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Register a new userLinear and Non-linear Susceptibilities from Diffusion Quantum Monte Carlo: Application to Periodic Hydrogen Chains
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We calculate the linear and non-linear susceptibilities of periodic longitudinal chains of hydrogen dimers with different bond-length alternations using a diffusion quantum Monte Carlo approach. These quantities are derived from the changes in electronic polarization as a function of applied finite electric field - an approach we recently introduced and made possible by the use of a Berry-phase, many-body electric-enthalpy functional. Calculated susceptibilities and hyper-susceptibilities are found to be in excellent agreement with the best estimates available from quantum chemistry - usually extrapolations to the infinite-chain limit of calculations for chains of finite length. It is found that while exchange effects dominate the proper description of the susceptibilities, second hyper-susceptibilities are greatly affected by electronic correlations. We also assess how different approximations to the nodal surface of the many-body wavefunction affect the accuracy of the calculated susceptibilities.
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We present the extension of variational Monte Carlo (VMC) to the calculation of electronic excitation energies and oscillator strengths using time-dependent linear-response theory. By exploiting the analogy existing between the linear method for wave-function optimisation and the generalised eigenvalue equation of linear-response theory, we formulate the equations of linear-response VMC (LR-VMC). This LR-VMC approach involves the first-and second-order derivatives of the wave function with respect to the parameters. We perform first tests of the LR-VMC method within the Tamm-Dancoff approximation using single-determinant Jastrow-Slater wave functions with different Slater basis sets on some singlet and triplet excitations of the beryllium atom. Comparison with reference experimental data and with configuration-interaction-singles (CIS) results shows that LR-VMC generally outperforms CIS for excitation energies and is thus a promising approach for calculating electronic excited-state properties of atoms and molecules.
We provide a pedagogical introduction to the two main variants of real-space quantum Monte Carlo methods for electronic-structure calculations: variational Monte Carlo (VMC) and diffusion Monte Carlo (DMC). Assuming no prior knowledge on the subject, we review in depth the Metropolis-Hastings algorithm used in VMC for sampling the square of an approximate wave function, discussing details important for applications to electronic systems. We also review in detail the more sophisticated DMC algorithm within the fixed-node approximation, introduced to avoid the infamous Fermionic sign problem, which allows one to sample a more accurate approximation to the ground-state wave function. Throughout this review, we discuss the statistical methods used for evaluating expectation values and statistical uncertainties. In particular, we show how to estimate nonlinear functions of expectation values and their statistical uncertainties.
Path integral Monte Carlo approach is used to study the coupled quantum dynamics of the electron and nuclei in hydrogen molecule ion. The coupling effects are demonstrated by comparing differences in adiabatic Born--Oppenheimer and non-adiabatic simulations, and inspecting projections of the full three-body dynamics onto adiabatic Born--Oppenheimer approximation. Coupling of electron and nuclear quantum dynamics is clearly seen. Nuclear pair correlation function is found to broaden by 0.040 a_0 and average bond length is larger by 0.056 a_0. Also, non-adiabatic correction to the binding energy is found. Electronic distribution is affected less, and therefore, we could say that the adiabatic approximation is better for the electron than for the nuclei.
The disiloxane molecule is a prime example of silicate compounds containing the Si-O-Si bridge. The molecule is of significant interest within the field of quantum chemistry, owing to the difficulty in theoretically predicting its properties. Herein, the linearisation barrier of disiloxane is investigated using a fixed-node diffusion Monte Carlo (FNDMC) approach, which is currently the most reliable {it ab initio} method in accounting for an electronic correlation. Calculations utilizing the density functional theory (DFT) and the coupled cluster method with single and double substitutions, including noniterative triples (CCSD(T))are carried out alongside FNDMC for comparison. Two families of basis sets are used to investigate the disiloxane linearisation barrier - Dunnings correlation-consistent basis sets cc-pV$x$Z ($x = $ D, T, and Q) and their core-valence correlated counterparts, cc-pCV$x$Z. It is concluded that FNDMC successfully predicts the disiloxane linearisation barrier and does not depend on the completeness of the basis sets as much as DFT or CCSD(T), thus establishing its suitability.
We report an accurate study of interactions between Benzene molecules using variational quantum Monte Carlo (VMC) and diffusion quantum Monte Carlo (DMC) methods. We compare these results with density functional theory (DFT) using different van der Waals (vdW) functionals. In our QMC calculations, we use accurate correlated trial wave functions including three-body Jastrow factors, and backflow transformations. We consider two benzene molecules in the parallel displaced (PD) geometry, and find that by highly optimizing the wave function and introducing more dynamical correlation into the wave function, we compute the weak chemical binding energy between aromatic rings accurately. We find optimal VMC and DMC binding energies of -2.3(4) and -2.7(3) kcal/mol, respectively. The best estimate of the CCSD(T)/CBS limit is -2.65(2) kcal/mol [E. Miliordos et al, J. Phys. Chem. A 118, 7568 (2014)]. Our results indicate that QMC methods give chemical accuracy for weakly bound van der Waals molecular interactions, comparable to results from the best quantum chemistry methods.
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