A diffusion quantum Monte Carlo study on the lowest singlet and triplet electronic states of BN molecule

Ab initio calculation of both the lowest singlet and triplet electronic states of BN has been performed by the fixed-node Ornstein-Uhlenbeck diffusion quantum Monte Carlo method with the floating spherical Gaussian orbitals and spherical Gaussian geminals. The Monte Carlo calculation gives equilibrium bond lengths and equilibrium harmonic frequencies of 1.3317(7) A and 1529(7) cm(-1), respectively, for the lowest triplet state and 1.2751(7) A and 1709(8) cm(-1), respectively, for the lowest singlet state. Also, the Monte Carlo calculation reports an energy separation of 178(83) cm(-1) between the two electronic states and recommends the ground state is the lowest triplet state.     

Probing the spin multiplicity of gas-phase polycyclic aromatic hydrocarbons through their infrared emission spectrum: A theoretical study

The anharmonic infrared emission spectrum following an optical excitation has been calculated for a variety of polycyclic aromatic hydrocarbon molecules in their ground singlet electronic state or in their triplet state. The computational protocol relies on second-order perturbation theory and involves a quartic vibrational Hamiltonian, the vibrational quantum numbers being sampled according to a Monte Carlo procedure. In the case of neutral naphthalene, the IR spectrum obtained in the (ground) singlet state differs significantly from the spectrum in the triplet state, especially for out-of-plane CH bending modes. Although not as prominent, spectral differences in larger molecules are still observable.     

Importance sampling for quantum Monte Carlo in manifolds: addressing the time scale problem in simulations of molecular aggregates

Several importance sampling strategies are developed and tested for stereographic projection diffusion Monte Carlo in manifolds. We test a family of one parameter trial wavefunctions for variational Monte Carlo in stereographically projected manifolds which can be used to produce importance sampling. We use the double well potential in one dimensional Euclidean space to study systematically sampling issues for diffusion Monte Carlo. We find that diffusion Monte Carlo with importance sampling in manifolds is orders of magnitude more efficient compared to unguided diffusion Monte Carlo. Additionally, diffusion Monte Carlo with importance sampling in manifolds can overcome problems with nonconfining potentials and can suppress quasiergodicity effectively. We obtain the ground state energy and the wavefunction for the Stokmayer trimer.     

Path integral ground state study of finite-size systems: application to small (parahydrogen)N (N=2-20) clusters

We use the path integral ground state method to study the energetic and structural properties of small para-H2 clusters of sizes ranging from 2 to 20 molecules. A fourth order formula is used to approximate the short imaginary-time propagator and two interaction potentials are considered. Our results are compared to those of exact basis set calculations and other quantum Monte Carlo methods when available. We find that for all cluster sizes considered, our results show a lower ground state energy than literature values obtained by diffusion Monte Carlo and variational Monte Carlo. For the dimer and trimer, ground state energies are in good agreement with exact results obtained using the discrete variable representation. Structural properties are found to be insensitive to the choice of interaction potential. We explore the use of Pekeris coordinates to analyze the importance of linear arrangement in trimers and for trimers within clusters of larger size.     

Quantum Monte Carlo simulations of selected ammonia clusters (n = 2-5): isotope effects on the ground state of typical hydrogen bonded systems

Variational Monte Carlo, diffusion Monte Carlo, and stereographic projection path integral simulations are performed on eight selected species from the (NH(3))(n), (ND(3))(n), (NH(2)D)(n), and (NH(3))(n-1)(ND(3)) clusters. Each monomer is treated as a rigid body with the rotation spaces mapped by the stereographic projection coordinates. We compare the energy obtained from path integral simulations at several low temperatures with those obtained by diffusion Monte Carlo, for two dimers, and we find that at 4 K, the fully deuterated dimer energy is in excellent agreement with the ground state energy of the same. The ground state wavefunction for the (NH(3))(2-5) clusters is predominantly localized in the global minimum of the potential energy. In all simulations of mixed isotopic substitutions, we find that the heavier isotope is almost exclusively the participant in the hydrogen bond.     

Rydberg states with quantum Monte Carlo

Calculations on Rydberg states are performed using quantum Monte Carlo methods. Excitation energies and singlet-triplet splittings are calculated for two model systems, the carbon atom (3P and 1P) and carbon monoxide ((1Sigma and 3Sigma). Kohn-Sham wave functions constructed from open-shell localized Hartree-Fock orbitals are used as trial and guide functions. The fixed-node diffusion quantum Monte Carlo (FN-DMC) method depends strongly on the wave function's nodal hypersurface. Nodal artefacts are investigated for the ground state of the carbon atom. Their effect on the FN-DMC results can be analyzed quantitatively. FN-DMC leads to accurate excitation energies but to less accurate singlet-triplet splittings. Variational Monte Carlo calculations are able to reproduce the experimental results for both the excitation energies and the singlet-triplet splittings.     

Quantum monte carlo methods for constrained systems

The torsional ground state for ethane, the torsional, rotational, and mixed torsional and rotational ground state of propane are computed with a version of diffusion Monte Carlo adapted to handle the geometric complexity of curved spaces such as the Ramachandra space. The quantum NVT ensemble average for the mixed torsional and rotational degrees of freedom of propane is computed, using a version of Monte Carlo path integral, also adapted to handle curved spaces. These three problems are selected to demonstrate the generality and the applicability of the approaches described. The spaces of coordinates can be best constructed from the parameters of continuous Lie groups, and alternative methods based on vector spaces, where extended Lagrangian terms would be too cumbersome to implement. We note that the geometric coupling between the torsions and the rotations of propane produces a substantial effect on the ground state energy of propane, and that the quantum effects on the energy of propane are quite large even well above room temperature. © 2014 Wiley Periodicals, Inc.     

Quantum Monte Carlo study of the ground state and low-lying excited states of the scandium dimer

A large set of electronic states of scandium dimer has been calculated using high-level theoretical methods such as quantum diffusion Monte Carlo (DMC), complete active space perturbation theory as implemented in GAMESS-US, coupled-cluster singles, doubles, and triples, and density functional theory (DFT). The 3 Sigma u and 5 Sigma u states are calculated to be close in energy in all cases, but whereas DFT predicts the 5 Sigma u state to be the ground state by 0.08 eV, DMC and CASPT2 calculations predict the 3 Sigma u to be more stable by 0.17 and 0.16 eV, respectively. The experimental data available are in agreement with the calculated frequencies and dissociation energies of both states, and therefore we conclude that the correct ground state of scandium dimer is the 3 Sigma u state, which breaks with the assumption of a 5 Sigma u ground state for scandium dimer, believed throughout the past decades.     

Experimental evidence for the triplet-like spin state appearing in ground-state singlet biradicals as a key feature for generalized ferrimagnetic spin alignment

The authors have previously proposed a theoretical model for exotic spin alignment in organic molecular assemblages: The alternating chain of organic biradicals in a singlet (Sb=0) ground state and monoradicals with S=1/2 has a ferrimagnetic ground state for the whole chain, which has been termed generalized ferrimagnetism. An important feature of the generalized ferrimagnetic spin alignment has been found in the deviation of the expectation value Sb2 of the biradical spin from zero. Even a triplet-like spin state Sb2=2 (Sb=1) has been predicted in the theoretical calculations. In this study, we have found experimental evidence for the pseudo-triplet state appearing in the ground-state singlet biradical of a real open-shell compound. At first, we have demonstrated from theoretical calculations that the singlet biradical has Sb2=2 (Sb=1) in a molecular pair with an S=1 metal ion as well as with the S=1/2 monoradical. The pseudo-triplet state of the biradical affords a singlet state of the whole system of the biradical-metal ion pair, which is readily detectable in experiments for verifying the theoretical prediction. As a model compound for the biradical-metal ion pair, a transition metal complex, [(bnn)(Ni(hfac)2)1.5(H2O)] (1), has been synthesized from a nitronyl nitroxide-based ground-state singlet biradical bnn and Ni(hfac)2. From X-ray crystallographic analyses, the compound contains a molecular pair of bnn and Ni(hfac)2, which serves as a model system under the above theoretical studies. It has been found from the analysis of the temperature dependence of magnetic susceptibility that the bnn-Ni(hfac)2 pair has the singlet (S=0) ground state. The singlet ground state of the pair results from an antiparallel coupling of the pseudo-triplet of the biradical and the S=1 spin on the Ni ion. The pseudo-triplet state in the ground-state singlet biradical has thus been verified experimentally, which is crucially important to realize the generalized ferrimagnetic spin alignment.     

Monte Carlo computation of ground‐state energy derivatives

Monte Carlo is a simple technique, which uses random numbers to compute ground‐state energies of small molecules (and quantum systems in general). The results always have a small statistical error, which poses a major obstacle when estimating properties defined as ground‐state‐energy derivatives (such as the molecule's geometry, its vibrational frequencies, polarizabilities, etc.). In this article, we present and demonstrate an approach that makes an accurate Monte–Carlo estimation of such derivatives possible. This is achieved by realizing that the simulation constitutes an autocorrelated stochastic process, whose proper analysis then enables us to estimate various energy derivatives as a combination of total correlation between readily computable quantities. The resulting procedure is a natural extension of the usual Monte Carlo algorithm for computing the ground‐state energy, with relatively small computational overhead. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

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.     

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.     

Projector Monte Carlo method based on Slater determinants: a new sampling method for singlet state calculations

A new sampling method is proposed for projector Monte Carlo (PMC) calculations based on Slater determinants (SD) in singlet states. Using the symmetry of the ?? and ?? electron determinants, the number of configurations to be considered can be about one-half of the original sampling. We applied the new sampling to the PMC-SD calculations of the H₂O molecule in the ground state. The results were always improved by the new sampling method both for the equilibrium and for bond-stretched structures.     

Quantum Monte Carlo calculations of the potential energy curve of the helium dimer

We report results of two quantum Monte Carlo methods -- variational Monte Carlo and diffusion Monte Carlo -- on the potential energy curve of the helium dimer. In contrast to previous quantum Monte Carlo calculations on this system, we have employed trial wave functions of the Slater-Jastrow form and used the fixed node approximation for the fermion nodal surface. We find both methods to be in excellent agreement with the best theoretical results at short range. In addition, the diffusion Monte Carlo results give very good agreement across the whole potential energy curve, while the Slater-Jastrow wave function fails to bind the dimer at all.     

Photophysical Properties of Benzoylgermane and para‐Substituted Derivatives: Substituent Effects on Electronic Transitions

In the present study, a selection of basic substitution patterns on benzoyl(trimethyl)germane was investigated using time‐dependent density‐functional theory (TDDFT) to explore the influence on the stability and on the relative order of the lowest excited electronic states. The theoretical results are in agreement with absorption and fluorescence measurements. We show that electron‐withdrawing groups decrease the energetic level of the lowest singlet and triplet state relative to the electron‐pushing systems resulting in red‐shifted radiative transitions (fluorescence). In the first triplet state electron‐withdrawing groups lead to an increased dissociation barrier and a close approach with the singlet ground state before the transition state in the triplet state is reached, favoring radiationless ground‐state recovery. The results are also in good agreement with empirical concepts of organic chemistry, therefore providing simple rules for synthetic strategies towards tuning the excited‐state properties of benzoylgermanes.     

"Reduced" distributed monopole model for the efficient prediction of energy transfer in condensed phases

We propose a methodology for the realistic simulation and prediction of resonance energy transfer in condensed phases based on a combination of computer simulations of phase morphologies and of a distributed monopole model for the radiationless transfer. The heavy computational demands of the method are moderated by the introduction of a transition charges reduction scheme, originally developed for ground state interactions [Berardi, R. et al. Chem. Phys. Lett. 2004, 389, 373]. We demonstrate the scheme for a condensed glass phase formed by perylene monoimide end-capped 9,9-(di n,n)octylfluorene trimers, recently studied as light-harvesting materials, where we couple a coarse-grained Monte Carlo simulation of the molecular organization and a master equation approach modeling the energy diffusion process.     

应用Monte Carlo方法计算He原子包含电子相关作用的基态能量

应用Monte Carlo方法计算He原子包含电子相关波函数的基态能量,获得了与精确值非常接近的结果．实践表明,应用Monte Carlo方法有可能在多电子体系中直接采用包含任意2个电子间距离ry的函数作为变分函数来考虑电子相关作用．     

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.     

The ground state tunneling splitting and the zero point energy of malonaldehyde: a quantum Monte Carlo determination

Quantum dynamics calculations of the ground state tunneling splitting and of the zero point energy of malonaldehyde on the full dimensional potential energy surface proposed by Yagi et al. [J. Chem. Phys. 1154, 10647 (2001)] are reported. The exact diffusion Monte Carlo and the projection operator imaginary time spectral evolution methods are used to compute accurate benchmark results for this 21-dimensional ab initio potential energy surface. A tunneling splitting of 25.7+/-0.3 cm-1 is obtained, and the vibrational ground state energy is found to be 15 122+/-4 cm-1. Isotopic substitution of the tunneling hydrogen modifies the tunneling splitting down to 3.21+/-0.09 cm-1 and the vibrational ground state energy to 14 385+/-2 cm-1. The computed tunneling splittings are slightly higher than the experimental values as expected from the potential energy surface which slightly underestimates the barrier height, and they are slightly lower than the results from the instanton theory obtained using the same potential energy surface.     

表面扩散对CO氧化反应一级相变点的影响：蒙特卡罗模拟

CO氧化反应无论在化学工业还是在环境保护化学中都占有重要一席，特别是它常被用作研究多相催化反应基本过程的模型反应．研究表明，这一反应体系具有复杂的动力学行为，其中包括表面吸附物种的动力学相变、速率振荡和催化剂表面的结构重排等四人们还发现，当CO和O。按化学计量