Jastrow correlated and quantum Monte Carlo calculations for the low-lying states of the carbon atom

Different computational methods are employed to calculate excitation energies of the carbon atom. Explicitly correlated wave functions have been obtained in a Variational Monte Carlo calculation. Fixed node Diffusion Monte Carlo calculations for the lowest energy excited states of a given symmetry are reported. A systematic and quantitative analysis of the performance of the different schemes in the calculation of the excitation energy of up to 27 excited states of the carbon atom is carried out. The quality of the different methods have been studied in terms of the deviation with respect to the experimental excitation energies. A good agreement with the experimental values has been reached.     

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.     

Auxiliary-field quantum Monte Carlo calculations of molecular systems with a Gaussian basis

We extend the recently introduced phaseless auxiliary-field quantum Monte Carlo (QMC) approach to any single-particle basis and apply it to molecular systems with Gaussian basis sets. QMC methods in general scale favorably with the system size as a low power. A QMC approach with auxiliary fields, in principle, allows an exact solution of the Schrodinger equation in the chosen basis. However, the well-known sign/phase problem causes the statistical noise to increase exponentially. The phaseless method controls this problem by constraining the paths in the auxiliary-field path integrals with an approximate phase condition that depends on a trial wave function. In the present calculations, the trial wave function is a single Slater determinant from a Hartree-Fock calculation. The calculated all-electron total energies show typical systematic errors of no more than a few millihartrees compared to exact results. At equilibrium geometries in the molecules we studied, this accuracy is roughly comparable to that of coupled cluster with single and double excitations and with noniterative triples [CCSD(T)]. For stretched bonds in H(2)O, our method exhibits a better overall accuracy and a more uniform behavior than CCSD(T).     

Relativistic all-electron configuration interaction calculations on the gold atom

We present the results of relativistic and non-relativistic self-consistent field and configuration interaction calculations for the gold atom, using the spin-free no-pair Hamiltonian in a basis set expansion. A new basis set for the gold atom is discussed and its results in relativistic and non-relativistic self-consistent field calculations are compared to those of numerical Dirac-Hartree-Focic and Hartree-Fock calculations, respectively. Excitation energies, electron affinities and ionization potentials were calculated using a multi-reference configuration interaction technique and are in reasonable agreement with experiment in the relativistic case.     

Dissociation energy of the water dimer from quantum Monte Carlo calculations

We report a study of the electronic dissociation energy of the water dimer using quantum Monte Carlo techniques. We have performed variational quantum Monte Carlo and diffusion quantum Monte Carlo (DMC) calculations of the electronic ground state of the water monomer and dimer using all-electron and pseudopotential approaches. We have used Slater-Jastrow trial wave functions with B3LYP type single-particle orbitals, into which we have incorporated backflow correlations. When backflow correlations are introduced, the total energy of the water monomer decreases by about 4-5 mhartree, yielding a DMC energy of -76.428 30(5) hartree, which is only 10 mhartree above the experimental value. In our pseudopotential DMC calculations, we have compared the total energies of the water monomer and dimer obtained using the locality approximation with those from the variational scheme recently proposed by Casula [Phys. Rev. B 74, 161102(R) (2006)]. The time step errors in the Casula scheme are larger, and the extrapolation of the energy to zero time step always lies above the result obtained with the locality approximation. However, the errors cancel when energy differences are taken, yielding electronic dissociation energies within error bars of each other. The dissociation energies obtained in our various all-electron and pseudopotential calculations range between 5.03(7) and 5.47(9) kcalmol and are in good agreement with experiment. Our calculations give monomer dipole moments which range between 1.897(2) and 1.909(4) D and dimer dipole moments which range between 2.628(6) and 2.672(5) D.     

Spectroscopic data for the LiH molecule from pseudopotential quantum Monte Carlo calculations

Quantum Monte Carlo and quantum chemistry techniques are used to investigate pseudopotential models of the lithium hydride (LiH) molecule. Interatomic potentials are calculated and tested by comparing with the experimental spectroscopic constants and well depth. Two recently developed pseudopotentials are tested, and the effects of introducing a Li core polarization potential are investigated. The calculations are sufficiently accurate to isolate the errors from the pseudopotentials and core polarization potential. Core-valence correlation and core relaxation are found to be important in determining the interatomic potential.     

Monte Carlo calculations of hole size distributions: Simulation of positron annihilation spectroscopy

Consequences are explored of a hole size distribution in an amorphous polymer for the ortho-positronium (o-Ps) lifetime (τ₃) and intensity (I₃), determined by positron annihilation lifetime spectroscopy. The disordered lattice model, with a vacancy fraction h as a central quantity, is used to represent the equation-of-state behavior of the polymer. By means of Monte Carlo simulations, we obtain the cluster size distribution as a function of h and hence temperature. The predicted average cluster size and the cluster concentration are compared to τ₃ and I₃ data, respectively, for bisphenol-a polycarbonate. Furthermore, the influence of an o-Ps lifetime distribution on the experimental mean τ₃ is investigated. By mimicking the computational methods used in experimental analysis, agreement between experiment and theory in respect to τ₃ and to I₃ in the melt ensues. In the glass, however, the experimental I₃ becomes increasingly smaller with decreasing temperature than is computed. These deviations may result from a distortion of the equilibrium free volume. © 1992 John Wiley & Sons, Inc.     

Excited electronic state calculations by the transcorrelated variational Monte Carlo method: application to a helium atom

We have implemented the excited electronic state calculations for a helium atom by the transcorrelated variational Monte Carlo (TC-VMC) method. In this method, Jastrow-Slater-type wave function is efficiently optimized not only for the Jastrow factor but also for the Slater determinant. Since the formalism for the TC-VMC method is based on the variance minimization, excited states as well as the ground state calculations are feasible. It is found that both the first and the second excitation energies given by TC-VMC are much closer to the experimental data than those given by the variational Monte Carlo method with using the Hartree-Fock orbitals. The successful results in the TC-VMC method are considered to be due to the nodal optimization of the wave functions.     

An optimized initialization algorithm to ensure accuracy in quantum Monte Carlo calculations

Quantum Monte Carlo (QMC) calculations require the generation of random electronic configurations with respect to a desired probability density, usually the square of the magnitude of the wavefunction. In most cases, the Metropolis algorithm is used to generate a sequence of configurations in a Markov chain. This method has an inherent equilibration phase, during which the configurations are not representative of the desired density and must be discarded. If statistics are gathered before the walkers have equilibrated, contamination by nonequilibrated configurations can greatly reduce the accuracy of the results. Because separate Markov chains must be equilibrated for the walkers on each processor, the use of a long equilibration phase has a profoundly detrimental effect on the efficiency of large parallel calculations. The stratified atomic walker initialization (STRAW) shortens the equilibration phase of QMC calculations by generating statistically independent electronic configurations in regions of high probability density. This ensures the accuracy of calculations by avoiding contamination by nonequilibrated configurations. Shortening the length of the equilibration phase also results in significant improvements in the efficiency of parallel calculations, which reduces the total computational run time. For example, using STRAW rather than a standard initialization method in 512 processor calculations reduces the amount of time needed to calculate the energy expectation value of a trial function for a molecule of the energetic material RDX to within 0.01 au by 33%.     

Efficient protocol for quantum Monte Carlo calculations of hydrogen abstraction barriers: Application to methanol

Accurate calculation of hydrogen abstraction reaction barriers is a challenging problem, often requiring high level quantum chemistry methods that scale poorly with system size. Quantum Monte Carlo (QMC) methods provide an alternative approach that exhibit much better scaling, but these methods are still computationally expensive. We describe approaches that can significantly reduce the cost of QMC calculations of barrier heights, using the hydrogen abstraction of methanol by a hydrogen atom as an illustrative example. By analysing the combined influence of trial wavefunctions and pseudopotential quadrature settings on the barrier heights, variance, and time‐step errors, we devise a simple protocol that minimizes the cost of the QMC calculations while retaining accuracy comparable to large‐basis coupled cluster theory. We demonstrate that this protocol is transferable to other hydrogen abstraction reactions.     

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.     

Binding of hydrogen on benzene, coronene, and graphene from quantum Monte Carlo calculations

Quantum Monte Carlo calculations with the diffusion Monte Carlo (DMC) method have been used to compute the binding energy curves of hydrogen on benzene, coronene, and graphene. The DMC results on benzene agree with both M?ller-Plessett second order perturbation theory (MP2) and coupled cluster with singles, doubles, and perturbative triples [CCSD(T)] calculations, giving an adsorption energy of ～25 meV. For coronene, DMC agrees well with MP2, giving an adsorption energy of ～40 meV. For physisorbed hydrogen on graphene, DMC predicts a very small adsorption energy of only 5 ± 5 meV. Density functional theory (DFT) calculations with various exchange-correlation functionals, including van der Waals corrected functionals, predict a wide range of binding energies on all three systems. The present DMC results are a step toward filling the gap in accurate benchmark data on weakly bound systems. These results can help us to understand the performance of current DFT based methods, and may aid in the development of improved approaches.     

Time-dependent quantum Monte Carlo and the stochastic quantization

We examine the relation between the recently proposed time-dependent quantum Monte Carlo (TDQMC) method and the principles of stochastic quantization. In both TDQMC and stochastic quantization, particle motion obeys stochastic guidance equations to preserve quantum equilibrium. In this way the probability density of the Monte Carlo particles corresponds to the modulus square of the many-body wave function at all times. However, in TDQMC, the motion of particles and guide waves occurs in physical space unlike in stochastic quantization where it occurs in configuration space. Hence, the practical calculation of time evolution of many-body fully correlated quantum systems becomes feasible within the TDQMC methodology. We illustrate the TDQMC technique by calculating the symmetric and antisymmetric ground state of a model one-dimensional helium atom, and the time evolution of the dipole moment when the atom is irradiated by a strong ultrashort laser pulse.     

Quantum Monte Carlo calculations of the dimerization energy of borane

Accurate thermodynamic data are required to improve the performance of chemical hydrides that are potential hydrogen storage materials. Boron compounds are among the most interesting candidates. However, different experimental measurements of the borane dimerization energy resulted in a rather wide range (-34.3 to -39.1) ± 2 kcal/mol. Diffusion Monte Carlo (DMC) simulations usually recover more than 95% of the correlation energy, so energy differences rely less on error cancellation than other methods. DMC energies of BH(3), B(2)H(6), BH(3)CO, CO, and BH(2)(+) allowed us to predict the borane dimerization energy, both via the direct process and indirect processes such as the dissociation of BH(3)CO. Our D(e) = -43.12(8) kcal/mol, corrected for the zero point energy evaluated by considering the anharmonic contributions, results in a borane dimerization energy of -36.59(8) kcal/mol. The process via the dissociation of BH(3)CO gives -34.5(2) kcal/mol. Overall, our values suggest a slightly less D(e) than the most recent W4 estimate D(e) = -44.47 kcal/mol [A. Karton and J. M. L. Martin, J. Phys. Chem. A 111, 5936 (2007)]. Our results show that reliable thermochemical data for boranes can be predicted by fixed node (FN)-DMC calculations.     

Reagents for electrophilic amination: a quantum Monte Carlo study

Electrophilic amination is an appealing synthetic strategy to construct carbon-nitrogen bonds. The authors explore the use of the quantum Monte Carlo method and a proposed variant of the electron pair localization function--the electron pair localization function density--as a measure of the nucleophilicity of nitrogen lone pairs as a possible screening procedure for electrophilic reagents.     

Equilibrium states of self-assembly systems: Monte Carlo simulations

We investigated the equilibrium states of the self-assembly of amphiphilic molecules in water. The amphiphiles are represented by chains of the type H1T4, where H is the hydrophilic part of the molecule and T is its hydrophobic portion formed by four monomers. We have performed Monte Carlo simulations on a two-dimensional lattice, in which each water molecule occupies a single site, and the amphiphiles occupy five sites of the lattice. We have determined the aggregate distribution curves for the system at low concentration and fixed temperature. We have shown that the criterion to determine the equilibrium states of the system, based on the stabilization of energy curves as a function of the simulation time, is not reliable. The best way to ensure that the equilibrium state was reached was to follow the route to equilibrium of all aggregate sizes of the system.     

Energies of the first row atoms from quantum Monte Carlo

All-electron variational and diffusion quantum Monte Carlo calculations of the ground state energies of the first row atoms (from Li to Ne) are reported. The authors use trial wave functions of four types: single-determinant Slater-Jastrow wave functions, multideterminant Slater-Jastrow wave functions, single-determinant Slater-Jastrow wave functions with backflow transformations, and multideterminant Slater-Jastrow wave functions with backflow transformations. At the diffusion quantum Monte Carlo level and using their multideterminant Slater-Jastrow wave functions with backflow transformations, they recover 99% or more of the correlation energies for Li, Be, B, C, N, and Ne, 97% for O, and 98% for F.     

Monte Carlo calculations of the mean squared force in molecular liquids

The mean squared intermolecular force (F²₁) on a molecule in a diatomic liquid has been evaluated by a Monte Carlo calculation at reduced density p^* = 0.8 and reduced temperature 7^* = 0.72. The isotropic intermolecular potential is of Lennard-Jones form; anisotropic multipolar and overlap potentials of various strengths are used. For the largest strengths studied, the anisotropic contribution to (F²₁) is about 50–60% of the isotropic one.