Path integral Monte Carlo approach for weakly bound van der Waals complexes with rotations: algorithm and benchmark calculations

A path integral Monte Carlo technique suitable for the treatment of doped helium clusters with inclusion of the rotational degrees of freedom of the dopant is introduced. The extrapolation of the results to the limit of infinite Trotter number is discussed in detail. Benchmark calculations for small weakly bound (4)He(N)--OCS clusters are presented. The Monte Carlo results are compared with those of basis set calculations for the He--OCS dimer. A technique to analyze the orientational imaginary time correlation function is suggested. It allows one to obtain information regarding the effective rotational constant for a doped helium cluster based on a model for the rotational Hamiltonian. The renormalization of the effective rotational constant for (4)He(N)--OCS clusters derived from the orientational imaginary time correlation function is in good agreement with experimental results.     

Rotational structure of small 4He clusters seeded with HF, HCl, and HBr molecules

Diffusion Monte Carlo calculations are performed for ground and excited rotational states of HX(4He)N, complexes with N相似文献   

Quantum monte carlo vibrational dynamics in a property-based interaction potential scheme for weakly bound clusters

The typical shallowness of the potential surfaces of weakly bound clusters implies sizable ground-state vibrational excursions in the weak modes, a feature often complicated by considerable anharmonicity. The difficulties of vibrational analysis are exacerbated as the number of weak modes increases with the number of molecules in a cluster. Quantum Monte Carlo (QMC) approaches offer a general suitability to the problem of vibrational dynamics of weakly bound clusters in that they can fully account for anharmonicity and large amplitude motions. We report on the effectiveness and convergence behavior of diffusion quantum Monte Carlo for both energies and the key spectroscopic values of vibrationally averaged rotational constants. QMC involves recurring evaluations of the interaction potential, and we show how property-based, two-and three-body potentials (e.g., those involving intrinsic molecular tensor properties) may be carefully linked to the QMC propagation steps. © 1997 by John Wiley & Sons, Inc.     

Rotational excitations of N2O in small helium clusters and the role of Bose permutation symmetry

We present a detailed study of the energetics, structures, and Bose properties of small clusters of (4)He containing a single nitrous oxide (N(2)O) molecule, from N=1 (4)He up to sizes corresponding to completion of the first solvation shell around N(2)O (N=16 (4)He). Ground state properties are calculated using the importance-sampled rigid-body diffusion Monte Carlo method, rotational excited state calculations are made with the projection operator imaginary time spectral evolution method, and Bose permutation exchange and associated superfluid properties are calculated with the finite temperature path integral method. For N< or =5 the helium atoms are seen to form an equatorial ring around the molecular axis, at N=6 helium density starts to occupy the second (local) minimum of the N(2)O-He interaction at the oxygen side of the molecule, and N=9 is the critical size at which there is onset of helium solvation all along the molecular axis. For N> or =8 six (4)He atoms are distributed in a symmetric, quasirigid ring around N(2)O. Path integral calculations show essentially complete superfluid response to rotation about the molecular axis for N> or =5, and a rise of the perpendicular superfluid response from zero to appreciable values for N> or =8. Rotational excited states are computed for three values of the total angular momentum, J=1-3, and the energy levels fitted to obtain effective spectroscopic constants that show excellent agreement with the experimentally observed N dependence of the effective rotational constant B(eff). The non-monotonic behavior of the rotational constant is seen to be due to the onset of long (4)He permutation exchanges and associated perpendicular superfluid response of the clusters for N> or =8. We provide a detailed analysis of the role of the helium solvation structure and superfluid properties in determining the effective rotational constants.     

The conformers of hydroxyacetaldehyde

Both two and eighteen dimensional quantum diffusion Monte Carlo (DMC) calculations were used to study the isomers of hydroxyacetaldehyde. A total of four unique minima, and the transition states connecting them, were located. Both two and eighteen dimensional potential energy surfaces were generated and used in the DMC runs. The rotational constants for the global minimum were predicted for all experimentally identified isotopomers and an approximate equilibrium structure obtained by combining our theoretical results with the experimentally observed rotational constants. The results obtained for the remaining isomers indicate that not all of them can be isolated in the gas phase.     

Rotational spectra of rare isotopic species of bromofluoromethane: determination of the equilibrium structure from ab initio calculations and microwave spectroscopy

Guided by theoretical predictions, the rotational spectra of the mono- and bideuterated species of bromofluoromethane, CDH(79)BrF, CDH(81)BrF, CD(2) (79)BrF, and CD(2) (81)BrF, have been recorded for the first time. Assignment of a few hundred rotational transitions led to the accurate determination of the ground-state rotational constants, all of the quartic and most of the sextic centrifugal distortion constants, as well as the full bromine quadrupole-coupling tensor for both (79)Br and (81)Br, in good agreement with corresponding theoretical predictions based on high-level coupled-cluster calculations. The rotational spectra of the (13)C containing species (13)CH(2) (79)BrF and (13)CH(2) (81)BrF have been observed in natural abundance and have been assigned, thus allowing the determination of the rotational and centrifugal distortion constants as well as the bromine quadrupole-coupling tensor. Furthermore, empirical equilibrium structures have been obtained within a least-squares fit procedure using the available experimental ground-state rotational constants for various isotopic species. Vibrational effects have been accounted for in the analysis using vibration-rotation interaction constants derived from anharmonic force fields computed at the second-order Moller-Plesset perturbation theory as well as coupled-cluster (CC) levels. The empirical equilibrium geometries obtained in this way agree well with the corresponding theoretical predictions obtained from CC calculations [at the CCSD(T) level] after extrapolation to the complete basis set limit and inclusion of core-valence correlation corrections and relativistic effects.     

OCS in para-hydrogen clusters: rotational dynamics and superfluidity

We present a detailed analysis of the rotational excitations of the linear OCS molecule solvated by a variable number of para-hydrogen molecules (9 < or = N < or = 17). The effective rotational constant extracted from the fit of the rotational energy levels decreases up to N = 13, indicating near-rigid coupling between OCS rotations and para-hydrogen motion. Departure from rigidity is instead seen for larger clusters with 14 < or = N < or = 17. Path-integral Monte Carlo calculations show that the N dependence of the effective rotational constant can be explained in terms of a partial superfluid response of para-hydrogen to rotations about an axis perpendicular to the OCS axis. Complete para-hydrogen superfluid response to rotations about the OCS axis is found for N > or = 10.     

High-resolution infrared spectrum of the nu1 Ba nd of eta5-C5H5NiNO

Gas-phase rotational constants and distortion constants have been determined for the nu1 (v=1) excited vibrational state of cyclopentadienylnickel nitrosyl (C5H5NiNO) using a high-resolution Fourier transform spectrometer system at Kitt Peak, Arizona. The rotationally resolved lines have been measured for the C-H symmetric stretch vibration (nu1=3110 cm(-1)). In the present analysis, over 150 lines have been assigned and fitted using a rigid-rotor Hamiltonian with centrifugal distortion. The vibrational band center, excited-state rotational constants, and distortion constants derived from the measured spectrum for this prolate symmetric-top molecule are nuo=3110.4129(4) cm(-1), A'=0.14328(8) cm(-1), B'=C'=0.041285(1) cm(-1), DJ'=0.078(1) kHz, DJK'=2.23(4) kHz, and DK'=-2.63(2) kHz, respectively. Several different combination differences, with a common upper state, were calculated for different K stacks for the observed spectra, and the consistency of the lower state rotational constants obtained provided further support for the current assignment. The ground-state rotational constant (B') derived from this combination differences analysis agrees with the previously obtained Fourier transform microwave value to within 0.15%. However, ground-state rotational constants, A' and B', have been fixed in the present analysis to avoid correlation effects and to get more accurate results. The new measured parameters are compared with the previously obtained results from Fourier transform microwave and infrared spectroscopy measurements. The C-H vibration stretching frequency and rotational constants were calculated using density functional theory calculations, and these were quite helpful in resolving ambiguities in the fitting procedure and for initial assignments of measured lines.     

An investigation of the molecular geometry and electronic structure of nitryl chloride by a combination of rotational spectroscopy and ab initio calculations

The ground-state rotational spectra of the six isotopomers (16)O(2) (14)N(35)Cl, (16)O(2) (14)N(37)Cl, (18)O(16)O(14)N(35)Cl, (18)O(2) (14)N(35)Cl, (16)O(2) (15)N(35)Cl, and (16)O(2) (15)N(37)Cl of nitryl chloride were observed with a pulsed-jet, Fourier-transform microwave spectrometer to give rotational constants, Cl and (14)N nuclear quadrupole coupling, and spin-rotation coupling constants. These spectroscopic constants were interpreted to give r(0), r(s), and r(m) ((2)) versions of the molecular geometry and information about the electronic redistribution at N when nitryl chloride is formed from NO(2) and a Cl atom. The r(m) ((2)) geometry has r(N-Cl)=1.8405(6) A, r(N-O)=1.1929(2) A, and the angle ONO=131.42(4) degrees , while the corresponding quantities for the r(s) geometry are 1.8489 A, 1.1940 A, and 131.73 degrees , respectively. Electronic structure calculations at CCSD(T)cc-pVXZ (X=T, Q, or 5) levels of theory were carried out to give a r(e) geometry, vibration-rotation corrections to equilibrium rotational constants, and values of the (35)Cl and (14)N nuclear hyperfine (quadrupole and spin-rotation) coupling constants in good agreement with experiment. The equilibrium geometry at the CCSD(T)/cc-pV5Z level of theory has r(N-Cl)=1.8441 A, r(N-O)=1.1925 A and the angle ONO=131.80 degrees . The observed rotational constants were corrected for the vibration-rotation effects calculated ab initio to yield semiempirical equilibrium constants which were then fitted to give the following semiempirical equilibrium geometry: r(N-Cl)=1.8467(2) A, r(N-O)=1.1916(1) A, and the angle ONO=131.78(3) degrees .     

Small para-hydrogen clusters doped with carbon monoxide: quantum Monte Carlo simulations and observed infrared spectra

The structures and rotational dynamics of clusters of a single carbon monoxide molecule solvated in para-hydrogen, (paraH(2))(N)-CO, have been simulated for sizes up to N=17 using the reptation Monte Carlo technique. The calculations indicate the presence of two series of R(0) rotational transitions with J=1<--0 for cold clusters, similar to those predicted and observed in the case of He(N)-CO. Infrared spectra of these clusters have been observed in the region of the C-O stretch ( approximately 2143 cm(-1)) in a pulsed supersonic jet expansion using a tunable diode laser probe. With the help of the calculations, the observed R(0) rotational transitions have been assigned up to N=9 for the b-type series and N=14 for the a-type series. Theory and experiment agree rather well, except that theory tends to overestimate the b-type energies. The (paraH(2))(12)-CO cluster is calculated to be particularly stable and (relatively) rigid, corresponding to completion of the first solvation shell, and it is observed to have the strongest a-type transition.     

Comparison of the experimental, semi-experimental and ab initio equilibrium structures of acetylene: influence of relativisitic effects and of the diagonal Born-Oppenheimer corrections

The equilibrium structure of acetylene (also named ethyne) has been reinvestigated to resolve the small discrepancies noted between different determinations. The size of the system as well as the large amount of available experimental data provides the quite unique opportunity to check the magnitude and relevance of various contributions to equilibrium structure as well as to verify the accuracy of experimental results. With respect to pure theoretical investigation, quantum-chemical calculations at the coupled-cluster level have been employed together with extrapolation to the basis set limit, consideration of higher excitations in the cluster operator, inclusion of core correlation effects as well as relativistic and diagonal Born-Oppenheimer corrections. In particular, it is found that the extrapolation to the complete basis set limit, the inclusion of higher excitations in the electronic-correlation treatment and the relativistic corrections are of the same order of magnitude. It also appears that a basis set as large as a core-valence quintuple-zeta set is required for accurately accounting for the inner-shell correlation contribution. From a pure experimental point of view, the equilibrium structure has been determined using very accurate rotational constants recently obtained by a "global analysis" (that is to say that all non-negligible interactions are explicitly included in the Hamiltonian matrix) of rovibrational spectra. Finally, a semi-experimental equilibrium structure (where the equilibrium rotational constants are obtained from the experimental ground state rotational constants and computed rovibrational corrections) has been obtained from the available experimental ground-state rotational constants for ten isotopic species corrected for computed vibrational corrections. Such a determination led to the revision of the ground-state rotational constants of two isotopologues, thus showing that structural determination is a good method to identify errors in experimental rotational constants. The three structures are found in a very good agreement, and our recommended values are r(CC) = 120.2958(7) pm and r(CH) = 106.164(1) pm.     

Microwave spectra and molecular structures of (Z)-pent-2-en-4-ynenitrile and maleonitrile.

Accurate equilibrium structures have been determined for (Z)-pent-2-en-4-ynenitrile (8) and maleonitrile (9) by combining microwave spectroscopy data and ab initio quantum chemistry calculations. The microwave spectra of 10 isotopomers of 8 and 5 isotopomers of 9 were obtained using a pulsed nozzle Fourier transform microwave spectrometer. The ground-state rotational constants were adjusted for vibration-rotation interaction effects calculated from force fields obtained from ab initio calculations. The resultant equilibrium rotational constants were used to determine structures that are in very good agreement with those obtained from high-level ab initio calculations (CCSD(T)/cc-pVTZ). The geometric parameters in 8 and 9 are very similar; they also do not differ significantly from the all-carbon analogue, (Z)-hex-3-ene-1,5-diyne (7), the parent molecule for the Bergman cyclization. A small deviation from linearity about the alkyne and cyano linkages is observed for 7-9 and several related species where accurate equilibrium parameters are available. The data on 7-9 should be of interest to radioastronomy and may provide insights on the formation and interstellar chemistry of unsaturated species such as the cyanopolyynes.     

Path integral methods for rotating molecules in superfluids

We present a path integral Monte Carlo (PIMC) methodology for quantum simulation of molecular rotations in superfluid environments such as helium and para-hydrogen that combines the sampling of rotational degrees of freedom for a molecular impurity with multilevel Metropolis sampling of Bose permutation exchanges for the solvating species. We show how the present methodology can be applied to the evaluation of imaginary time rotational correlation functions of the molecular impurity, from which the effective rotational constants can be extracted. The combined rotation/permutation sampling approach allows for the first time explicit assessment of the effect of Bose permutations on molecular rotation dynamics, and the converse, i.e., the effect of molecular rotations on permutation exchanges and local superfluidity. We present detailed studies showing that the effect of Bose permutations in the solvating environment is more significant for the dynamics of heavy than light molecules in helium, and that Bose permutation exchanges are slightly enhanced locally by molecular rotation. Finally, the examples studied here reveal a size dependence of rotational excitations for molecules possessing a strongly anisotropic interaction with helium in 4HeN clusters between N approximately 20 and N approximately 10(3).     

The isotropic nuclear magnetic shielding constants of acetone in supercritical water: a sequential Monte Carlo/quantum mechanics study including solute polarization

The nuclear isotropic shielding constants sigma((17)O) and sigma((13)C) of the carbonyl bond of acetone in water at supercritical (P=340.2 atm and T=673 K) and normal water conditions have been studied theoretically using Monte Carlo simulation and quantum mechanics calculations based on the B3LYP6-311++G(2d,2p) method. Statistically uncorrelated configurations have been obtained from Monte Carlo simulations with unpolarized and in-solution polarized solute. The results show that solvent effects on the shielding constants have a significant contribution of the electrostatic interactions and that quantitative estimates for solvent shifts of shielding constants can be obtained modeling the water molecules by point charges (electrostatic embedding). In supercritical water, there is a decrease in the magnitude of sigma((13)C) but a sizable increase in the magnitude of sigma((17)O) when compared with the results obtained in normal water. It is found that the influence of the solute polarization is mild in the supercritical regime but it is particularly important for sigma((17)O) in normal water and its shielding effect reflects the increase in the average number of hydrogen bonds between acetone and water. Changing the solvent environment from normal to supercritical water condition, the B3LYP6-311++G(2d,2p) calculations on the statistically uncorrelated configurations sampled from the Monte Carlo simulation give a (13)C chemical shift of 11.7+/-0.6 ppm for polarized acetone in good agreement with the experimentally inferred result of 9-11 ppm.     

Quantum Monte Carlo study of the Ne atom and the Ne+ ion

We report all-electron and pseudopotential calculations of the ground-state energies of the neutral Ne atom and the Ne(+) ion using the variational and diffusion quantum Monte Carlo (DMC) methods. We investigate different levels of Slater-Jastrow trial wave function: (i) using Hartree-Fock orbitals, (ii) using orbitals optimized within a Monte Carlo procedure in the presence of a Jastrow factor, and (iii) including backflow correlations in the wave function. Small reductions in the total energy are obtained by optimizing the orbitals, while more significant reductions are obtained by incorporating backflow correlations. We study the finite-time-step and fixed-node biases in the DMC energy and show that there is a strong tendency for these errors to cancel when the first ionization potential (IP) is calculated. DMC gives highly accurate values for the IP of Ne at all the levels of trial wave function that we have considered.     

Rotational spectrum of cyanoacetylene solvated with helium atoms

The high resolution microwave spectra of He(N)-HCCCN clusters were studied in the size ranges of 1-18 and 25-31. In the absence of an accompanying infrared study, rotational excitation energies were computed by the reptation quantum Monte Carlo method and used to facilitate the search and assignment of R(0) transitions from N > 6, as well as R(1) transitions with N > 1. The assignments in the range of 25-31 are accurate to +/-2 cluster size units, with an essentially certain relative ordering. The rotational transition frequencies decrease with N = 1-6 and then show oscillatory behavior for larger cluster sizes, which is now recognized to be a manifestation of the onset and microscopic evolution of superfluidity. For cluster sizes beyond completion of the first solvation shell the rotational frequencies increase significantly above the large-droplet limit. This behavior, common to other linear molecules whose interaction with He features a strong nearly equatorial minimum, is analyzed using path integral Monte Carlo simulations. The He density in the incipient second solvation shell is shown to open a new channel for long permutation cycles, thus increasing the decoupling of the quantum solvent from the rotation of the dopant molecule.     

Quantum Monte Carlo for the x-ray absorption spectrum of pyrrole at the nitrogen K-edge

Fixed-node diffusion Monte Carlo (FNDMC) is used to simulate the x-ray absorption spectrum of a gas-phase pyrrole molecule at the nitrogen K-edge. Trial wave functions for core-excited states are constructed from ground-state Kohn-Sham determinants substituted with singly occupied natural orbitals from configuration interaction with single excitations calculations of the five lowest valence-excited triplet states. The FNDMC ionization potential (IP) is found to lie within 0.3 eV of the experimental value of 406.1 ± 0.1 eV. The transition energies to anti-bonding virtual orbitals match the experimental spectrum after alignment of IP values and agree with the existing assignments.     

Full optimization of Jastrow-Slater wave functions with application to the first-row atoms and homonuclear diatomic molecules

We pursue the development and application of the recently introduced linear optimization method for determining the optimal linear and nonlinear parameters of Jastrow-Slater wave functions in a variational Monte Carlo framework. In this approach, the optimal parameters are found iteratively by diagonalizing the Hamiltonian matrix in the space spanned by the wave function and its first-order derivatives, making use of a strong zero-variance principle. We extend the method to optimize the exponents of the basis functions, simultaneously with all the other parameters, namely, the Jastrow, configuration state function, and orbital parameters. We show that the linear optimization method can be thought of as a so-called augmented Hessian approach, which helps explain the robustness of the method and permits us to extend it to minimize a linear combination of the energy and the energy variance. We apply the linear optimization method to obtain the complete ground-state potential energy curve of the C(2) molecule up to the dissociation limit and discuss size consistency and broken spin-symmetry issues in quantum Monte Carlo calculations. We perform calculations for the first-row atoms and homonuclear diatomic molecules with fully optimized Jastrow-Slater wave functions, and we demonstrate that molecular well depths can be obtained with near chemical accuracy quite systematically at the diffusion Monte Carlo level for these systems.     

Rotational spectra of 1-chloro-2-fluoroethylene. II. Equilibrium structures of the cis and trans isomer

Equilibrium structures for the cis and trans isomer of 1-chloro-2-fluoroethylene are reported. The structures are obtained within a least-squares fit procedure using the available experimental ground-state rotational constants for various isotopic species of both forms. Vibrational effects were eliminated before the analysis using vibration-rotation interaction constants derived from computed quadratic and cubic force fields with the required quantum chemical calculations carried out using second-order Moller-Plesset perturbation as well as coupled-cluster (CC) theory. The semiexperimental or empirical equilibrium geometries obtained in this way agree well with the corresponding theoretical predictions obtained from CC calculations [at the CCSD(T) level] after extrapolation to the complete basis-set limit and inclusion of core-valence correlation corrections. The present results allow a detailed analysis of the geometrical differences between the two forms of 1-chloro-2-fluoroethylene. They are also compared to the structural data available for other halogenated ethylenes.