Ground and excited electronic states of azobenzene: a quantum Monte Carlo study

Large-scale quantum Monte Carlo (QMC) calculations of ground and excited singlet states of both conformers of azobenzene are presented. Remarkable accuracy is achieved by combining medium accuracy quantum chemistry methods with QMC. The results not only reproduce measured values with chemical accuracy but the accuracy is sufficient to identify part of experimental results which appear to be biased. Novel analysis of nodal surface structure yields new insights and control over their convergence, providing boost to the chemical accuracy electronic structure methods of large molecular systems.     

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.     

Linear-scaling fixed-node diffusion quantum Monte Carlo: accounting for the nodal information in a density matrix-based scheme

A reformulation of the fixed-node diffusion quantum Monte Carlo method (FN-DQMC) in terms of the N-particle density matrix is presented, which allows us to reduce the computational effort to linear for the evaluation of the local energy. The reformulation is based on our recently introduced density matrix-based approach for a linear-scaling variational QMC method [J. Kussmann et al., Phys. Rev. B. 75, 165107 (2007)]. However, within the latter approach of using the positive semi-definite N-particle trial density (rhoN T(R)=mid R:Psi(T)(R)mid R:(2)), the nodal information of the trial function is lost. Therefore, a straightforward application to the FN-DQMC method is not possible, in which the sign of the trial function is usually traced in order to confine the random walkers to their nodal pockets. As a solution, we reformulate the FN-DQMC approach in terms of off-diagonal elements of the N-particle density matrix rhoN T(R;R'), so that the nodal information of the trial density matrix is obtained. Besides all-electron moves, a scheme to perform single-electron moves within N-PDM QMC is described in detail. The efficiency of our method is illustrated for exemplary calculations.     

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.     

Zero-variance zero-bias quantum Monte Carlo estimators for the electron density at a nucleus

We derive new quantum Monte Carlo (QMC) estimators for the electronic density at the position of a point nucleus using the zero-variance and zero-bias principles. The resulting estimators are highly efficient, and are significantly simpler to implement and use than alternative methods, as they contain no adjustable parameters. In addition, they can be used in both variational and diffusion QMC calculations. Our best estimator is used to calculate the most accurate available estimates of the total electron density at the nucleus for the first-row atoms Li-Ne, the Ar atom, and the diatomic molecules B(2), N(2), and F(2).     

A novel parallel algorithm for large-scale Fock matrix construction with small locally distributed memory architectures: RT parallel algorithm

We developed a novel parallel algorithm for large-scale Fock matrix calculation with small locally distributed memory architectures, and named it the "RT parallel algorithm." The RT parallel algorithm actively involves the concept of integral screening, which is indispensable for reduction of computing times with large-scale biological molecules. The primary characteristic of this algorithm is parallel efficiency, which is achieved by well-balanced reduction of both communicating and computing volume. Only the density matrix data necessary for Fock matrix calculations are communicated, and the data once communicated are reutilized for calculations as many times as possible. The RT parallel algorithm is a scalable method because required memory volume does not depend on the number of basis functions. This algorithm automatically includes a partial summing technique that is indispensable for maintaining computing accuracy, and can also include some conventional methods to reduce calculation times. In our analysis, the RT parallel algorithm had better performance than other methods for massively parallel processors. The RT parallel algorithm is most suitable for massively parallel and distributed Fock matrix calculations for large-scale biological molecules with more than thousands of basis functions.     

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).     

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.     

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.     

Scalable fine-grained parallelization of plane-wave-based ab initio molecular dynamics for large supercomputers

Many systems of great importance in material science, chemistry, solid-state physics, and biophysics require forces generated from an electronic structure calculation, as opposed to an empirically derived force law to describe their properties adequately. The use of such forces as input to Newton's equations of motion forms the basis of the ab initio molecular dynamics method, which is able to treat the dynamics of chemical bond-breaking and -forming events. However, a very large number of electronic structure calculations must be performed to compute an ab initio molecular dynamics trajectory, making the efficiency as well as the accuracy of the electronic structure representation critical issues. One efficient and accurate electronic structure method is the generalized gradient approximation to the Kohn-Sham density functional theory implemented using a plane-wave basis set and atomic pseudopotentials. The marriage of the gradient-corrected density functional approach with molecular dynamics, as pioneered by Car and Parrinello (R. Car and M. Parrinello, Phys Rev Lett 1985, 55, 2471), has been demonstrated to be capable of elucidating the atomic scale structure and dynamics underlying many complex systems at finite temperature. However, despite the relative efficiency of this approach, it has not been possible to obtain parallel scaling of the technique beyond several hundred processors on moderately sized systems using standard approaches. Consequently, the time scales that can be accessed and the degree of phase space sampling are severely limited. To take advantage of next generation computer platforms with thousands of processors such as IBM's BlueGene, a novel scalable parallelization strategy for Car-Parrinello molecular dynamics is developed using the concept of processor virtualization as embodied by the Charm++ parallel programming system. Charm++ allows the diverse elements of a Car-Parrinello molecular dynamics calculation to be interleaved with low latency such that unprecedented scaling is achieved. As a benchmark, a system of 32 water molecules, a common system size employed in the study of the aqueous solvation and chemistry of small molecules, is shown to scale on more than 1500 processors, which is impossible to achieve using standard approaches. This degree of parallel scaling is expected to open new opportunities for scientific inquiry.     

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.     

Energetics of binuclear spin transition complexes

The electronic structures of five binuclear iron(II) complexes, four of which display spin transitions between the low-spin (LS) and high-spin (HS) electronic states, are studied by density functional theory (DFT) calculations. Three electronic states, corresponding to [LS-LS], [LS-HS], and [HS-HS] electronic configurations, are characterized. The nature of the ground state agrees with the experimentally observed magnetic state of complexes stabilized at low temperatures. The results of the calculations agree with the conclusion of the phenomenological model, that the enthalpy of the [LS-HS] state must be lower than the average enthalpy of the [LS-LS] and [HS-HS] states, to create conditions for a two-step spin transition. The exchange parameters between Fe(II) ions in the [HS-HS] states are evaluated. It is shown that all complexes are weakly antiferromagnetic and the synergy between two spin transition centers is mainly of elastic origin.     

Two-body Reduced Density Matrix Reconstruction for Van der Waals Systems

A method for the calculation of the electronic energy of a correlated system is presented. This approach is based on the reconstruction of the total two-body reduced density matrix by doing separate configurations interaction calculations on fragments. The method has been tested on Van der Waals systems and has been implemented by considering restrictive N-representability conditions. It is shown that the computational strategy presented in this work can describe with good accuracy weak dispersion interactions, and considerably lowers the size-consistency error of a classical configuration interaction calculation.     

Fast prediction of hydration free energies for SAMPL4 blind test from a classical density functional theory

We report the performance of a classical density functional theory (CDFT) in the competition for the solvation free-energy category of the SAMPL4 blind prediction event. The theoretical calculations were carried out with the TIP3P water model and different combinations of solute configurations and molecular force fields. In comparison with the experimental data, the blind test yields an average unsigned error of 2.38 kcal/mol and the root mean square deviation of 2.99 kcal/mol. Whereas these numbers are significantly larger than the best results from explicit-solvent MD simulations, we find that the theoretical performance is sensitive to both the molecular force fields and solute configurations and that a comparable level of accuracy can be achieved by a judicious selection of the solute configurations and the force-field parameters. Most importantly, CDFT reduces the computational cost of MD simulation by almost 3 orders of magnitude, making it very attractive for large-scale hydration free-energy calculations (e.g., screening the aqueous solubility of drug-like molecules).     

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.     

Theoretical characterization of titanyl phthalocyanine as a p-type organic semiconductor: short intermolecular pi-pi interactions yield large electronic couplings and hole transport bandwidths

The charge-transport properties of the triclinic phase II crystal of titanyl phthalocyanine (alpha-TiOPc) are explored within both a hopping and bandlike regime. Electronic coupling elements in convex- and concave-type dimers are calculated using density functional theory, and the relationship between molecular structure and crystal packing structure in model dimer configurations is considered. Hole transport bandwidths derived from crystal structure dimers are compared to those obtained from electronic band structure calculations; very good agreement between the two approaches is found. The calculations predict large hole bandwidths, on the order of 0.4 eV, and correspondingly very low hole reorganization energies.     

Efficient Calculation of Absorption Spectra in Solution: Approaches for Selecting Representative Solvent Configurations and for Reducing the Number of Explicit Solvent Molecules

Dye-sensitized solar cells(DSSCs) are one of the most promising renewable energy technologies. Charge transfer and charge transport are pivotal processes in DSSCs, which govern solar energy capture and conversion. These processes can be probed using modern electronic structure methods. Because of the heterogeneity and complexity of the local environment of a chromophore in DSSCs(such as solvatochromism and chromophore aggregation), a part of the solvation environment should be treated explicitly during the calculation. However, because of the high computational cost and unfavorable scaling with the number of electrons of high-level quantum mechanical methods, approaches to explicitly treat the local environment need careful consideration. Two problems must be tackled to reduce computational cost. First, the number of configurations representing the solvent distribution should be limited as much as possible. Second, the size of the explicit region should be kept relatively small. The purpose of this study is to develop efficient computational approaches to select representative configurations and to limit the explicit solvent region to reduce the computational cost for later(higher-level) quantum mechanical calculations. For this purpose, an ensemble of solvent configurations around a 1-methyl-8-oxyquinolinium betaine(QB) dye molecule was generated using Monte Carlo simulations and molecular mechanics force fields. Then, a fitness function was developed using data from inexpensive electronic structure calculations to reduce the number of configurations. Specific solvent molecules were also selected for explicit treatment based on a distance criterion, and those not selected were treated as background charges. The configurations and solvent molecules selected proved to be good representatives of the entire ensemble; thus, expensive electronic structure calculations need to be performed only on this subset of the system, which significantly reduces the computational cost.     

Parallel algorithm for efficient calculation of second derivatives of conformational energy function in internal coordinates

A parallel algorithm for efficient calculation of the second derivatives (Hessian) of the conformational energy in internal coordinates is proposed. This parallel algorithm is based on the master/slave model. A master processor distributes the calculations of components of the Hessian to one or more slave processors that, after finishing their calculations, send the results to the master processor that assembles all the components of the Hessian. Our previously developed molecular analysis system for conformational energy optimization, normal mode analysis, and Monte Carlo simulation for internal coordinates is extended to use this parallel algorithm for Hessian calculation on a massively parallel computer. The implementation of our algorithm uses the message passing interface and works effectively on both distributed-memory parallel computers and shared-memory parallel computers. We applied this system to the Newton–Raphson energy optimization of the structures of glutaminyl transfer RNA (Gln-tRNA) with 74 nucleotides and glutaminyl-tRNA synthetase (GlnRS) with 540 residues to analyze the performance of our system. The parallel speedups for the Hessian calculation were 6.8 for Gln-tRNA with 24 processors and 11.2 for GlnRS with 54 processors. The parallel speedups for the Newton–Raphson optimization were 6.3 for Gln-tRNA with 30 processors and 12.0 for GlnRS with 62 processors. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1716–1723, 1998