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.     

A study of H+H2 and several H-bonded molecules by phaseless auxiliary-field quantum Monte Carlo with plane wave and Gaussian basis sets

The authors present phaseless auxiliary-field (AF) quantum Monte Carlo (QMC) calculations of the ground states of some hydrogen-bonded systems. These systems were selected to test and benchmark different aspects of the new phaseless AF QMC method. They include the transition state of H+H(2) near the equilibrium geometry and in the van der Walls limit, as well as the H(2)O, OH, and H(2)O(2) molecules. Most of these systems present significant challenges for traditional independent-particle electronic structure approaches, and many also have exact results available. The phaseless AF QMC method is used either with a plane wave basis with pseudopotentials or with all-electron Gaussian basis sets. For some systems, calculations are done with both to compare and characterize the performance of AF QMC under different basis sets and different Hubbard-Stratonovich decompositions. Excellent results are obtained using as input single Slater determinant wave functions taken from independent-particle calculations. Comparisons of the Gaussian based AF QMC results with exact full configuration interaction show that the errors from controlling the phase problem with the phaseless approximation are small. At the large basis-size limit, the AF QMC results using both types of basis sets are in good agreement with each other and with experimental values.     

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.     

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.     

Bond breaking with auxiliary-field quantum Monte Carlo

Bond stretching mimics different levels of electron correlation and provides a challenging test bed for approximate many-body computational methods. Using the recently developed phaseless auxiliary-field quantum Monte Carlo (AF QMC) method, we examine bond stretching in the well-studied molecules BH and N(2) and in the H(50) chain. To control the sign/phase problem, the phaseless AF QMC method constrains the paths in the auxiliary-field path integrals with an approximate phase condition that depends on a trial wave function. With single Slater determinants from unrestricted Hartree-Fock as trial wave function, the phaseless AF QMC method generally gives better overall accuracy and a more uniform behavior than the coupled cluster CCSD(T) method in mapping the potential-energy curve. In both BH and N(2), we also study the use of multiple-determinant trial wave functions from multiconfiguration self-consistent-field calculations. The increase in computational cost versus the gain in statistical and systematic accuracy are examined. With such trial wave functions, excellent results are obtained across the entire region between equilibrium and the dissociation limit.     

Auxiliary-field quantum Monte Carlo study of first- and second-row post-d elements

A series of calculations for the first- and second-row post-d elements (Ga-Br and In-I) are presented using the phaseless auxiliary-field quantum Monte Carlo (AF QMC) method. This method is formulated in a Hilbert space defined by any chosen one-particle basis and maps the many-body problem into a linear combination of independent-particle solutions with external auxiliary fields. The phase/sign problem is handled approximately by the phaseless formalism using a trial wave function, which in our calculations was chosen to be the Hartree-Fock solution. We used the consistent correlated basis sets of Peterson et al. [J. Chem. Phys. 119, 11099 (2003); 119, 11113 (2003)], which employ a small-core relativistic pseudopotential. The AF QMC results are compared with experiment and with those from density functional (generalized gradient approximation and B3LYP) and CCSD(T) calculations. The AF QMC total energies agree with CCSD(T) to within a few millihartrees across the systems and over several basis sets. The calculated atomic electron affinities, ionization energies, and spectroscopic properties of dimers are, at large basis sets, in excellent agreement with experiment.     

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 ground state with a fourth-order propagator: application to condensed helium

Ground state properties of condensed helium are calculated using the path integral ground state (PIGS) method. A fourth-order approximation is used as short (imaginary) time propagator. We compare our results with those obtained with other quantum Monte Carlo (QMC) techniques and different propagators. For this particular application, we find that the fourth-order propagator performs comparably to the pair product approximation, and is far superior to the primitive approximation. Results obtained for the equation of state of condensed helium show that PIGS compares favorably to other QMC methods traditionally utilized for this type of calculation.     

A density functional and quantum Monte Carlo study of glutamic acid in vacuo and in a dielectric continuum medium

We present density functional theory (DFT) and quantum Monte Carlo (QMC) calculations of the glutamic acid and glutamate ion in vacuo and in various dielectric continuum media within the polarizable continuum model (PCM). In DFT, we employ the integral equation formalism variant of PCM while, in QMC, we use a PCM scheme we have developed to include both surface and volume polarization. We investigate the gas-phase protonation thermochemistry of the glutamic acid using a large set of structural conformations, and find that QMC is in excellent agreement with the best available theoretical and experimental results. For the solvated glutamic acid and glutamate ion, we perform DFT calculations for dielectric constants, ε, between 4 and 78. We find that the glutamate ion in the zwitterionic form is more stable than the non-zwitterionic form over the whole range of dielectric constants, while the glutamic acid is more stable in its non-zwitterionic form at ε = 4. The dielectric constant at which the two glutamic acid species have the same energy depends on the cavity size and lies between 5 and 12.5. We validate these results with QMC for the two limiting values of the dielectric constant, and find qualitative agreement with DFT even though the solvent polarization is less pronounced at the QMC level.     

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.     

Excitation energies of retinal chromophores: critical role of the structural model

We employ a variety of highly-correlated approaches including quantum Monte Carlo (QMC) and the n-electron valence state perturbation theory (NEVPT2) to compute the vertical excitation energies of retinal protonated Schiff base (RPSB) models in the gas phase. We find that the NEVPT2 excitation energies are in good agreement with the QMC values and confirm our previous findings that the complete-active-space perturbation (CASPT2) approach yields accurate excitations for RPSB models only when the more recent zero-order IPEA Hamiltonian is employed. The excitations computed with the original zero-order formulation of CASPT2 are instead systematically red-shifted by more than 0.3 eV. We then focus on the full 11-cis retinal chromophore and show that the M06-2X and MP2 approaches provide reliable ground-state equilibrium structures for this system while the complete-active-space self-consistent field (CASSCF) geometry is characterized by significantly higher ground-state energies at the NEVPT2 and CASPT2 level. Our calibration of the structural model together with the general agreement of all highly-correlated excited-state methods allows us to reliably assign a value of about 2.3 eV to the vertical excitation of 11-cis RPSB in the gas-phase.     

Disentanglement of triplet and singlet states of azobenzene: direct EELS detection and QMC modeling

Singlet and triplet excited states of trans-azobenzene have been measured in the gas phase by electron energy loss spectroscopy (EELS). In order to interpret the strongly overlapping singlet and triplet bands in the spectra a set of large-scale correlated quantum Monte-Carlo (QMC) simulations was performed. The EELS/QMC combination of methods yields an excellent agreement between theory and experiment and for the two low-lying excited singlet and two low-lying triplet states permitted their unambiguous assignment. In addition, EELS revealed two overlapping electronic states in the band commonly assigned as S(2), the lower one with a pronounced vibrational structure, the upper one structureless. Finally, the agreement between theory and experiment was shown to further increase by taking computationally into account the finite temperature effects.     

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.     

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.     

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.     

新型香豆素硼氟荧光染料的合成及其光学性能

以邻氨基苯甲酸甲酯和4-二乙胺基水杨醛为原料,合成了一个新的香豆素喹啉衍生物3-{2-［8-(1H-苯并咪唑-2-基)喹啉-2-基］乙烯基}-7-二乙胺基香豆素(QMC),再与BF₃·Et₂O配位合成了硼氟配合物(BQMC),其结构经¹H NMR和MS(ESI)表征。并对BQMC的光学性能进行了研究。结果表明：BQMC的最大吸收波长在二氧六环中为490 nm,在DMSO中为532 nm; BQMC的最大发射波长在正己烷中为618 nm,在DMSO中为679 nm,与配体QMC相比,最大吸收波长红移了近50 nm,最大发射波长红移了近100 nm, BQMC的Stokes位移值从115 nm增至183 nm。在固态下,BQMC在750~825 nm之间有较宽的荧光发射峰,具有较强荧光。     

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.     

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.