Using Diffusion Monte Carlo Wave Functions to Analyze the Vibrational Spectra of H₇O₃⁺ and H₉O₄⁺

Abstract

An approach for evaluating spectra from ground state probability amplitudes (GSPA) obtained from diffusion Monte Carlo (DMC) simulations is extended to improve the description of excited state energies and allow for coupling among vibrational excited states. This approach is applied to studies of the protonated water trimer and tetramer, and their deuterated analogs. These ions provide models for solvated hydronium, and analysis of these spectra provides insights into spectral signatures of proton transfer in aqueous environments. In this approach, we obtain a separable set of internal coordinates from the DMC ground state probability amplitude. A basis is then developed from products of the DMC ground state wave function and low-order polynomials in these internal coordinates. This approach provides a compact basis in which the Hamiltonian and dipole moment matrix are evaluated and used to obtain the spectrum. The resulting spectra are in good agreement with experiment and in many cases provide comparable agreement to the results obtained using much larger basis sets. In addition, the compact basis allows for interpretation of the spectral features and how they evolve with cluster size and deuteration.

Diffusion Monte Carlo approaches for studying nuclear quantum effects in fluxional molecules

“…There are several approaches that can be used to obtain the probability amplitude, and we will focus on three, which have been used in studies of molecular vibrations. Examples include molecular ions like , 74 , 75,76 and H + (H 2 O) n 27,77,78 …”

“…On the other hand, we know that considerable information is encoded in the ground state wave function. In a second approach, which we call the ground state probability amplitude (GSPA) approximation, we analyze the ground state probability amplitude to obtain transition energies and intensities for transitions involving one or two quanta of excitation 78,93,94 . In this way only the ground state DMC calculation is needed to obtain the spectrum.…”

“…The evaluation of the expectation value of the kinetic energy operator, ⟨ T ⟩, is less obvious as it requires derivatives with respect to the internal coordinates. On the other hand, we can utilize the relationships between ⟨ p 2 ⟩ and ⟨ q 2 ⟩ for the harmonic oscillator to develop approximate expressions for ⟨ T ⟩ in terms of expectation values of q n 78,93 …”

“…Additional details of the approach can be found in our earlier studies, particularly Ref. 78. In that work, we showed that the results of the GSPA approach provides spectra for H 3 O 2 − , 93 H 5 O 2 + , 94 H 7 O 3 + , and H 9 O 4 + 78 that are in good agreement with other approaches, specifically the VSCF/VCI approach coded in the MULTIMODE program developed by Bowman and co‐workers 95 and fixed‐node DMC calculations.…”

Exploring the Origins of Spectral Signatures of Strong Hydrogen Bonding in Protonated Water Clusters

“…As examples, we will focus on protonated water clusters with 2–4 water molecules. These clusters have O D H stretching frequencies that vary from 1000 to 2600 cm –1 . ,,− At the same time, transitions have been assigned by experiment and theory to combinations of the shared proton stretch and the displacement of the donor and acceptor in H + (H 2 O) 2 , and H + (H 2 O) 4 , but not in the case of H + (H 2 O) 3 .…”