Electronic quantum Monte Carlo calculations of atomic forces, vibrations, and anharmonicities

Atomic forces are calculated for first-row monohydrides and carbon monoxide within electronic quantum Monte Carlo (QMC). Accurate and efficient forces are achieved by using an improved method for moving variational parameters in variational QMC. Newton's method with singular value decomposition (SVD) is combined with steepest-descent (SD) updates along directions rejected by the SVD, after initial SD steps. Dissociation energies in variational and diffusion QMC agree well with the experiment. The atomic forces agree quantitatively with potential-energy surfaces, demonstrating the accuracy of this force procedure. The harmonic vibrational frequencies and anharmonicity constants, derived from the QMC energies and atomic forces, also agree well with the experimental values.     

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.     

Toward the exact solution of the electronic Schrödinger equation for noncovalent molecular interactions: worldwide distributed quantum monte carlo calculations

Quantum Monte Carlo (QMC) calculations on the stacked (st) and Watson/Crick (wc) bound adenine/thymine (A/T) and cytosine/guanine (C/G) DNA base pair complexes were made possible with the first large scale distributed computing project in ab initio quantum chemistry, Quantum Monte Carlo at Home (QMC@HOME). The results for the interaction energies (wc-A/T = 15.7 kcal/mol, wc-C/G = 30.2 kcal/mol, st-A/T = 13.1 kcal/mol, st-C/G = 19.6 kcal/mol) are in very good agreement with the best known coupled-cluster based estimates. The accuracy of these values is further supported by calculations on the S22 benchmark set of noncovalently bound systems, for which we obtain a small mean absolute deviation of 0.68 kcal/mol. Our results support previous claims that the stacking energies are of comparable magnitude to the interactions of the commonly discussed hydrogen-bonded motif. Furthermore, we show that QMC can serve as an advantageous alternative to conventional wave function methods for large noncovalently bound systems. We also investigated in detail all technical parameters of the QMC simulations and recommend a careful optimization procedure of the Jastrow correlation factors in order to obtain numerically stable and reliable results.     

Computing the energy of a water molecule using multideterminants: a simple, efficient algorithm

Quantum Monte Carlo (QMC) methods such as variational Monte Carlo and fixed node diffusion Monte Carlo depend heavily on the quality of the trial wave function. Although Slater-Jastrow wave functions are the most commonly used variational ansatz in electronic structure, more sophisticated wave functions are critical to ascertaining new physics. One such wave function is the multi-Slater-Jastrow wave function which consists of a Jastrow function multiplied by the sum of Slater determinants. In this paper we describe a method for working with these wave functions in QMC codes that is easy to implement, efficient both in computational speed as well as memory, and easily parallelized. The computational cost scales quadratically with particle number making this scaling no worse than the single determinant case and linear with the total number of excitations. Additionally, we implement this method and use it to compute the ground state energy of a water molecule.     

Unusual adsorption site behavior in PCN-14 metal-organic framework predicted from Monte Carlo simulation

The adsorption equilibrium of methane in PCN-14 was simulated by the Monte Carlo technique in the grand canonical ensemble. A new force field was proposed for the methane/PCN-14 system, and the temperature dependence of the molecular siting was investigated. A detailed study of the statistics of the center of mass and potential energy showed a surprising site behavior with no energy barriers between weak and strong sites, allowing open metal sites to guide methane molecules to other neighboring sites. Moreover, this study showed that a model assuming weakly adsorbing open metal clusters in PCN-14, densely populated only at low temperatures (below 150 K), can explain published experimental data. These results also explain previously observed discrepancies between neutron diffraction experiments and Monte Carlo simulations.     

Water as a solute: competitive shell formation in (He,Ne) mixed microdroplets

Quantum Monte Carlo (QMC) stochastic calculations are carried out for a series of mixed rare gas clusters containing He and Ne which further include one H(2)O molecule as a single dopant. The ab initio potentials employed in the calculations, and the structural details provided by the QMC results, clearly reveal that the differences in the interaction forces which exist between the two solvent adatoms and the molecular solute are causing strongly competing environments that generate preferential shell structuring when surrounding the water molecule. The different behaviour of the two solvents, and the energetics of mixing, are analyzed in detail for small aggregates and for larger mixtures, revealing structural effects which originate from the different networking between solvent adatoms.     

Energy-consistent pseudopotentials for quantum Monte Carlo calculations

The authors present scalar-relativistic energy-consistent Hartree-Fock pseudopotentials for the main-group elements. The pseudopotentials do not exhibit a singularity at the nucleus and are therefore suitable for quantum Monte Carlo (QMC) calculations. They demonstrate their transferability through extensive benchmark calculations of atomic excitation spectra as well as molecular properties. In particular, they compute the vibrational frequencies and binding energies of 26 first- and second-row diatomic molecules using post-Hartree-Fock methods, finding excellent agreement with the corresponding all-electron values. They also show their pseudopotentials give superior accuracy than other existing pseudopotentials constructed specifically for QMC. Finally, valence basis sets of different sizes (VnZ with n=D,T,Q,5 for first and second rows, and n=D,T for third to fifth rows) optimized for our pseudopotentials are also presented.     

Theoretical modeling of ionization energies of argon clusters: nuclear delocalization effects

Temperature dependence of vertical ionization energies is modeled for small argon clusters (N ≤ 13) using classical parallel-tempering Monte Carlo methods and extended interaction models based on the diatomics-in-molecules approach. Quantum effects at the zero temperature are also discussed in terms of zero-point nuclear vibrations, either at the harmonic approximation level or at the fully anharmonic level using the diffusion Monte Carlo calculations. Both approaches lead to a considerable improvement of the theoretical predictions of argon clusters ionization energies and represent a realistic way of modeling of ionization energies for weakly bound and floppy complexes in general. A thorough comparison with a recent electron-impact experiment [O. Echt et al., J. Chem. Phys. 123, 084313 (2005)] is presented and a novel interpretation of the experimental data is proposed.     

Identification of two distinct electron binding motifs in the anionic water clusters: a vibrational spectroscopic study of the (H2O)6- isomers

Photoelectron spectroscopy of the water cluster anions, (H2O)n-, has revealed that several isomeric forms are present for most sizes, and here, we use vibrational spectroscopy to address the structure of the (H2O)6- isomer that more weakly binds the extra electron. To overcome the severe line broadening that occurs in the OH stretching region of this isomer caused by fast electron autodetachment, we concentrate on the low-energy bending modes of the perdeutero isotopomer. Sharp spectroscopic signatures are recovered for two isomers using argon predissociation spectroscopy, and the resulting bands are heavily overlapped. To extract their independent contributions to the observed spectra, we exploit the substantial dependence of their relative populations on the number of attached argon atoms in the (D2O)6-.Ar(m) clusters, determined by photoelectron spectroscopy. The vibrational spectra of each isomer can then be isolated by spectral subtraction, which is implemented with a covariance mapping approach. The resulting band patterns establish that the more weakly binding isomer does not display the characteristic electron-binding motif common to the more strongly bound isomer class. Whereas the strongly binding isomer features a single water molecule pointing toward the excess electron cloud with both of its hydrogen atoms, the spectrum of the more weakly binding isomer suggests a structure where the electron is bound by a number of dangling OH groups corresponding to water molecules in acceptor-donor binding sites.     

精确固定节面量子Monte Carlo差值法

提出了精确固定节面量子Monte Carlo差值法, 这个新算法能够在精确固定节面量子Monte Carlo方法的基础上直接计算两个体系之间的能量差, 且使计算结果的统计误差达到10-5 hartree 数量级, 获得电子相关能90%以上. 我们把这个新算法应用于分子势能面的研究中, 使用一个“刚性移动”模型, 利用Jacobi变换使分子两个几何构型的能量计算具有很好的正相关性, 因而能得到准确的能量差值, 由此就可以得到精确的分子势能面.     

Pair potential of liquid metallic Be from electron theory compared and contrasted with recent ab initio work on the free-space beryllium dimer

Two decades ago, Perrot and March [F. Perrot and N.H. March, Phys. Rev. A. 41, 4521 (1990)] used electron theory to derive an oscillatory pair potential between the beryllium nuclei in liquid metal beryllium. They predict a first minimum at 2.1?Å, followed by a larger repulsive hump at 2.8?Å. Here, we compare and contrast this result for liquid beryllium with the recent ab initio work by Koput and the present quantum Monte Carlo (QMC) calculation on the beryllium dimer in free space. Koput situates the minimum in the potential curve for the free-space dimer at 2.4?Å and it is quite similar in depth to that for liquid metallic beryllium. Our QMC curve is similar, with the minimum at 2.33?Å. They are tabulated in this letter.     

Quantum Monte Carlo for large chemical systems: Implementing efficient strategies for petascale platforms and beyond

Various strategies to implement efficiently quantum Monte Carlo (QMC) simulations for large chemical systems are presented. These include: (i) the introduction of an efficient algorithm to calculate the computationally expensive Slater matrices. This novel scheme is based on the use of the highly localized character of atomic Gaussian basis functions (not the molecular orbitals as usually done), (ii) the possibility of keeping the memory footprint minimal, (iii) the important enhancement of single‐core performance when efficient optimization tools are used, and (iv) the definition of a universal, dynamic, fault‐tolerant, and load‐balanced framework adapted to all kinds of computational platforms (massively parallel machines, clusters, or distributed grids). These strategies have been implemented in the QMC=Chem code developed at Toulouse and illustrated with numerical applications on small peptides of increasing sizes (158, 434, 1056, and 1731 electrons). Using 10–80 k computing cores of the Curie machine (GENCI‐TGCC‐CEA, France), QMC=Chem has been shown to be capable of running at the petascale level, thus demonstrating that for this machine a large part of the peak performance can be achieved. Implementation of large‐scale QMC simulations for future exascale platforms with a comparable level of efficiency is expected to be feasible. © 2013 Wiley Periodicals, Inc.     

A path-integral Langevin equation treatment of low-temperature doped helium clusters

We present an implementation of path integral molecular dynamics for sampling low temperature properties of doped helium clusters using Langevin dynamics. The robustness of the path integral Langevin equation and white-noise Langevin equation [M. Ceriotti, M. Parrinello, T. E. Markland, and D. E. Manolopoulos, J. Chem. Phys. 133, 124104 (2010)] sampling methods are considered for those weakly bound systems with comparison to path integral Monte Carlo (PIMC) in terms of efficiency and accuracy. Using these techniques, convergence studies are performed to confirm the systematic error reduction introduced by increasing the number of discretization steps of the path integral. We comment on the structural and energetic evolution of He(N)-CO(2) clusters from N = 1 to 20. To quantify the importance of both rotations and exchange in our simulations, we present a chemical potential and calculated band origin shifts as a function of cluster size utilizing PIMC sampling that includes these effects. This work also serves to showcase the implementation of path integral simulation techniques within the molecular modelling toolkit [K. Hinsen, J. Comp. Chem. 21, 79 (2000)], an open-source molecular simulation package.     

Photodissociation spectroscopy of Zn+(H2O) and Zn+(D2O)

We report on a study of the photodissociation spectroscopy of weakly bound Zn+(H2O) and Zn+(D2O) complexes. The work is supported by ab initio electronic structure calculations of the ground and low-lying excited energy surfaces. We assign two molecular absorption bands in the near UV correlating to Zn+ (4s-4p)-based transitions, and identify vibrational progressions associated with both intermolecular and intramolecular vibrational modes of the cluster. Partially resolved rotational structure is consistent with a C(2V) equilibrium complex geometry. Experimental spectroscopic constants are in very good agreement with ab initio theoretical predictions. Results are compared with previous work on main group and transition metal ion-H2O clusters.     

A sparse algorithm for the evaluation of the local energy in quantum Monte Carlo

A new algorithm is presented for the sparse representation and evaluation of Slater determinants in the quantum Monte Carlo (QMC) method. The approach, combined with the use of localized orbitals in a Slater-type orbital basis set, significantly extends the size molecule that can be treated with the QMC method. Application of the algorithm to systems containing up to 390 electrons confirms that the cost of evaluating the Slater determinant scales linearly with system size.     

Isomerization dynamics and thermodynamics of ionic argon clusters

The dynamics and thermodynamics of small Ar(n) (+) clusters, n=3, 6, and 9, are investigated using molecular dynamics (MD) and exchange Monte Carlo (MC) simulations. A diatomic-in-molecule Hamiltonian provides an accurate model for the electronic ground state potential energy surface. The microcanonical caloric curves calculated from MD and MC methods are shown to agree with each other, provided that the rigorous conservation of angular momentum is accounted for in the phase space density of the MC simulations. The previously proposed projective partition of the kinetic energy is used to assist MD simulations in interpreting the cluster dynamics in terms of inertial, internal, and external modes. The thermal behavior is correlated with the nature of the charged core in the cluster by computing a dedicated charge localization order parameter. We also perform systematic quenches to establish a connection with the various isomers. We find that the Ar(3) (+) cluster is very stable in its linear ground state geometry up to about 300 K, and then isomerizes to a T-shaped isomer in which a quasineutral atom lies around a charged dimer. In Ar(6) (+) and Ar(9) (+), the covalent trimer core is solvated by neutral atoms, and the weakly bound solvent shell melts at much lower energies, occasionally leading to a tetramer or pentamer core with weakly charged extremities. At high energies the core itself becomes metastable and the cluster transforms into Ar(2) (+) solvated by a fluid of neutral argon atoms.     

Manager-worker-based model for the parallelization of quantum Monte Carlo on heterogeneous and homogeneous networks

A manager-worker-based parallelization algorithm for Quantum Monte Carlo (QMC-MW) is presented and compared with the pure iterative parallelization algorithm, which is in common use. The new manager-worker algorithm performs automatic load balancing, allowing it to perform near the theoretical maximal speed even on heterogeneous parallel computers. Furthermore, the new algorithm performs as well as the pure iterative algorithm on homogeneous parallel computers. When combined with the dynamic distributable decorrelation algorithm (DDDA) [Feldmann et al., J Comput Chem 28, 2309 (2007)], the new manager-worker algorithm allows QMC calculations to be terminated at a prespecified level of convergence rather than upon a prespecified number of steps (the common practice). This allows a guaranteed level of precision at the least cost. Additionally, we show (by both analytic derivation and experimental verification) that standard QMC implementations are not "perfectly parallel" as is often claimed.     

Electronically excited rubidium atom in helium clusters and films. II. Second excited state and absorption spectrum

Following our work on the study of helium droplets and film doped with one electronically excited rubidium atom Rb(?) ((2)P) [M. Leino, A. Viel, and R. E. Zillich, J. Chem. Phys. 129, 184308 (2008)], we focus in this paper on the second excited state. We present theoretical studies of such droplets and films using quantum Monte Carlo approaches. Diffusion and path integral Monte Carlo algorithms combined with a diatomics-in-molecule scheme to model the nonpair additive potential energy surface are used to investigate the energetics and the structure of Rb(?)He(n) clusters. Helium films as a model for the limit of large clusters are also considered. As in our work on the first electronic excited state, our present calculations find stable Rb(?)He(n) clusters. The structures obtained are however different with a He-Rb(?)-He exciplex core to which more helium atoms are weakly attached, preferentially on one end of the core exciplex. The electronic absorption spectrum is also presented for increasing cluster sizes as well as for the film.     

Ground state of small mixed helium and spin-polarized tritium clusters: a quantum Monte Carlo study

We report results for the ground-state energy and structural properties of small (4)He-T↓ clusters consisting of up to four T↓ and eight (4)He atoms. These results have been obtained using very well-known (4)He-(4)He and T↓- T↓ interaction potentials and several models for the (4)He- T↓ interatomic potential. All the calculations have been performed with variational and diffusion Monte Carlo methods. It takes at least three atoms to form a mixed bound state. In particular, for small clusters the binding energies are significantly affected by the precise form of the (4)He- T↓ interatomic potential but the stability limits remain unchanged. The only exception is the (4)He(2)T↓ trimer whose stability in the case of the weakest (4)He- T↓ interaction potential is uncertain while it seems stable for other potentials. The mixed trimer (4)He(T↓)(2), a candidate for the Borromean state, is not bound. All other studied clusters are stable. Some of the weakest bound clusters can be classified as quantum halo as a consequence of having high probability of being in a classically forbidden region.