Michele Ceotto

We present a single-trajectory semiclassical method of spectroscopic accuracy for the calculation of molecular vibrational energies. The century old challenge of extending the Brillouin, Wentzel, and Kramers quantization rule for accurate predictions of energy levels in multidimensional systems is answered in two steps. One is ensuring that the semiclassical energy estimate agrees with vibrational perturbation theory. This is achieved by adding a constant energy shift of order ℏ2 to the quantization condition, which is readily estimated through knowledge of the third and fourth potential derivatives. The second is adapting the Fourier transform method to obtain an objective criterion for the validity of the adiabatic switching technique, which lies at the heart of the implementation of the Einstein–Brillouin–Keller semiclassical quantization method in multidimensional systems. The Fourier coefficients are calculated approximately by means of a single classical trajectory introduced to ascertain that indeed the actions were reasonably well conserved during the adiabatic switching phase. The result is a rather accurate single trajectory based quantization method. The theory is tested on bi-dimensional Hénon–Heiles models and on the non-rotating water molecule. When comparing with second-order perturbation theory and the current semiclassical accuracy, our approach is by far more accurate. This is remarkable, especially when considering that accurate energy evaluation on an absolute scale is important not only on the conceptual level of modification of the century old semiclassical quantization approximation but also in practice, as it affects different problems, such as non-adiabatic transitions, reaction rates, and isotopic effects.

We use the Meyer–Miller formalism and the Caldeira–Leggett model with its associated and discretized spectral density formalism, to explore the impact of harmonic oscillator baths on the spectral line shapes of single- and two-spinI=12 NMR spin systems. The complex coefficients associated with the spin degrees of freedom are treated as classical position, qn, and momentum, pn, variables to investigate the coupling to the classical harmonic bath oscillators. The expressions derived for the motion of the density matrix elements associated with the observable NMR signal and modulated by the bath oscillators are used in the numerical simulations of NMR spectra. Unlike existing relaxation theories such as the Redfield theory, the method is not limited to short, bath correlation times. This is considered a strength of the method, and simulations have been performed at bath correlation times considered to be on the limit or beyond regimes where Redfield theory usually is applicable. Simulated line shapes are considerably broader than those predicted by Redfield theory. These results are discussed in terms of inclusion of nonsecular bath frequencies and how properties of the bath oscillators are defined.

The combination band just above 2000 cm−1 appearing in the infrared spectrum of liquid water is well known from experiments, and it is thought to originate from the combination of bending motions of the water molecules and the large-amplitude libration modes of the condensed phase. While classical simulations cannot genuinely reproduce this band, here we show that this exquisitely quantum signal can be simulated by on-the-fly ab initio semiclassical molecular dynamics. The number of atoms involved in reproducing this combination band, which is also known as the “association band” of liquid water, shows that this condensed phase signal is quite local.

This review, aimed at both the expert and general audience, describes the main methods to simulate vibrational spectroscopy from classical trajectories. It serves as an introduction to simulation of nuclear quantum effects in vibrational dynamics.

Many amino acids are neutral in the gas phase but are found in the zwitterionic form in water due to their interaction with the hydrogen bond network of the solvent. For instance, glycine is known to switch from neutral to its zwitterionic form in about 6-10 solvating molecules. In this article, we employ terahertz (THz) vibrational spectroscopy at 0.37 K in helium nanodroplets in synergy with DFT molecular dynamics to study the H-bonding network changes from neutral to zwitterionic glycine. Zwitterionization is found to result in an increased absorption for the fully deuterated zwitterionic species solvated by 10 water molecules between 150 and 300 cm^-1 experimentally and confirmed by calculations based on DFT quasi-classical trajectory dynamics. The experimental observation of a spectral signal at about 320 cm^-1 for the zwitterionic complex is rationalized based on a suitable cross-correlation function between the H and O atoms which are involved in the solvating process. This study deciphers how zwitterionization implies a rearrangement of the H-bonding network.

Classical-trajectory-based methods calculate the vibrational spectrum of a molecular system as the Fourier transform of an appropriate time correlation function. In this paper, we assess the quantumness of different approaches derived from the path-integral representation of quantum mechanics. We focus on power spectra obtained by means of semiclassical (SC) dynamics, centroid molecular dynamics (CMD), ring polymer molecular dynamics (RPMD), and its thermostatted version (TRPMD). Our calculations also include classical and quasi-classical trajectory (QCT) simulations as examples of results based on a purely classical propagator. Calculations are performed for a three-dimensional anharmonic model system and the non-rotating gas-phase water molecule. We show that typical features of classical calculations, such as sum-of-frequency combination bands and overtones, difference bands, and spectroscopic signals at negative frequencies, are found for classical, QCT, CMD, and (T)RPMD spectra. Conversely, these features are basically absent in semiclassical calculations, which show just a reminiscence of the underlying classical trajectory. The overall accuracy of the results compared to quantum mechanical values is always better for SC methods. Classical results depend on the initial sampling distributions, and their accuracy is of the same order as CMD, RPMD, and TRPMD simulations, i.e., an order of magnitude lower than for semiclassical approaches. Our main conclusion is that when it comes to molecular vibrational spectroscopy calculations, semiclassical methods have a predominant quantum character, being able to include also real-time coherence effects, while CMD, RPMD, and TRPMD are prevalently classical, reproducing just the anharmonicity related to the zero point energy or quantum statistical distribution.

Noble gas cryogenic matrices and their effects on the tunneling reactivity of embedded molecules.

Recently—Lanzi et al., J. Chem. Phys. 160, 214107 (2024)—we introduced a time averaged approach to infrared (IR) spectroscopy. The pivotal advance in that paper was represented by the possibility to get accurate semiclassical estimates of the IR absorption intensities and associated transition frequencies from a single calculation. However, the method relies on the convergence of Monte Carlo integrations based on the generation of thousands of pairs of semiclassical trajectories. This makes the approach highly accurate but limited to small, few-atom molecules. Here, we build on the theoretical grounds of that work to extend the application of the method to larger molecules. The goal is achieved by moving to tailored single-pair trajectory calculations and introducing a partially time-independent approximation to the real part of the coherent state overlap. Upon testing the level of accuracy on small molecules such as water, formaldehyde, and methane, we calculate IR spectra for ethanol and glycine. Vibrational intensities and frequencies are found to be fairly accurate, and the method can be straightforwardly applied to larger molecular systems.

In this work, we propose a method to compute semiclassical absorption spectra of nonadiabatic systems. We first report the working formula for the absorption cross section for diabatically coupled systems and review the main features of the Meyer–Miller–Stock–Thoss Hamiltonian and its semiclassical propagation. Then, by combining the mapped Hamiltonian and the initial value representation formalism, we introduce a time-averaged semiclassical method for the calculation of the absorption spectrum, which also accounts for nonadiabatic effects in vibronic spectroscopy. After improving an already existing symplectic algorithm for the symplectic phase space propagation, we consider a model system to benchmark our semiclassical approach against exact quantum mechanical calculations. Finally, we test our method on the four mode model of pyrazine—a fundamental benchmark in the field of nonadiabatic vibronic spectroscopy—for understanding the potentiality and limitations of our semiclassical approach.