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The Journal of Chemical Physics

Vibronic energies and spectra of molecular dimers

Alexander Eisfeld, Lars Braun, Walter T. Strunz, J S Briggs, J. Beck, Volker Engel

Published Mar 30, 2005• 82 citations
Publisher

Abstract

We consider three distinct methods of calculating the vibronic levels and absorption spectra of molecular dimers coupled by dipole-dipole interactions. The first method is direct diagonalization of the vibronic Hamiltonian in a basis of monomer eigenstates. The second method is to use creation and annihilation operators leading in harmonic approximation to the Jaynes-Cummings Hamiltonian. The adiabatic approximation to this problem provides insight into spectral behavior in the weak and strong coupling limits. The third method, which serves as a check on the accuracy of the previous methods, is a numerically exact solution of the time-dependent Schrodinger equation. Using these methods, dimer spectra are calculated for three separate dye molecules and show good agreement with measured spectra.

DOI
10.1063/1.1861883

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We consider three distinct methods of calculating the vibronic levels and absorption spectra of molecular dimers coupled by dipole-dipole interactions. The first method is direct diagonalization of the vibronic Hamiltonian in a basis of monomer eigenstates. The second method is to use creation and annihilation operators leading in harmonic approximation to the Jaynes-Cummings Hamiltonian. The adiabatic approximation to this problem provides insight into spectral behavior in the weak and strong coupling limits. The third method, which serves as a check on the accuracy of the previous methods, is a numerically exact solution of the time-dependent Schrodinger equation. Using these methods, dimer spectra are calculated for three separate dye molecules and show good agreement with measured spectra.
We present a quantum algorithm for calculating the vibronic spectrum of a molecule, a useful but classically hard problem in chemistry. We show several advantages over previous quantum approaches: vibrational anharmonicity is naturally included; after measurement, some state information is preserved for further analysis; and there are potential error-related benefits. Considering four triatomic molecules, we numerically study truncation errors in the harmonic approximation. Further, in order to highlight the fact that our quantum algorithm's primary advantage over classical algorithms is in simulating anharmonic spectra, we consider the anharmonic vibronic spectrum of sulfur dioxide. In the future, our approach could aid in the design of materials with specific light-harvesting and energy transfer properties, and the general strategy is applicable to other spectral calculations in chemistry and condensed matter physics.
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Spectroscopy is one of the most accurate probes of the molecular world. However, predicting molecular spectra accurately is computationally difficult because of the presence of entanglement between electronic and nuclear degrees of freedom. Although quantum computers promise to reduce this computational cost, existing quantum approaches rely on combining signals from individual eigenstates, an approach that is difficult to scale because the number of eigenstates grows exponentially with molecule size. Here, we introduce a method for scalable analog quantum simulation of molecular spectroscopy, by performing simulations in the time domain. Our approach can treat more complicated molecular models than previous ones, requires fewer approximations, and can be extended to open quantum systems with minimal overhead. We present a direct mapping of the underlying problem of time-domain simulation of molecular spectra to the degrees of freedom and control fields available in a trapped-ion quantum simulator. We experimentally demonstrate our algorithm on a trapped-ion device, exploiting both intrinsic electronic and motional degrees of freedom, showing excellent quantitative agreement for a single-mode vibronic photoelectron spectrum of SO2_22​.
Measuring vibronic spectra probes dynamical processes in molecular systems. When interpreted via suitable theoretical tools, the experimental data provides comprehensive information about the system in question. For complex many-body problems, such an approach usually requires the formulation of proper classical-like approximations, which is particularly challenging if multiple electronic states are involved. In this work, we express the imaginary-time shifted time correlation function and, thus, the vibronic spectrum in terms of the so-called Matsubara dynamics, which combines quantum statistics and classical-like dynamics. By applying the Matsubara approximation in the adiabatic limit, we derive a formal generalization of the existing Matsubara dynamics formalism to multiple potential energy surfaces (PESs), which, however, does not feature all the defining properties of its single-PES counterpart though suffering equally from the sign problem. The mathematical analysis for two shifted harmonic oscillators suggests a new modified method to practically simulate the standard correlation function via Matsubara-like dynamics. Importantly, this modified method samples the thermal Wigner function without suffering from the sign problem and yields an accurate approximation to the vibronic absorption spectrum, not only for the harmonic system but also for the anharmonic one.
We present expressions for rates of radiationless transitions in two-level systems with arbitrary coupling to a set of damped vibrational modes; calculations are limited to transitions slower than vibrational relaxation. Explicit results are discussed within the harmonic approximation and Condon approximation; systematic methods are introduced for treating non-Condon and anharmonic effects. Results relevant to experiment are (1) significant deviations from the energy-gap law when a small number of vibrational modes is coupled to the transition, (2) dependence of transition rate on homogeneous and inhomogeneous vibrational linewidths, (3) nonexponential decay for transitions with vibrational frequency shifts, and (4) persistence of electronic coherence for long times either at low temperature or when frequency shifts are small. Our approach differs from previous work in the partitioning of the Hamiltonian and in the methods of evaluating operator averages; these differences are discussed in relation to the adiabatic approximation and the irreversibility of the transition.
Using second-order perturbation theory in the light-matter interaction, we derive an analytical approximation for the vibronic populations of a diatomic system excited by ultrabroadband frequency-entangled photons and evaluate the population dynamics for different degrees of entanglement between photon pairs. Our analytical approach makes the same predictions as previously derived via numerical solutions of the complete Schrödinger equation [H. Oka, ], with the added advantage of providing clear physical insights into the vibronic selectivity as a function of the degree of photon correlations while requiring significantly reduced computational effort. Specifically, our analytical expression for the probability of vibronic excitation includes a factor which predicts the enhancement of vibrational selectivity as a function of the degree correlation between the entangled photon pairs, the targeted vibrational energy level, and the vibrational molecular structure encoded in the Franck-Condon factors. Our results illustrate the importance of going beyond the usual approximations in second-order perturbation theory to capture the relevance of the vibrational structure of the molecular system of interest in order to gain a deeper understanding of the possible quantum-enhancement provided by the interaction between quantum light and matter.