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Quantum Monte Carlo

Molecular electrical properties from Quantum Monte Carlo calculations

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We use Quantum Monte Carlo (QMC) methods to study the polarizability and the quadrupole moment of the molecules like th ethyne (HCCH) using the Jastrow-Antisymmetrised Geminal Power (JAGP) wave function, a compact and strongly correlated variational ansatz. The compactness of the functional form and the full optimization of all its variational parameters, including linear and exponential coefficients in atomic orbitals, allow us to observe a fast convergence of the electrical properties with the size of the atomic and Jastrow basis sets. We also study the electronic density along the molecular axis by introducing a generalization for molecular systems of the small-variance improved estimator of the electronic density proposed by Assaraf  et al. [Phys. Rev. E, 75, 035701 (2007)].



Low-Lying Excited States of Ethylene by Quantum Monte Carlo

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In the recent article by Barborini, Sorella and Guidoni published on the Journal of chemical Theory & Computation[1], the structural optimization method developed by S. Sorella[2] has been applied to the study of the structures of the ground state and first excited triplet states of the ethylene molecule. All the calculations were done using an accurate and compact wave function based on Pauling's resonating valence bond representation: the Jastrow Antisymmetrized Geminal Power (JAGP). All structural and wave function parameters are optimized, including coefficients and exponents of the Gaussian primitives of the AGP and the Jastrow atomic orbitals. Bond lengths and bond anglesare calculated with a statistical error of about 0.1% and are in good agreement with the available experimental data. The Variational and Diffusion Monte Carlo calculations estimate vertical and adiabatic excitation energies in the ranges 4.623(10), 4.688(5) eV and 3.001(5)‚ 3.091(5) eV, respectively. The adiabatic gap, which is in line with other correlated quantumchemistry methods, is slightly higher than the value estimated by recent photodissociation experiments. Our results demonstratehow Quantum Monte Carlo calculations have become a promising and computationally affordable tool for the structural optimization of correlated molecular systems.



Figure 1. We represent the geometrical relaxation of the triplet vertical excitation to it's adiabatic equilibrium, has shown in the movie: Triplet Ethylene geometrical optimization through Quantum Monte Carlo methods


[1] Barborini M., Sorella S., Guidoni L., J. Chem. Theory Comput. 8,1260-1269 (2012)

[2] S. Sorella and S. Capriotti, J. Chem. Phys. 133, 234111 (2010)


Structure and harmonic frequencies of water molecule and dimer by Quantum Monte Carlo

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The correct description of water-water interactions is still a challenge for many electronic structure methods, such as density functional theory. the Quantum Monte Carlo methods have proven to describe  correctly both the dipole moment and the binding energy of the water dimer1 the latter being crucial for a proper description of the Hydrogen bond.


Figure 1 : The component  along the x axis of the forces acting on the oxygen atom of the water monomer as a function of the atomic movement ?R of the oxygen


As variational wave function we used an Antisymmetrized Geminal power with a Jastrow factor (JAGP), fully optimized through a stochastic reconfiguration procedure (SRH)2. Within this scheme we obtained Variational Monte Carlo (VMC) results, which are of the same quality than those obtained by the Diffusion Monte Carlo (LRDMC)2 a much more computationally demanding scheme. In the present contribution we have used the extended AGP molecular orbitals scheme described in reference3 to study the electronic and structural properties of the water monomer and dimer. Ionic forces are calculated at the VMC level using the scheme introduced in reference4. Normal modes and harmonic frequencies are calculated for the water monomer and compared with the experimental data and quantum chemistry calculation such as Coupled Cluster5,6.


1 F. Sterpone et al., J. Chem. Theo. Comp., 4, 1428-1434 (2008)

2 S. Sorella, Phys. Rev. B 64, 024512 (2001)

3M. Marchi et al., J. Chem. Phys. 131, 154116 (2009)

4C. Attaccalite and S. Sorella, Phys. Rev. Lett. 100, 114501 (2008)

5D. Feller, A. Peterson, J. Chem. Phys. 131, 154306 (2009)

6P.H.-L. Sit,, N. Marzari, J. Chem. Phys. 122, 204510 (2005)

7C. Filippi and C. J. Umrigar, Phys. Rev. B, 61R, 16291 (2000)


Water Hydrogen Bonding

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Using Quantum Monte Carlo we studied the dissociation energy and the dispersion curve of the water dimer, a prototype of hydrogen bonded system. Our calculations are based ona wave function which is a modern and fully correlated implementation of the Pauling's valence bond idea: the Jastrow Antisymmetrised Geminal Power (JAGP) [Casula et al. J. Chem. Phys. 2003, 119, 6500-6511]. With this variational wave function we obtain a binding energy of -4.5(0.1) kcal/ mol that is only slightly increased to -4.9(0.1) kcal/mol by using the Lattice Regularized Diffusion Monte Carlo (LRDMC). This projection technique allows for the substantial improvement in the correlation energy of a given variational guess and indeed, when applied to the JAGP, yields a binding energy in fair agreement with the value of -5.0 kcal/mol reported by experiments and other theoretical works. The minimum position, the curvature, and the asymptotic behavior of the dispersion curve are well reproduced both at the variational and the LRDMC level. Moreover, thanks to the simplicity and the accuracy of our variational approach, we are able to dissect the various contributions  to the binding energy of the water dimer in a systematic and controlled way. This is achieved by appropriately switching off determinantal and Jastrow variational terms in the JAGP. Within this scheme, we estimate that the dispersive van der Waals contribution to the electron correlation is substantial and amounts to 1.5(0.2) kcal/mol, this value being comparable with the intermolecular covalent energy that we find to be 1.1(0.2) kcal/mol. The present Quantum Monte Carlo approach based on the JAGP wave function is revealed as a promising tool for the interpretation and the quantitative description of weakly interacting systems, where both dispersive and covalent energy contributions play an important role.


Variational Monte Carlo density countour of the water dimer


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