Finite Temperature Path Integral Monte Research Articles

Developments and applications of computational infrared spectroscopy in non-bonded systems: Quantal and classical systems

Infrared (IR) spectroscopy, responding to molecular vibrations, is one of the most important tools in understanding the behavior of molecules. For complex systems, because of the relatively dense spectra lines, it could be very difficult to assign IR spectra merely by experience, an instance of which is non-bonded system. For middle-size system, theory and computation, however, can handle part of this problem by construct the potential energy surfaces (PESs) of system following a nuclear motion calculation classic or quantum mechanically. For large-size non-bonded system, although it is hard to calculate the properties of the whole system directly, by decomposing the system into quasi-isolated parts, the spectra can be calculated from the first principle using some approximations, which belong to the toolchain of computational spectroscopy. In this review, we recall some of these methodology based on perturbation theory. (1) In the research of van der Waals complexes, intramolecular vibrations are separated from intermolecular motion via Born-Oppenheimer approximation and first order Rayleigh-Schrodinger perturbation theory. For the ground and first excited state of the chromophores, rigid body intermolecular PESs are build including the relative orientation of the rigid molecules. Based on the intermolecular PESs, rotation and intermolecular radial stretching are treated using Discrete Variable Representation/Finite Basis Representation (DVR/FBR) fully quantum mechanically. The rovibrational spectra are then obtained by the gap between energy levels and the transition dipole moments. (2) Spectroscopy of quantum clusters, where chromophores molecules are caged in helium or hydrogen molecules solvent, are another important topic where perturbation theory and quantum simulation get involved. As previous systems, accurate two-body intermolecular PESs are also needed. The potential of the system is then represented by the many-body expansion, often truncated at two-body term. Quantum effect of the rigid molecules is simulated by finite temperature Path Integral Monte Carlo (PIMC) method. Worm operator is used to take exchange phenomena of the boson into account. Rotation of the chromophore molecule and the boson exchange were found to be very important in the simulation of quantum clusters. By studying IR spectra of quantum cluster, microscopic superfluidity was discovered and confirmed. (3) In bulk system like solution and biological systems, computation of IR spectra remains a challenge. The birth of quantum vibrational perturbation (QVP) theory gives an opportunity of considering the quantum effect and the chemical environment in the same scheme. Regular molecular dynamics simulation (MD) is executed to deal with the solvent fluctuation, and then quantal molecular vibration of chromophore is calculated via DVR quantum solver based on low dimensional cut of intramolecular vibrational coordinate. At each MD step, the instantaneous vibration frequencies are computed by perturbation theory. This mixed quantum mechanical/classic mechanical, or quasi-classical MD simulation will generate the instantaneous frequencies as function of time. Using line shape theory for quasi-classical MD, the spectra line of such system can be obtained. All three situations rely on perturbation theory more or less, which can be very computationally efficient. Because the main part of the IR transition gap can be corrected by experimental data, these methods can focus on transition frequency shift without considering error canceling artifact. In the future, systems containing stronger secondary bond need more efforts in the development of calculation methodology. Kinetic coupling is also an interesting topic to be developed in the coming days. Besides, the new proceeding in electronic structure theory helps a lot in the computational IR spectroscopy.

Static field-gradient polarizabilities of small atoms and molecules at finite temperature.

In this work, we propose new field-free estimators of static field-gradient polarizabilities for finite temperature path-integral Monte Carlo method. Namely, dipole-quadrupole polarizability A, dipole-dipole-quadrupole polarizability B, and quadrupole-quadrupole polarizability C are computed for several up to two-electron systems: H, H-, He, Li+, Be2+, Ps2, PsH, H2+, H2, H3+, and HeH+. We provide complementary data for ground state electronic properties within the adiabatic approximation and demonstrate good agreement with available values in the literature. More importantly, we present fully non-adiabatic results from 50 K to 1600 K, which allow us to analyze and discuss strong thermal coupling and rovibrational effects in total field-gradient polarizabilities. These phenomena are most relevant but clearly overlooked, e.g., in the construction of modern polarizable force field models. However, our main purpose is demonstrating the accuracy and simplicity of our approach in a problem that is generally challenging.

Solidification ofHe4clusters adsorbed on graphene

We determined the ground state of $^{4}\mathrm{He}_{N}$ clusters adsorbed on one side of graphene for selected cluster sizes in the range from $N=20$ to $N=127$. For all investigated clusters variational and diffusion Monte Carlo simulations were performed at $T=0$ K, and in addition for a selected subset finite temperature path integral Monte Carlo. At $T=0$ K the liquid or solid character of each cluster was investigated by restricting the phase using corresponding importance sampling trial-wave functions. The $^{4}\mathrm{He}$-graphene interaction was modeled as a sum of individual $^{4}\mathrm{He}$-C interactions, where both isotropic and anisotropic models were tested; also the effect of the substrate-mediated McLachlan interaction was investigated. We have found homogeneous crystallization in models of anisotropic interactions, starting from clusters with $N=26$ atoms in simulations without the McLachlan interaction, and between $N=37$ and 61 when it is included. The atoms become increasingly delocalized as one moves from the center of the cluster to the perimeter, evidenced by the Lindemann parameter. On the other hand, in the case of the isotropic interaction model, a liquidlike structure is more favorable for all considered cluster sizes. We use a liquid-drop model to extrapolate the energy per particle to the $N\ensuremath{\rightarrow}\ensuremath{\infty}$ limit, and the results are compared with the values obtained in studies of bulk $^{4}\mathrm{He}$ on graphene. Low-temperature path integral Monte Carlo simulations are in agreement with ground-state results.

Exchange-correlation energy for the three-dimensional homogeneous electron gas at arbitrary temperature

We fit finite-temperature path integral Monte Carlo calculations of the exchange-correlation energy of the 3D finite-temperature homogeneous electron gas in the warm-dense regime (r_{s} = (3/4\pi n)^{1/3} a_{B}^{-1} < 40 and \Theta = T/T_{F} > 0.0625). In doing so, we construct a Pad\'{e} approximant which collapses to Debye-H\"{u}ckel theory in the high-temperature, low-density limit. Likewise, the zero-temperature limit matches the numerical results of ground-state quantum Monte Carlo, as well as analytical results in the high-density limit.

Superfluid State of 4He on Graphane and Graphene–Fluoride: Anisotropic Roton States

We explore the phase behavior of Helium films on two variants of graphene: graphane (graphene coated with H, denoted GH) and graphene–fluoride (GF). A semiempirical interaction with these substrates is used in T=0 K Path Integral Ground State and finite temperature Path Integral Monte Carlo simulations. We predict that 4He forms anisotropic fluid states at low coverage. This behavior differs qualitatively from that on graphite because of the different surface composition, symmetry and spacing of the adsorption sites. The 4He ground state on both substrates is thus a self-bound anisotropic superfluid with a superfluid fraction ρs/ρ lower than 1 due to the corrugation of the adsorption potential. In the case of GF such corrugation is so large that ρs/ρ=0.6 at T=0 K and the superfluid is essentially restricted to move in a multiconnected space, along the bonds of a honeycomb lattice. We predict a superfluid transition temperature T≃ 0.25 (1.1) K for 4He on GF (GH). We have studied the elementary excitation spectrum of 4He on GF at equilibrium density finding a phonon–maxon–roton dispersion relation that is strongly anisotropic in the roton region. We conclude that these new platforms for adsorption studies offer the possibility of studying novel superfluid phases of quantum condensed matter.

Finite temperature path integral Monte Carlo simulations of structural and dynamical properties of ArN−CO2 clusters

We report finite temperature quantum mechanical simulations of structural and dynamical properties of Ar(N)-CO(2) clusters using a path integral Monte Carlo algorithm. The simulations are based on a newly developed analytical Ar-CO(2) interaction potential obtained by fitting ab initio results to an anisotropic two-dimensional Morse/Long-range function. The calculated distributions of argon atoms around the CO(2) molecule in Ar(N)-CO(2) clusters with different sizes are consistent to the previous studies of the configurations of the clusters. A first-order perturbation theory is used to quantitatively predict the CO(2) vibrational frequency shift in different clusters. The first-solvation shell is completed at N = 17. Interestingly, our simulations for larger Ar(N)-CO(2) clusters showed several different structures of the argon shell around the doped CO(2) molecule. The observed two distinct peaks (2338.8 and 2344.5 cm(-1)) in the υ(3) band of CO(2) may be due to the different arrangements of argon atoms around the dopant molecule.

Local Coarse-Grained Approximation to Path Integral Monte Carlo Integration for Fermion Systems

An approximate treatment of exchange in finite-temperature path integral Monte Carlo simulations for fermions has been proposed. In this method, some of the fine details of density matrix due to permutations have been smoothed over or averaged out by using the coarse-grained approximation. The practical usefulness of the method is tested for interacting fermions in a three dimensional harmonic well. The results show that, the present method not only reduces the sign fluctuation of the density matrix, but also avoid the fermion system collapsing into boson system at low temperatures. The method is substantiated to be exact when applied to free particles.

Exact ground state Monte Carlo method for Bosons without importance sampling

Generally "exact" quantum Monte Carlo computations for the ground state of many bosons make use of importance sampling. The importance sampling is based either on a guiding function or on an initial variational wave function. Here we investigate the need of importance sampling in the case of path integral ground state (PIGS) Monte Carlo. PIGS is based on a discrete imaginary time evolution of an initial wave function with a nonzero overlap with the ground state, which gives rise to a discrete path which is sampled via a Metropolis-like algorithm. In principle the exact ground state is reached in the limit of an infinite imaginary time evolution, but actual computations are based on finite time evolutions and the question is whether such computations give unbiased exact results. We have studied bulk liquid and solid (4)He with PIGS by considering as initial wave function a constant, i.e., the ground state of an ideal Bose gas. This implies that the evolution toward the ground state is driven only by the imaginary time propagator, i.e., there is no importance sampling. For both phases we obtain results converging to those obtained by considering the best available variational wave function (the shadow wave function) as initial wave function. Moreover we obtain the same results even by considering wave functions with the wrong correlations, for instance, a wave function of a strongly localized Einstein crystal for the liquid phase. This convergence is true not only for diagonal properties such as the energy, the radial distribution function, and the static structure factor, but also for off-diagonal ones, such as the one-body density matrix. This robustness of PIGS can be traced back to the fact that the chosen initial wave function acts only at the beginning of the path without affecting the imaginary time propagator. From this analysis we conclude that zero temperature PIGS calculations can be as unbiased as those of finite temperature path integral Monte Carlo. On the other hand, a judicious choice of the initial wave function greatly improves the rate of convergence to the exact results.

Properties of Bose-Einstein condensates in a quasi-one-dimensional box trap

We present numerical studies of Bose-Einstein condensates in an optical box trap. The box trap is modeled by using Gaussian-wall or hard-wall trapping potentials along the boundary of the box to mimic a recent experimental setup. In order to study a quasi-one-dimensional system, the Gaussian walls are separated differently along the axial and radial directions. Furthermore, the two-body interaction is described by a hard-sphere potential, whose radius equals the $s$-wave scattering length. Using a finite-temperature path integral Monte Carlo method, we have calculated the density profiles of the system as a function of the temperature, the strength of the two-body interaction, and the number of particles. Our numerical results show clearly the Tonks-gas--like behavior in the strong interaction limit. In addition, we have compared our numerical data with the experimental data and theoretical results, and found that our simulation data agree with them quantitatively.

Finite-temperature properties of binary mixtures of two Bose-Einstein condensates

This work reports studies of a mixture of two interacting Bose condensates in a quasi-one-dimensional geometry using a finite-temperature path-integral Monte Carlo method. For weakly interacting dilute gases, the interactions between atoms are modeled by a hard-sphere potential whose core radius equals its corresponding scattering length. The effect of both the temperature and the interspecies interaction on the static properties, such as the density profile and the superfluid fraction, is discussed. Our results show that for repulsive intra- and interspecies interactions, the presence of the interspecies interactions dramatically changes the structure of both the density profile and the superfluid fraction, and two species are seen to partially separate in space, and there is a finite-size effect on the phase separation between two partially separating Bose-Einstein condensates. In general, our results agree with the theoretical predictions and experimental observations.

Rovibrational Spectra for the HCCCN·HCN and HCN·HCCCN Binary Complexes in 4He Droplets

Rovibrational spectra are measured for the HCCCN*HCN and HCN*HCCCN binary complexes in helium droplets at low temperature. Though no Q-branch is observed in the infrared spectrum of the linear HCN*HCCCN dimer, which is consistent with previous experimental results obtained for other linear molecules, a prominent Q-branch is found in the corresponding infrared spectrum of the HCCCN*HCN complex. This Q-branch, which is reminiscent of the spectrum of a parallel band of a prolate symmetric top, implies that some component of the total angular momentum is parallel to the molecular axis. The appearance of this particular spectroscopic feature is analyzed here in terms of a nonsuperfluid helium density induced by the molecular interactions. Finite temperature path integral Monte Carlo simulations are performed using potential energy surfaces calculated with second-order Möller-Plesset perturbation theory, to investigate the structural and superfluid properties of both HCCCN*HCN(4He)N and HCN*HCCCN(4He)N clusters with N < or = 200. Explicit calculation of local and global nonsuperfluid densities demonstrates that this difference in the rovibrational spectra of the HCCCN*HCN and HCN*HCCCN binary complexes in helium can be accounted for by local differences in the superfluid response to rotations about the molecular axis, i.e., different parallel nonsuperfluid densities. The parallel and perpendicular nonsuperfluid densities are found to be correlated with the locations and strengths of extrema in the dimer interaction potentials with helium, differences between which derive from the variable extent of polarization of the CN bond in cyanoacetylene and the hydrogen-bonded CH unit in the two isomers. Calculation of the corresponding helium moments of inertia and effective rotational constants of the binary complexes yields overall good agreement with the experimental values.

Finite-temperature properties of quasi-two-dimensional Bose-Einstein condensates

Using the finite-temperature path integral Monte Carlo method, we investigate dilute, trapped Bose gases in a quasi-two-dimensional (quasi-2D) geometry. The quantum particles have short-range, $s$-wave interactions described by a hard-sphere potential whose core radius equals its corresponding scattering length. The effect of both the temperature and the interparticle interaction on the equilibrium properties such as the total energy, the density profile, and the superfluid fraction is discussed. We compare our accurate results with both the semiclassical approximation and the exact results of an ideal Bose gas. Our results show that for repulsive interactions (i) the minimum value of the aspect ratio, where the system starts to behave quasi-2D, increases as the two-body interaction strength increases; (ii) the superfluid fraction for a quasi-two-dimensionally Bose gas is distinctly different from that for both a quasi-1D Bose gas and a true 3D system, i.e., the superfluid fraction for a quasi-2D Bose gas decreases faster than that for a quasi-1D system and a true 3D system with increasing temperature, and shows a stronger dependence on the interaction strength; (iii) the superfluid fraction for a quasi-2D Bose gas lies well below the values calculated from the semiclassical approximation; and (iv) the Kosterlitz-Thouless transition temperature decreases as the strength of the interaction increases.

Density dependence of the hydrodynamic response to SF6 rotation in superfluid helium

We examine the density dependence of the hydrodynamic response of superfluid helium to classical rotational motion of a molecular impurity within the assumption of an adiabatically following helium density. The sensitivity of the hydrodynamic response to small changes in the helium density is assessed by performing three-dimensional hydrodynamic calculations for different fits to a microscopic helium density around the octahedral SF6 molecule generated by finite-temperature path integral Monte Carlo simulations. The sensitivity to systematic errors in the helium solvation density is assessed by comparing the hydrodynamic results obtained with finite-temperature path integral Monte Carlo densities to the corresponding results obtained using zero-temperature diffusion Monte Carlo densities that possess trial function bias. Our analysis shows that the finite-temperature densities provide a robust upper bound on the hydrodynamic response that amounts to at most 10% of the experimentally measured moment of inertia increment for SF6 at low temperature. We also address theoretical consistency requirements on the numerically derived velocity flows and present modifications of the hydrodynamic equations that are required by incorporation of higher-order quantum phase correlations.

Theoretical calculations of zero-temperature absorption spectra of Li in solid H2

We employ variational and diffusion Monte Carlo methods to calculate the ground state properties of both pure and Li doped solid H2. The absorption spectra of Li in the H2 solid are calculated from the sampled ground state configurations and a pseudothermal semiclassical spectral line theory, based on the Franck–Condon principle for a condensed phase system. The T=0 numerical results of various thermodynamic properties of the pure and doped solid agree well with those from previous theoretical calculations. However, the Li spectra differ significantly from results of a finite temperature path integral Monte Carlo calculation [D. Scharf et al., J. Chem. Phys. 99, 9013 (1993)], which employed a different Li*–H2 potential. The differences in two calculations are extensively discussed here, and comparisons are also made with available experimental data. We demonstrate that accurate measurements of the Li absorption spectrum provide a powerful means to probe the local structures of the Li trapping sites.