Kenta Hongo

A benchmark quantum Monte Carlo study of the ground state chromium dimer

We report variational and diffusion quantum Monte Carlo (VMC and DMC) studies of the binding curve of the ground-state chromium dimer. We employed various single determinant (SD) or multi-determinant (MD) wavefunctions multiplied by a Jastrow fuctor as a trial/guiding wavefunction. The molecular orbitals (MOs) in the SD were calculated using restricted or unrestricted Hartree-Fock or density functional theory (DFT) calculations where five commonly-used local (SVWN5), semi-local (PW91PW91 and BLYP), and hybrid (B1LYP and B3LYP) functionals were examined. The MD expansions were obtained from the complete-active space SCF, generalized valence bond, and unrestricted configuration interaction methods. We also adopted the UB3LYP-MOs to construct the MD expansion (UB3LYP-MD) and optimized their coefficients at the VMC level. In addition to the wavefunction dependence, we investigated the time-step bias in the DMC calculation and the effects of pseudopotentials and backflow transformation for the UB3LYP-SD case. Some of the VMC binding curves show a flat or quite shallow well bottom, which gets recovered deeper by DMC. All the DMC binding curves have a minimum indicating a bound state, but the comparison of atomic and molecular energies gives rise to a negative binding energy for all the DMC as well as VMC calculations.

A quantum Monte Carlo study of the ground state chromium dimer

We report variational and diffusion quantum Monte Carlo (VMC and DMC) studies of the binding curve of the ground-state chromium dimer. We employed various single determinant (SD) or multi-determinant (MD) wavefunctions multiplied by a Jastrow fuctor as a trial/guiding wavefunction. The molecular orbitals (MOs) in the SD were calculated using restricted or unrestricted Hartree-Fock or density functional theory (DFT) calculations where five commonly-used local (SVWN5), semi-local (PW91PW91 and BLYP), and hybrid (B1LYP and B3LYP) functionals were examined. The MD expansions were obtained from the complete-active space SCF, generalized valence bond, and unrestricted configuration interaction methods. We also adopted the UB3LYP-MOs to construct the MD expansion (UB3LYP-MD) and optimized their coefficients at the VMC level. In addition to the wavefunction dependence, we investigated the time-step bias in the DMC calculation and the effects of pseudopotentials and backflow transformation for the UB3LYP-SD case. Some of the VMC binding curves show a flat or quite shallow well bottom, which gets recovered deeper by DMC. All the DMC binding curves have a minimum indicating a bound state, but the comparison of atomic and molecular energies gives rise to a negative binding energy for all the DMC as well as VMC calculations.

The Importance of Electron Correlation on Stacking Interaction of Adenine-Thymine Base-Pair Step in B-DNA: A Quantum Monte Carlo Study

We report fixed-node diffusion Monte Carlo (DMC) calculations of stacking interaction energy between two adenine(A)-thymine(T) base pairs in B-DNA (AA:TT), for which reference data are available, obtained from a complete basis set estimate of CCSD(T) (coupled-cluster with singles, doubles, and perturbative triples). We consider four sets of nodal surfaces obtained from self-consistent field calculations and examine how the different nodal surfaces affect the DMC potential energy curves of the AA:TT molecule and the resulting stacking energies. We find that the DMC potential energy curves using the different nodes look similar to each other as a whole. We also benchmark the performance of various quantum chemistry methods, including Hartree-Fock (HF) theory, second-order Møller-Plesset perturbation theory (MP2), and density functional theory (DFT). The DMC and recently developed DFT results of the stacking energy reasonably agree with the reference, while the HF, MP2, and conventional DFT methods give unsatisfactory results.

Diffusion Monte Carlo Study of Para-Diiodobenzene Polymorphism Revisited

We revisit our investigation of the diffusion Monte Carlo (DMC) simulation of para-diiodobenzene (p-DIB) molecular crystal polymorphism. [See J. Phys. Chem. Lett. 2010, 1, 1789-1794.] We perform, for the first time, a rigorous study of finite-size effects and choice of nodal surface on the prediction of polymorph stability in molecular crystals using fixed-node DMC. Our calculations are the largest that are currently feasible using the resources of the K-computer and provide insights into the formidable challenge of predicting such properties from first principles. In particular, we show that finite-size effects can influence the trial nodal surface of a small (1 × 1 × 1) simulation cell considerably. Therefore, we repeated our DMC simulations with a 1 × 3 × 3 simulation cell, which is the largest such calculation to date. We used a density functional theory (DFT) nodal surface generated with the PBE functional, and we accumulated statistical samples with ∼6.4 × 10(5) core hours for each polymorph. Our final results predict a polymorph stability that is consistent with experiment, but they also indicate that the results in our previous paper were somewhat fortuitous. We analyze the finite-size errors using model periodic Coulomb (MPC) interactions and kinetic energy corrections, according to the CCMH scheme of Chiesa, Ceperley, Martin, and Holzmann. We investigate the dependence of the finite-size errors on different aspect ratios of the simulation cell (k-mesh convergence) in order to understand how to choose an appropriate ratio for the DMC calculations. Even in the most expensive simulations currently possible, we show that the finite size errors in the DMC total energies are much larger than the energy difference between the two polymorphs, although error cancellation means that the polymorph prediction is accurate. Finally, we found that the T-move scheme is essential for these massive DMC simulations in order to circumvent population explosions and large time-step biases.

Random number generators tested on quantum Monte Carlo simulations

We have tested and compared several (pseudo) random number generators (RNGs) applied to a practical application, ground state energy calculations of molecules using variational and diffusion Monte Carlo metheds. A new multiple recursive generator with 8th‐order recursion (MRG8) and the Mersenne twister generator (MT19937) are tested and compared with the RANLUX generator with five luxury levels (RANLUX‐[0–4]). Both MRG8 and MT19937 are proven to give the same total energy as that evaluated with RANLUX‐4 (highest luxury level) within the statistical error bars with less computational cost to generate the sequence. We also tested the notorious implementation of linear congruential generator (LCG), RANDU, for comparison.

Valence Band Engineering of Layered Bismuth Oxyhalides toward Stable Visible-Light Water Splitting: Madelung Site Potential Analysis

A layered oxychloride Bi4NbO8Cl is a visible-light responsive catalyst for water splitting, with its remarkable stability ascribed to the highly dispersive O-2p orbitals in the valence band, the origin of which, however, remains unclear. Here, we systematically investigate four series of layered bismuth oxyhalides, BiOX (X = Cl, Br, I), Bi4NbO8X (X = Cl, Br), Bi2GdO4X (X = Cl, Br), and SrBiO2X (X = Cl, Br, I), and found that Madelung site potentials of anions capture essential features of the valence band structures of these materials. The oxide anion in fluorite-like blocks (e.g., [Bi2O2] slab in Bi4NbO8Cl) is responsible for the upward shift of the valence band, and the degree of electrostatic destabilization changes depending on building layers and their stacking sequence. This study suggests that the Madelung analysis enables a prediction and design of the valence band structures of bismuth and other layered oxyhalides and is applicable even to a compound where DFT calculation is difficult to perform.

Bayesian molecular design with a chemical language model

The aim of computational molecular design is the identification of promising hypothetical molecules with a predefined set of desired properties. We address the issue of accelerating the material discovery with state-of-the-art machine learning techniques. The method involves two different types of prediction; the forward and backward predictions. The objective of the forward prediction is to create a set of machine learning models on various properties of a given molecule. Inverting the trained forward models through Bayes’ law, we derive a posterior distribution for the backward prediction, which is conditioned by a desired property requirement. Exploring high-probability regions of the posterior with a sequential Monte Carlo technique, molecules that exhibit the desired properties can computationally be created. One major difficulty in the computational creation of molecules is the exclusion of the occurrence of chemically unfavorable structures. To circumvent this issue, we derive a chemical language model that acquires commonly occurring patterns of chemical fragments through natural language processing of ASCII strings of existing compounds, which follow the SMILES chemical language notation. In the backward prediction, the trained language model is used to refine chemical strings such that the properties of the resulting structures fall within the desired property region while chemically unfavorable structures are successfully removed. The present method is demonstrated through the design of small organic molecules with the property requirements on HOMO-LUMO gap and internal energy. The R package iqspr is available at the CRAN repository.

Unified interpretation of Hund’s first and second rules for 2p and 3p atoms

A unified interpretation of Hunds first and second rules for 2p (C, N, O) and 3p (Si, P, S) atoms is given by Hartree-Fock (HF) and multiconfiguration Hartree-Fock (MCHF) methods. Both methods exactly satisfy the virial theorem, in principle, which enables one to analyze individual components of the total energy E(=T+V(en)+V(ee)), where T, V(en), and V(ee) are the kinetic, the electron-nucleus attraction, and the electron-electron repulsion energies, respectively. The correct interpretation for each of the two rules can only be achieved under the condition of the virial theorem 2T+V=0 by investigating how V(en) and V(ee) interplay to attain the lower total potential energy V(=V(en)+V(ee)). The stabilization of the more stable states for all the 2p and 3p atoms is ascribed to a greater V(en) that is caused by contraction of the valence orbitals accompanied with slight expansion of the core orbitals. The contraction of the valence orbitals for the two rules is a consequence of reducing the Hartree screening of the nucleus at short interelectronic distances. The reduced screening in the first rule is due to a greater amount of Fermi hole contributions in the state with the highest total spin-angular momentum S. The reduced screening in the second rule is due to the fact that two valence electrons are more likely to be on opposite sides of the nucleus in the state with the highest total orbital-angular momentum L. For each of the two rules, the inclusion of correlation does not qualitatively change the HF interpretation, but HF overestimates the energy difference ∣ΔE∣ between two levels being compared. The magnitude of the correlation energy is significantly larger for the lower L states than for the higher L states since two valence electrons in the lower L states are less likely to be on opposite sides of the nucleus. The MCHF evaluation of ∣ΔE∣ is in excellent agreement with experiment. The present HF and MCHF calculations demonstrate the above statements that were originally given by Katriel [Theor. Chem. Acta 23, 309 (1972); 26, 163 (1972)]. We have, for the first time, analyzed the correlation-induced changes in the radial density distribution for the excited LS terms of the 2p and 3p atoms as well as for the ground LS term.

A Stable, Narrow-Gap Oxyfluoride Photocatalyst for Visible-Light Hydrogen Evolution and Carbon Dioxide Reduction

Mixed anion compounds such as oxynitrides and oxychalcogenides are recognized as potential candidates of visible-light-driven photocatalysts since, as compared with oxygen 2p orbitals, p orbitals of less electronegative anion (e.g., N3-, S2-) can form a valence band that has more negative potential. In this regard, oxyfluorides appear unsuitable because of the higher electronegativity of fluorine. Here we show an exceptional case, an anion-ordered pyrochlore oxyfluoride Pb2Ti2O5.4F1.2 that has a small band gap (ca. 2.4 eV). With suitable modification of Pb2Ti2O5.4F1.2 by promoters such as platinum nanoparticles and a binuclear ruthenium(II) complex, Pb2Ti2O5.4F1.2 worked as a stable photocatalyst for visible-light-driven H2 evolution and CO2 reduction. Density functional theory calculations have revealed that the unprecedented visible-light-response of Pb2Ti2O5.4F1.2 arises from strong interaction between Pb-6s and O-2p orbitals, which is enabled by a short Pb-O bond in the pyrochlore lattice due to the fluorine substitution.

Phonon dispersions and Fermi surfaces nesting explaining the variety of charge ordering in titanium-oxypnictides superconductors

There has been a puzzle between experiments and theoretical predictions on the charge ordering of layered titanium-oxypnictides superconductors. Unconventional mechanisms to explain this discrepancy have been argued so far, even affecting the understanding of superconductivity on the compound. We provide a new theoretical prediction, by which the discrepancy itself is resolved without any complicated unconventional explanation. Phonon dispersions and changes of nesting vectors in Fermi surfaces are clarified to lead to the variety of superlattice structures even for the common crystal structures when without CDW, including orthorhombic 2u2009×u20092u2009×u20091 one for BaTi2As2O, which has not yet been explained successfully so far, being different from tetragonal for BaTi2Sb2O and BaTi2Bi2O. The electronic structure analysis can naturally explain experimental observations about CDW including most latest ones without any cramped unconventional mechanisms.