Molecular Properties by Quantum Monte Carlo: An Investigation on the Role of the Wave Function Ansatz and the Basis Set in the Water Molecule

Zen, Andrea; Luo, Ye; Sorella, Sandro; Guidoni, Leonardo

doi:10.1021/ct400382m

Cited by 42 publications

(115 citation statements)

References 103 publications

(286 reference statements)

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“…The Jastrow factor is a symmetric positive function of the electronic positions that depends on the inter-particle distances, and describes the dynamical correlation among electrons. It is also particularly useful because, already in its simplest form, makes it possible to fulfill the electron-electron and electron-nucleus cusp conditions 41,50,51 . So far the JSD ansatz can be efficiently simulated within a quantum Monte Carlo 41,51 approach, that introduces no other bias than the statistical error, systematically vanishing with the simulation length.…”

Section: Methodological Aspects Of the Qmc-based Molecular Dynamicsmentioning

confidence: 99%

“…. , N/2 (N is the number of electrons), are a linear combination of the localized atomic hybrid orbitals 51 :…”

Section: A Determinant Part ψ Sd and Its Basis Setmentioning

confidence: 99%

“…The optimization is performed by using the correspondence between the single Slater determinant written in terms of molecular orbitals, and a truncated antisymmetrized geminal power (AGPn) 51,54 with n = N/2, with a geminal…”

Section: A Determinant Part ψ Sd and Its Basis Setmentioning

confidence: 99%

“…At variance of a previous QMC study 51 , in the present VMC-based molecular dynamics, we did not include in the Jastrow factor the electron-electron-nucleus-nucleus term…”

Section: B Jastrow Factor and Its Basis Setmentioning

confidence: 99%

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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: Methodological Aspects Of the Qmc-based Molecular Dynamicsmentioning

confidence: 99%

“…. , N/2 (N is the number of electrons), are a linear combination of the localized atomic hybrid orbitals 51 :…”

Section: A Determinant Part ψ Sd and Its Basis Setmentioning

confidence: 99%

Section: A Determinant Part ψ Sd and Its Basis Setmentioning

confidence: 99%

“…At variance of a previous QMC study 51 , in the present VMC-based molecular dynamics, we did not include in the Jastrow factor the electron-electron-nucleus-nucleus term…”

Section: B Jastrow Factor and Its Basis Setmentioning

confidence: 99%

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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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“…Since our method is not restricted to QMC we will not enter in the details of the wavefunction and the optimization methods, the interested reader can refer to our previous works. [18][19][20][21] In QMC one of the most important matrix that we have found useful for the dynamics is the so called "covariance matrix":…”

mentioning

confidence: 99%

Acceleratingab initioMolecular Dynamics and Probing the Weak Dispersive Forces in Dense Liquid Hydrogen

Mazzola

Sorella

2017

Phys. Rev. Lett.

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We propose an ab-initio molecular dynamics method, capable to reduce dramatically the autocorrelation time required for the simulation of classical and quantum particles at finite temperature. The method is based on an efficient implementation of a first order Langevin dynamics modified by means of a suitable, position dependent acceleration matrix S. Here we apply this technique, within a Quantum Monte Carlo (QMC) based wavefunction approach and within the Born-Oppheneimer approximation, for determining the phase diagram of high-pressure Hydrogen with simulations much longer than the autocorrelation time. With the proposed method, we are able to equilibrate in few hundreds steps even close to the liquid-liquid phase transition (LLT). Within our approach we find that the LLT transition is consistent with recent density functionals predicting a much larger transition pressures when the long range dispersive forces are taken into account.One of the most important problems in ab-initio molecular dynamics (MD) is the coexistence of much different time scales underlying physical processes, even when computing equilibrium finite temperature properties. This has been a challenge for most ab-initio simulations in systems of biophysical interest, the most striking one being protein folding [1,2], where the microscopic time scale of molecular vibration is of the order of f s, while the macroscopic time scale of the folding exceeds the µs. Also in water system simulations, the weak Van der Waals (vdW) interactions and the related hydrogen bond imply very difficult equilibration properties at ambient conditions, so that the most accurate simulations are based on force field fitting forces. We will show here that, a computationally expensive ab-initio method for dense liquid hydrogen can be combined with a sampling technique capable to reduce drastically the autocorrelation times. This method has the potential, due to its simplicity, to be applied with success also to much more complex systems and other ab-initio techniques.At variance of all previous attempts[3-10], we propose that an optimal way to get rid of different time scales is based on the use of first order Langevin dynamics:where T is the temperature, f Ri = −∂ Ri V ( R) and V R is an energy potential of the classical coordinates R, e.g. atomic positions. For S ij = δ ij this is the conventional first order Langevin dynamics (CFOLD). Preconditioned Langevin equations, formally similar to Eq. 40, have been already introduced in several fields different from molecular dynamics, such as gauge field theories[11], statistics [12] and machine learning [13], with different definitions of the preconditioning matrix S. Instead, the main idea of this work is based on the simple solution of CFOLD for the harmonic potential V (R) = −K R, where K is the elastic matrix term. In this case one is able to show that the i) the autocorrelation time is independent of temperature τ −1 corr = K min , where K min (K max ) is the lowest (largest) non-zero eigenvalue of the elastic matrix...

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Reduced‐scaling coupled cluster response theory: Challenges and opportunities

Crawford

Kumar

Bazanté

et al. 2019

WIREs Comput Mol Sci

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We review the current state of reduced-scaling electron correlation methods, particularly coupled-cluster theory for the simulation and prediction of molecular response properties. The successes of local-coupled-cluster and related approaches are well known for reaction energies, thermodynamic constants, dipole moments, and so forth-properties that depend primarily on the quality of the ground-state wave function. However, much more challenging are higher-order properties such as polarizabilities, hyperpolarizabilities, optical rotations, magnetizabilities, and others that also require accurate representation of the derivative of the wave function to external electromagnetic fields. We discuss a range of methods for improving the correlation domains of such perturbed wave functions, including the use of "perturbation-aware" natural orbitals that are customized for the property of interest. In addition, we consider the viability and potential of promising, but stillemerging methods such as stochastic and real-time coupled-cluster approaches, for which the localizability of the field-dependent wave function may be more controllable than for conventional response theory.

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Molecular Properties by Quantum Monte Carlo: An Investigation on the Role of the Wave Function Ansatz and the Basis Set in the Water Molecule

Cited by 42 publications

References 103 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

Acceleratingab initioMolecular Dynamics and Probing the Weak Dispersive Forces in Dense Liquid Hydrogen

Reduced‐scaling coupled cluster response theory: Challenges and opportunities

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