Diffusion Monte Carlo in Internal Coordinates

Isotope Effects on Ground and Excited States of Ethyl Cation, H+(C2H4)

The structure and spectra of ethyl cation, H⁺(C₂H₄), and its deuterated analogues are investigated using diffusion Monte Carlo (DMC). These calculations all show that the ground state wave function for H⁺(C₂H₄) is localized near the minimum energy configuration in which the excess proton is in a bridging configuration, although the amplitude of the vibrational motions of the bridging proton is large. Deuteration of the bridging proton reduces the amplitude of this motion, while deuteration of only the ethylenic hydrogen atoms in H⁺(C₂D₄) has little effect on the amplitude of the motion of the bridging proton. Excited states that are accessed by spectroscopically observed transitions in H⁺(C₂H₄) are calculated using fixed-node DMC. The calculated and measured frequencies for the states with one quantum of excitation in the ethylenic CH stretching vibrations show good agreement. We also explore the excited state with one quantum of excitation in the proton transfer vibration of the bridging proton and obtain a frequency of 616 cm^-1 for H⁺(C₂H₄). This frequency increases to 629 cm^-1 in H⁺(C₂D₄). Deuteration decreases this frequency to 491 and 495 cm^-1 in D⁺(C₂H₄) and D⁺(C₂D₄), respectively. The effects of partial deuteration on the frequencies of the CH stretching vibrations, and the corresponding probability amplitudes are also explored. Finally, we report the vibrationally averaged rotational constants for the four isotopologues of ethyl cation considered in this study.

Diffusion Monte Carlo simulations of gas phase and adsorbed D2-(H2)n clusters

We have computed ground state energies and analyzed radial distributions for several gas phase and adsorbed D₂(H₂)_n and HD(H₂)_n clusters. An external model potential designed to mimic ionic adsorption sites inside porous materials is used [M. Mella and E. Curotto, J. Phys. Chem. A 121, 5005 (2017)]. The isotopic substitution lowers the ground state energies by the expected amount based on the mass differences when these are compared with the energies of the pure clusters in the gas phase. A similar impact is found for adsorbed aggregates. The dissociation energy of D₂ from the adsorbed clusters is always much higher than that of H₂ from both pure and doped aggregates. Radial distributions of D₂ and H₂ are compared for both the gas phase and adsorbed species. For the gas phase clusters, two types of hydrogen-hydrogen interactions are considered: one based on the assumption that rotations and translations are adiabatically decoupled and the other based on nonisotropic four-dimensional potential. In the gas phase clusters of sufficiently large size, we find the heavier isotopomer more likely to be near the center of mass. However, there is a considerable overlap among the radial distributions of the two species. For the adsorbed clusters, we invariably find the heavy isotope located closer to the attractive interaction source than H₂, and at the periphery of the aggregate, H₂ molecules being substantially excluded from the interaction with the source. This finding rationalizes the dissociation energy results. For D₂-(H₂)_n clusters with n≥12, such preference leads to the desorption of D₂ from the aggregate, a phenomenon driven by the minimization of the total energy that can be obtained by reducing the confinement of (H₂)₁₂. The same happens for (H₂)₁₃, indicating that such an effect may be quite general and impact on the absorption of quantum species inside porous materials.

Advances in spectroscopy and dynamics of small and medium sized molecules and clusters

Investigations of the spectroscopy and dynamics of small- and medium-sized molecules and clusters represent a hot topic in atmospheric chemistry, biology, physics, atto- and femto-chemistry and astrophysics.

Smart darting diffusion Monte Carlo: Applications to lithium ion-Stockmayer clusters

In a recent investigation [K. Roberts et al., J. Chem. Phys. 136, 074104 (2012)], we have shown that, for a sufficiently complex potential, the Diffusion Monte Carlo (DMC) random walk can become quasiergodic, and we have introduced smart darting-like moves to improve the sampling. In this article, we systematically characterize the bias that smart darting moves introduce in the estimate of the ground state energy of a bosonic system. We then test a simple approach to eliminate completely such bias from the results. The approach is applied for the determination of the ground state of lithium ion-n-dipoles clusters in the n = 8-20 range. For these, the smart darting diffusion Monte Carlo simulations find the same ground state energy and mixed-distribution as the traditional approach for n < 14. In larger systems we find that while the ground state energies agree quantitatively with or without smart darting moves, the mixed-distributions can be significantly different. Some evidence is offered to conclude that introducing smart darting-like moves in traditional DMC simulations may produce a more reliable ground state mixed-distribution.

Probing the Relationship Between Large-Amplitude Motions in H5(+) and Proton Exchange Between H3(+) and H2

Understanding the spectroscopy and dynamics of H5(+) is central in gaining insights into the H3(+) + H2 → H5(+) → H2 + H3(+) proton transfer reaction. This molecular ion exhibits large-amplitude vibrations, which allow for the transfer of a proton between H3(+) and H2 even in its ground vibrational state. With vibrational excitation, the number of open channels for permutations of protons increase. In this work, the minimized energy path variant of diffusion Monte Carlo is used to investigate how the energetically accessible proton permutations evolve as H5(+) is dissociated into H3(+) + H2. Two mechanisms for proton permutation are investigated. The first is the proton hop, which correlates to large-amplitude vibrations of the central proton in H5(+). The second is the exchange of a pair of hydrogen atoms between H3(+) and H2. This mechanism requires several proton hops along with a 120° rotation of H3(+) within the H5(+) molecular ion. This analysis shows that while there is a narrow region of configuration space over which both isomerization processes are energetically accessible, full permutation of the five protons in H5(+) more likely occurs through a stepwise mechanism. Such full permutation of the protons becomes accessible when the shared proton stretch is excited to the vpt = 2 or 3 excited state. The effects of deuteration and rotational excitation of the H2 and H3(+) products are also investigated. Deuteration inhibits permutation of protons, while rotational excitation has only a small impact on these processes.

Assessing the Performance of the Diffusion Monte Carlo Method As Applied to the Water Monomer, Dimer, and Hexamer

The diffusion Monte Carlo (DMC) method is applied to the water monomer, dimer, and hexamer using q-TIP4P/F, one of the most simple empirical water models with flexible monomers. The bias in the time step (Δτ) and population size (Nw) is investigated. For the binding energies, the bias in Δτ cancels nearly completely, whereas a noticeable bias in Nw remains. However, for the isotope shift (e.g, in the dimer binding energies between (H2O)2 and (D2O)2), the systematic errors in Nw do cancel. Consequently, very accurate results for the latter (within ∼0.01 kcal/mol) are obtained with moderate numerical effort (Nw ∼ 10(3)). For the water hexamer and its (D2O)6 isotopomer, the DMC results as a function of Nw are examined for the cage and prism isomers. For a given isomer, the issue of the walker population leaking out of the corresponding basin of attraction is addressed by using appropriate geometric constraints. The population size bias for the hexamer is more severe, and to maintain accuracy similar to that of the dimer, Nw must be increased by ∼2 orders of magnitude. Fortunately, when the energy difference between the cage and prism is taken, the biases cancel, thereby reducing the systematic errors to within ∼0.01 kcal/mol when using a population of Nw = 4.8 × 10(5) walkers. Consequently, a very accurate result for the isotope shift is also obtained. Notably, both the quantum and isotope effects for the prism-cage energy difference are small.

Stochastic many-body perturbation theory for anharmonic molecular vibrations

A new quantum Monte Carlo (QMC) method for anharmonic vibrational zero-point energies and transition frequencies is developed, which combines the diagrammatic vibrational many-body perturbation theory based on the Dyson equation with Monte Carlo integration. The infinite sums of the diagrammatic and thus size-consistent first- and second-order anharmonic corrections to the energy and self-energy are expressed as sums of a few m- or 2m-dimensional integrals of wave functions and a potential energy surface (PES) (m is the vibrational degrees of freedom). Each of these integrals is computed as the integrand (including the value of the PES) divided by the value of a judiciously chosen weight function evaluated on demand at geometries distributed randomly but according to the weight function via the Metropolis algorithm. In this way, the method completely avoids cumbersome evaluation and storage of high-order force constants necessary in the original formulation of the vibrational perturbation theory; it furthermore allows even higher-order force constants essentially up to an infinite order to be taken into account in a scalable, memory-efficient algorithm. The diagrammatic contributions to the frequency-dependent self-energies that are stochastically evaluated at discrete frequencies can be reliably interpolated, allowing the self-consistent solutions to the Dyson equation to be obtained. This method, therefore, can compute directly and stochastically the transition frequencies of fundamentals and overtones as well as their relative intensities as pole strengths, without fixed-node errors that plague some QMC. It is shown that, for an identical PES, the new method reproduces the correct deterministic values of the energies and frequencies within a few cm(-1) and pole strengths within a few thousandths. With the values of a PES evaluated on the fly at random geometries, the new method captures a noticeably greater proportion of anharmonic effects.