Calculation of diabatic states from molecular properties

Polaritonic effects in the vibronic spectrum of molecules in an optical cavity

We present a new computational framework to describe polaritons, which treats photons and electrons on the same footing using coupled-cluster theory. As a proof of concept, we study the coupling between the first electronically excited state of carbon monoxide and an optical cavity. We focus, in particular, on how the interaction with the photonic mode changes the vibrational spectroscopic signature of the electronic state, and how this is affected when tuning the cavity frequency and the light-matter coupling strength. For this purpose, we consider different methodologies and investigate the validity of the Born-Oppenheimer approximation in such situations.

Diabatic States of Molecules

Quantitative simulations of electronically nonadiabatic molecular processes require both accurate dynamics algorithms and accurate electronic structure information. Direct semiclassical nonadiabatic dynamics is expensive due to the high cost of electronic structure calculations, and hence it is limited to small systems, limited ensemble averaging, ultrafast processes, and/or electronic structure methods that are only semiquantitatively accurate. The cost of dynamics calculations can be made manageable if analytic fits are made to the electronic structure data, and such fits are most conveniently carried out in a diabatic representation because the surfaces are smooth and the couplings between states are smooth scalar functions. Diabatic representations, unlike the adiabatic ones produced by most electronic structure methods, are not unique, and finding suitable diabatic representations often involves time-consuming nonsystematic diabatization steps. The biggest drawback of using diabatic bases is that it can require large amounts of effort to perform a globally consistent diabatization, and one of our goals has been to develop methods to do this efficiently and automatically. In this Feature Article, we introduce the mathematical framework of diabatic representations, and we discuss diabatization methods, including adiabatic-to-diabatic transformations and recent progress toward the goal of automatization.

A discontinuous basis enables numerically exact solution of the Schrödinger equation around conical intersections in the adiabatic representation

Solving the vibrational Schrödinger equation in the neighborhood of conical intersections in the adiabatic representation is a challenge. At the intersection point, first- and second-derivative nonadiabatic coupling matrix elements become singular, with the singularity in the second-derivative coupling (diagonal Born-Oppenheimer correction) being non-integrable. These singularities result from discontinuities in the vibronic functions associated with the individual adiabatic states, and our group has recently argued that these divergent matrix elements cancel when discontinuous adiabatic vibronic functions sum to a continuous total nonadiabatic wave function. Here we describe the realization of this concept: a novel scheme for the numerically exact solution of the Schrödinger equation in the adiabatic representation. Our approach is based on a basis containing functions that are discontinuous at the intersection point. We demonstrate that the individual adiabatic nuclear wave functions are themselves discontinuous at the intersection point. This proves that discontinuous basis functions are essential to any tractable method that solves the Schrödinger equation around conical intersections in the adiabatic representation with high numerical precision. We establish that our method provides numerically exact results by comparison to reference calculations performed in the diabatic representation. In addition, we quantify the energetic error associated with constraining the density to be zero at the intersection point, a natural approximation. Prospects for extending the present treatment of a two-dimensional model to systems of higher dimensionality are discussed.

Ab initio calculation of femtosecond-time-resolved photoelectron spectra of NO2 after excitation to the A-band

We present calculations of time-dependent photoelectron spectra of NO₂ after excitation to the A-band for comparison with extreme-ultraviolet (XUV) time-resolved photoelectron spectroscopy. We employ newly calculated potential energy surfaces of the two lowest-lying coupled ²A' states obtained from multi-reference configuration-interaction calculations to propagate the photo-excited wave packet using a split-step-operator method. The propagation includes the nonadiabatic coupling of the potential surfaces as well as the explicit interaction with the pump pulse centered at 3.1 eV (400 nm). A semiclassical approach to calculate the time-dependent photoelectron spectrum arising from the ionization to the eight energetically lowest-lying states of the cation allows us to reproduce the static experimental spectrum up to a binding energy of 16 eV and enables direct comparisons with XUV time-resolved photoelectron spectroscopy.

Charge Transport in Molecular Materials: An Assessment of Computational Methods

The booming field of molecular electronics has fostered a surge of computational research on electronic properties of organic molecular solids. In particular, with respect to a microscopic understanding of transport and loss mechanisms, theoretical studies assume an ever-increasing role. Owing to the tremendous diversity of organic molecular materials, a great number of computational methods have been put forward to suit every possible charge transport regime, material, and need for accuracy. With this review article we aim at providing a compendium of the available methods, their theoretical foundations, and their ranges of validity. We illustrate these through applications found in the literature. The focus is on methods available for organic molecular crystals, but mention is made wherever techniques are suitable for use in other related materials such as disordered or polymeric systems.

Constructing diabatic representations using adiabatic and approximate diabatic data--Coping with diabolical singularities

We have recently introduced a diabatization scheme, which simultaneously fits and diabatizes adiabatic ab initio electronic wave functions, Zhu and Yarkony J. Chem. Phys. 140, 024112 (2014). The algorithm uses derivative couplings in the defining equations for the diabatic Hamiltonian, H(d), and fits all its matrix elements simultaneously to adiabatic state data. This procedure ultimately provides an accurate, quantifiably diabatic, representation of the adiabatic electronic structure data. However, optimizing the large number of nonlinear parameters in the basis functions and adjusting the number and kind of basis functions from which the fit is built, which provide the essential flexibility, has proved challenging. In this work, we introduce a procedure that combines adiabatic state and diabatic state data to efficiently optimize the nonlinear parameters and basis function expansion. Further, we consider using direct properties based diabatizations to initialize the fitting procedure. To address this issue, we introduce a systematic method for eliminating the debilitating (diabolical) singularities in the defining equations of properties based diabatizations. We exploit the observation that if approximate diabatic data are available, the commonly used approach of fitting each matrix element of H(d) individually provides a starting point (seed) from which convergence of the full H(d) construction algorithm is rapid. The optimization of nonlinear parameters and basis functions and the elimination of debilitating singularities are, respectively, illustrated using the 1,2,3,4(1)A states of phenol and the 1,2(1)A states of NH3, states which are coupled by conical intersections.

Complex self-consistent field and multireference single- and double-excitation configuration interaction calculations for the Πg2 resonance state of N2−

Self-consistent field and multireference single- and double-excitation configuration interaction calculations employing the complex basis function technique are carried out for the (2)Pi(g) resonance state of the N(2) (-) molecule as well as several other anionic resonance states in the neighboring energy region. The results of calculations employing the same method for the (1)S (2s(2)) state of the He atom and the (1)Sigma(g) (+) (sigma(u) (2)) state of the H(2) molecule are found to be in good agreement with those of earlier work. The present theoretical treatment has succeeded for the first time in satisfying the rigorous criterion of the complex variational principle in computing the N(2) (-) resonance states, namely, a cusp in the plots of real versus imaginary components of the corresponding complex energies has been located at each internuclear distance. On this basis, it is found that the open-shell orbital in the lowest-energy adiabatic N(2) (-) resonance state of (2)Pi(g) symmetry changes its character from quite compact at large internuclear distance to relatively diffuse for r<2.3a(0). This is in contrast to all previous theoretical treatments of this system that have not rigorously satisfied the complex variational principle in their determination of this wave function.

BEYOND BORN-OPPENHEIMER: Molecular Dynamics Through a Conical Intersection

Nonadiabatic effects play an important role in many areas of physics and chemistry. The coupling between electrons and nuclei may, for example, lead to the formation of a conical intersection between potential energy surfaces, which provides an efficient pathway for radiationless decay between electronic states. At such intersections the Born-Oppenheimer approximation breaks down, and unexpected dynamical processes result, which can be observed spectroscopically. We review the basic theory required to understand and describe conical, and related, intersections. A simple model is presented, which can be used to classify the different types of intersections known. An example is also given using wavepacket dynamics simulations to demonstrate the prototypical features of how a molecular system passes through a conical intersection.