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Register a new userFully quantum description of the Zundel ion: combining variational quantum Monte Carlo with path integral Langevin dynamics
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We introduce a novel approach for a fully quantum description of coupled electron-ion systems from first principles. It combines the variational quantum Monte Carlo (QMC) solution of the electronic part with the path integral (PI) formalism for the quantum nuclear dynamics. On the one hand, the PI molecular dynamics includes nuclear quantum effects by adding a set of fictitious classical particles (beads) aimed at reproducing nuclear quantum fluctuations via a harmonic kinetic term. On the other hand, variational QMC can provide Born-Oppenheimer (BO) potential energy surfaces with a precision comparable to the most advanced post Hartree-Fock approaches, and with a favorable scaling with the system size. To deal with the intrinsic QMC noise, we generalize the PI molecular dynamics using a Langevin thermostat correlated according to the covariance matrix of QMC nuclear forces. The variational parameters of the QMC wave function are evolved during the nuclear dynamics, such that the BO potential energy surface is unbiased. Statistical errors on the wave function parameters are reduced by resorting to bead grouping average, which we show to be accurate and well controlled. Our general algorithm relies on a Trotter breakup between the dynamics driven by ionic forces and the one set by the harmonic interbead couplings. The latter is exactly integrated even in presence of the Langevin thermostat, thanks to the mapping onto an Ornstein-Uhlenbeck process. This framework turns out to be very efficient also in the case of deterministic ionic forces. The new implementation is validated on the Zundel ion by direct comparison with standard PI Langevin dynamics calculations made with a coupled cluster potential energy surface. Nuclear quantum effects are confirmed to be dominant over thermal effects well beyond room temperature giving the excess proton an increased mobility by quantum tunneling.
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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 properties of molecules and materials containing light nuclei are affected by their quantum mechanical nature. Modelling these quantum nuclear effects accurately requires computationally demanding path integral techniques. Considerable success has been achieved in reducing the cost of such simulations by using generalized Langevin dynamics to induce frequency-dependent fluctuations. Path integral generalized Langevin equation methods, however, have this far been limited to the study of static, thermodynamic properties due to the large perturbation to the systems dynamics induced by the aggressive thermostatting. Here we introduce a post-processing scheme, based on analytical estimates of the dynamical perturbation induced by the generalized Langevin dynamics, that makes it possible to recover meaningful time correlation properties from a thermostatted trajectory. We show that this approach yields spectroscopic observables for model and realistic systems which have an accuracy comparable to much more demanding approximate quantum dynamics techniques based on full path integral simulations.
We present an overview of the variational and diffusion quantum Monte Carlo methods as implemented in the CASINO program. We particularly focus on developments made in the last decade, describing state-of-the-art quantum Monte Carlo algorithms and software and discussing their strengths and their weaknesses. We review a range of recent applications of CASINO.
We investigate the use of optimized correlation consistent gaussian basis sets for the study of insulating solids with auxiliary-field quantum Monte Carlo (AFQMC). The exponents of the basis set are optimized through the minimization of the second order M{o}ller--Plesset perturbation theory (MP2) energy in a small unit cell of the solid. We compare against other alternative basis sets proposed in the literature, namely calculations in the Kohn--Sham basis and in the natural orbitals of an MP2 calculation. We find that our optimized basis sets accelerate the convergence of the AFQMC correlation energy compared to a Kohn--Sham basis, and offer similar convergence to MP2 natural orbitals at a fraction of the cost needed to generate them. We also suggest the use of an improved, method independent, MP2-based basis set correction that significantly reduces the required basis set sizes needed to converge the correlation energy. With these developments, we study the relative performance of these basis sets in LiH, Si and MgO, and determine that our optimized basis sets yield the most consistent results as a function of volume. Using these optimized basis sets, we systematically converge the AFQMC calculations to the complete basis set and thermodynamic limit and find excellent agreement with experiment for systems studied. Although we focus on AFQMC, our basis set generation procedure is independent of the subsequent correlated wavefunction method used.
We investigate the continuum limit that the number of beads goes to infinity in the ring polymer representation of thermal averages. Studying the continuum limit of the trajectory sampling equation sheds light on possible preconditioning techniques for sampling ring polymer configurations with large number of beads. We propose two preconditioned Langevin sampling dynamics, which are shown to have improved stability and sampling accuracy. We present a careful mode analysis of the preconditioned dynamics and show their connections to the normal mode, the staging coordinate and the Matsubara mode representation for ring polymers. In the case where the potential is quadratic, we show that the continuum limit of the preconditioned mass modified Langevin dynamics converges to its equilibrium exponentially fast, which suggests that the finite-dimensional counterpart has a dimension-independent convergence rate. In addition, the preconditioning techniques can be naturally applied to the multi-level quantum systems in the nonadiabatic regime, which are compatible with various numerical approaches.
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