional theory (TDDFT) for accurate and efficient treatment of the electronic structure, and time-dependent quantum dynamics of many-electron atomic and molecular systems. The conventional DFT calculations using approximate and explicit exchange-correlation energy functional contain spurious self-interaction energy and improper long-range asymptotic potential, preventing reliable treatment of the excited, resonance, and continuum states. We survey some recent developments of DFT/TDDFT with optimized effective potential (OEP) and self-interaction correction (SIC) for both atomic and molecular systems for overcoming some of the above mentioned difficulties. These DFT (TDDFT)/OEP-SIC approaches allow the use of orbital-independent single-particle local potential which is self-interaction free. In addition we discuss several numerical techniques recently developed for efficient and high-precision treatment of the self-interaction-free DFT/TDDFT equations. The usefulness of these procedures is illustrated by a few case studies of atomic, molecular, and condensed matter processes of current interests, including (a) autoionizing resonances, (b) relativistic OEP-SIC treatment of atomic structure (Z=2-106), (c) shell-filling electronic structure in quantum dots, (d) atomic and molecular processes in intense laser fields, including multiphoton ionization, and very-high-order harmonic generation, etc. For the time-dependent processes, an alternative Floquet formulation of TDDFT is introduced for time-independent treatment of multiphoton processes in intense periodic or quasiperiodic fields. We conclude this paper with some open questions and perspectives of TDDFT.     

Quantum delocalization of benzene in the ring puckering coordinates

The effect of quantum mechanical delocalization of atomic nuclei on the conformation of the six‐membered ring structure in two hydrocarbons, cyclohexane and benzene, is investigated using ab initio path integral approach. A striking feature of benzene species is revealed using ring puckering coordinate representation, which demonstrates that the zero point motion of the heavy atom skeleton dominates over the out‐of‐plane thermal motions of the ring. Even more unexpected is the fact, that this is true not only at low temperature of 150 K, at which such behavior would not be surprising, but also at room temperature, where the nuclear quantum effects are usually of lesser importance, especially in the case of such heavy nuclei as carbon. In view of this finding the planar conformation of benzene, whose equilibrium (T = 0 K) geometry results from the well‐known properties of the electronic structure, can be elucidated also at nonzero temperature. According to our simulations, it appears as a consequence of quantum delocalization of the carbon nuclei rather than a trivial time average over the classical configurations of the puckered ring. This interesting behavior is contrasted with the clearly nonplanar structure of cyclohexane, whose ring puckering states can be unequivocally assigned even if the nuclear delocalization is taken into account. © 2014 Wiley Periodicals, Inc.     

Nuclear quantum effects and hydrogen bonding in liquids

We have employed ab initio path integral molecular dynamics simulations to investigate the role of nuclear quantum effects on the strength of hydrogen bonds in liquid hydrogen fluoride. Nuclear quantum effects are shown to be responsible for a stronger hydrogen bond and an enhanced dipole-dipole interaction, which lead, in turn, to a shortening of the H...F intrachain distance. The simulation results are analyzed in terms of the electronic density shifts with respect to a purely classical treatment of the nuclei. The observed enhanced hydrogen-bond interaction, which arises from a coupling of intra- and intermolecular effects, should be a general phenomenon occurring in all hydrogen-bonded systems.     

Analysis of the atomic structure of colloidal quantum dots of the CdSe family: X-ray spectral diagnostics and computer modelling

Colloidal quantum dots of the CdSe family have been studied by X-ray absorption near edge structure (XANES) spectroscopy and computer modelling. CdK edge XANES spectra in colloidal quantum dots based on varisized CdSe nanoparticles have been recorded. Atomic structure of CdSe particles and also CdSe particles doped by transition metal atoms Mn and Co has been modelled based on the density functional theory. The embedding of the doping atoms is shown to result in considerable changes in the local atomic structure of CdSe particles. XANES spectra have been calculated above the CdK edge in CdSe particles, above the MnK edge in CdSe:Mn particles, above the CoK edge in CdSe:Co particles. The sensitivity of XANES spectroscopy to small changes in structural parameters of the nanoparticles of CdSe family has been demonstrated that furnishes an opportunity to apply it for the verification of atomic structure parameters around positions of cadmium and doping atoms of transition metals in quantum dots based on CdSe.     

A path integral molecular dynamics study on intermolecular hydrogen bond of acetic acid–arsenic acid anion and acetic acid–phosphoric acid anion clusters

We apply ab initio path integral molecular dynamics simulation employing ωB97XD as the quantum chemical calculation method to acetic acid–arsenic acid anion and acetic acid–phosphoric acid anion clusters to investigate the difference of the hydrogen bond structure and its fluctuation such as proton transfer. We found that the nuclear quantum effect enhanced the fluctuation of the hydrogen bond structure and proton transfer, which shows treatment of the nuclear quantum effect was essential to investigate these systems. The hydrogen bond in acetic acid–arsenic acid anion cluster showed characters related to low-barrier hydrogen bonds, while acetic acid–phosphoric acid anion cluster did not. We found non-negligible distinction between these two systems, which could not be found in conventional calculations. We suggest that the difference in amount of atomic charge of the atoms consisting the hydrogen bond is the origin of the difference between acetic acid–arsenic acid and acetic acid–phosphoric acid anion cluster. © 2018 Wiley Periodicals, Inc.