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Register a new userChemical accuracy from quantum Monte Carlo for the Benzene Dimer
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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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We report results of both Diffusion Quantum Monte Carlo(DMC) method and Reptation Quantum Monte Carlo(RMC) method on the potential energy curve of the helium dimer. We show that it is possible to obtain a highly accurate description of the helium dimer. An improved stochastic reconfiguration technique is employed to optimize the many-body wave function, which is the starting point for highly accurate simulations based on the Diffusion Quantum Monte Carlo(DMC) and Reptation Quantum Monte Carlo (RMC) methods. We find that the results of these methods are in excellent agreement with the best theoretical results at short range, especially recently developed Reptation Quantum Monte Carlo(RMC) method, yield practically accurate results with reduced statistical error, which gives very excellent agreement across the whole potential. For the equilibrium internuclear distance of 5.6 bohr, the calculated electronic energy with Reptation Quantum Monte Carlo(RMC) method is 5.807483599$pm$0.000000015 hartrees and the corresponding well depth is -11.003$pm$0.005 K.
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.
We propose a modified coupled cluster Monte Carlo algorithm that stochastically samples connected terms within the truncated Baker--Campbell--Hausdorff expansion of the similarity transformed Hamiltonian by construction of coupled cluster diagrams on the fly. Our new approach -- diagCCMC -- allows propagation to be performed using only the connected components of the similarity-transformed Hamiltonian, greatly reducing the memory cost associated with the stochastic solution of the coupled cluster equations. We show that for perfectly local, noninteracting systems, diagCCMC is able to represent the coupled cluster wavefunction with a memory cost that scales linearly with system size. The favorable memory cost is observed with the only assumption of fixed stochastic granularity and is valid for arbitrary levels of coupled cluster theory. Significant reduction in memory cost is also shown to smoothly appear with dissociation of a finite chain of helium atoms. This approach is also shown not to break down in the presence of strong correlation through the example of a stretched nitrogen molecule. Our novel methodology moves the theoretical basis of coupled cluster Monte Carlo closer to deterministic approaches.
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.
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.
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