Generalizing the self-healing diffusion Monte Carlo approach to finite temperature: A path for the optimization of low-energy many-body bases

Reboredo, Fernando A.; Kim, Jeongnim

doi:10.1063/1.4861222

Cited by 3 publications

(2 citation statements)

References 68 publications

(118 reference statements)

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“…Quantum Monte Carlo is a highly accurate wave-functionbased approach for electronic structure calculations 41 , that has been also recently extended for ab-initio simulations 39,40,[42][43][44][45][46] . In this work we have employed the first ab-initio molecular dynamics simulation of liquid water based entirely on QMC.…”

Section: Pacs Numbersmentioning

confidence: 99%

Ab initio molecular dynamics simulation of liquid water by quantum Monte Carlo

Zen

Luo

Mazzola

et al. 2015

The Journal of Chemical Physics

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Although liquid water is ubiquitous in chemical reactions at roots of life and climate on the earth, the prediction of its properties by high-level ab initio molecular dynamics simulations still represents a formidable task for quantum chemistry. In this article we present a room temperature simulation of liquid water based on the potential energy surface obtained by a many-body wave function through quantum Monte Carlo (QMC) methods. The simulated properties are in good agreement with recent neutron scattering and X-ray experiments, particularly concerning the position of the oxygen-oxygen peak in the radial distribution function, at variance of previous Density Functional Theory attempts. Given the excellent performances of QMC on large scale supercomputers, this work opens new perspectives for predictive and reliable ab-initio simulations of complex chemical systems. PACS numbers:The simulation by first principles of liquid water, the key element of human life and biological processes, has been a dream for several decades after the foundation of Density Functional theory (DFT), even within the restriction of the Born-Oppenheimer approximation for the heavy nuclei. Realistic simulations are particular important because, at the experimental level, it is not possible to clarify completely what are the relationships between the so many different and rich phases of water and the physical interactions between water molecules, determined by hydrogen bonding and weak longrange van der Waals (vdW) interactions. Moreover water is involved in many biological and chemical processes, and first principle simulations are useful to investigate and rationalize such important mechanisms.The first attempted simulations date back to the pioneer works by Car and Parrinello 1-3 , within an efficient ab-initio molecular dynamics (AIMD) based on DFT. The comparison with the experiments, at that time available, provided a pretty good agreement with the oxygen-oxygen (O-O) radial distribution function (RDF), as far as the positions of the peaks were concerned, but the overall shape given by the simulation was overstructured. After these first studies, many other works reporting standard DFT-based simulations have been published, but the agreement with the experimental data is still not satisfactory on many aspects. The equilibrium density at ambient pressure (1 atm ∼ 10 −4 GPa), is far to be consistent with the expected one (1 gr/cm 3 ) though recent DFT functionals including van der Waals substantially reduce this discrepancy 4 . The simulated diffusion 5 is much lower than what is expected from experiments 6 , and, at least in some functionals (namely, PBE and BLYP), the solidification of water occurs at a temperature which is unrealistically large (∼ 410 K), so that some of the present DFT simulations of liquid water should be considered supercooled metastable phases 6,7 .The DFT results (about which we provide a brief summary in Tab. I) appear to be substantially influenced by the choice of the functional 5,8 , but also, within a ...

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Section: Pacs Numbersmentioning

confidence: 99%

Ab initio molecular dynamics simulation of liquid water by quantum Monte Carlo

Zen

Luo

Mazzola

et al. 2015

The Journal of Chemical Physics

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“…They proposed a way to iteratively generate new trial wave functions to get a better nodal surface. They generalized the method to excited states 52 and finite temperatures 53 and also applied for large systems such as C 20 . 54 Very recently, McFarland and Manousakis 55 reported successful energy minimizations with approximated and exact FN gradients.…”

Section: Introductionmentioning

confidence: 99%

Beyond Single-Reference Fixed-Node Approximation in Ab Initio Diffusion Monte Carlo Using Antisymmetrized Geminal Power Applied to Systems with Hundreds of Electrons

Nakano,

Sorella,

Alfè

et al. 2024

J. Chem. Theory Comput.

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Diffusion Monte Carlo (DMC) is an exact technique to project out the ground state (GS) of a Hamiltonian. Since the GS is always bosonic, in Fermionic systems, the projection needs to be carried out while imposing antisymmetric constraints, which is a nondeterministic polynomial hard problem. In practice, therefore, the application of DMC on electronic structure problems is made by employing the fixed-node (FN) approximation, consisting of performing DMC with the constraint of having a fixed, predefined nodal surface. How do we get the nodal surface? The typical approach, applied in systems having up to hundreds or even thousands of electrons, is to obtain the nodal surface from a preliminary mean-field approach (typically, a density functional theory calculation) used to obtain a single Slater determinant. This is known as single reference. In this paper, we propose a new approach, applicable to systems as large as the C 60 fullerene, which improves the nodes by going beyond the single reference. In practice, we employ an implicitly multireference ansatz (antisymmetrized geminal power wave function constraint with molecular orbitals), initialized on the preliminary mean-field approach, which is relaxed by optimizing a few parameters of the wave function determining the nodal surface by minimizing the FN-DMC energy. We highlight the improvements of the proposed approach over the standard single-reference method on several examples and, where feasible, the computational gain over the standard multireference ansatz, which makes the methods applicable to large systems. We also show that physical properties relying on relative energies, such as binding energies, are affordable and reliable within the proposed scheme.

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Ab initio molecular dynamics with noisy forces: Validating the quantum Monte Carlo approach with benchmark calculations of molecular vibrational properties

Luo

Zen

Sorella

2014

The Journal of Chemical Physics

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We present a systematic study of a recently developed ab initio simulation scheme based on molecular dynamics and quantum Monte Carlo. In this approach, a damped Langevin molecular dynamics is employed by using a statistical evaluation of the forces acting on each atom by means of quantum Monte Carlo. This allows the use of an highly correlated wave function parametrized by several variational parameters and describing quite accurately the Born-Oppenheimer energy surface, as long as these parameters are determined at the minimum energy condition. However, in a statistical method both the minimization method and the evaluation of the atomic forces are affected by the statistical noise. In this work, we study systematically the accuracy and reliability of this scheme by targeting the vibrational frequencies of simple molecules such as the water monomer, hydrogen sulfide, sulfur dioxide, ammonia, and phosphine. We show that all sources of systematic errors can be controlled and reliable frequencies can be obtained with a reasonable computational effort. This work provides convincing evidence that this molecular dynamics scheme can be safely applied also to realistic systems containing several atoms.

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Generalizing the self-healing diffusion Monte Carlo approach to finite temperature: A path for the optimization of low-energy many-body bases

Cited by 3 publications

References 68 publications

Ab initio molecular dynamics simulation of liquid water by quantum Monte Carlo

Ab initio molecular dynamics simulation of liquid water by quantum Monte Carlo

Beyond Single-Reference Fixed-Node Approximation in Ab Initio Diffusion Monte Carlo Using Antisymmetrized Geminal Power Applied to Systems with Hundreds of Electrons

Ab initio molecular dynamics with noisy forces: Validating the quantum Monte Carlo approach with benchmark calculations of molecular vibrational properties

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