Construction of electronic diabatic states within a molecular orbital scheme

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.

Coupling electrons and vibrations in molecular quantum chemistry

We derive an electron-vibration model Hamiltonian in a quantum chemical framework and explore the extent to which such a Hamiltonian can capture key effects of nonadiabatic dynamics. The model Hamiltonian is a simple two-body operator, and we make preliminary steps at applying standard quantum chemical methods to evaluate its properties, including mean-field theory, linear response, and a primitive correlated model. The Hamiltonian can be compared to standard vibronic Hamiltonians, but it is constructed without reference to potential energy surfaces through direct differentiation of the one- and two-electron integrals at a single reference geometry. The nature of the model Hamiltonian in the harmonic and linear-coupling regime is investigated for pyrazine, where a simple time-dependent calculation including electron-vibration correlation is demonstrated to exhibit the well-studied population transfer between the S₂ and S₁ excited states.

Analysis of geometric phase effects in the quantum-classical Liouville formalism

We analyze two approaches to the quantum-classical Liouville (QCL) formalism that differ in the order of two operations: Wigner transformation and projection onto adiabatic electronic states. The analysis is carried out on a two-dimensional linear vibronic model where geometric phase (GP) effects arising from a conical intersection profoundly affect nuclear dynamics. We find that the Wigner-then-Adiabatic (WA) QCL approach captures GP effects, whereas the Adiabatic-then-Wigner (AW) QCL approach does not. Moreover, the Wigner transform in AW-QCL leads to an ill-defined Fourier transform of double-valued functions. The double-valued character of these functions stems from the nontrivial GP of adiabatic electronic states in the presence of a conical intersection. In contrast, WA-QCL avoids this issue by starting with the Wigner transform of single-valued quantities of the full problem. As a consequence, GP effects in WA-QCL can be associated with a dynamical term in the corresponding equation of motion. Since the WA-QCL approach uses solely the adiabatic potentials and non-adiabatic derivative couplings as an input, our results indicate that WA-QCL can capture GP effects in two-state crossing problems using first-principles electronic structure calculations without prior diabatization or introduction of explicit phase factors.

Space-time contours to treat intense field-dressed molecular states

In this article we consider a molecular system exposed to an intense short-pulsed external field. It is a continuation of a previous publication [A. K. Paul, S. Adhikari, D. Mukhopadhyay et al., J. Phys. Chem. A 113, 7331 (2009)] in which a theory is presented that treats quantum effects due to nonclassical photon states (known also as Fock states). Since these states became recently a subject of intense experimental efforts we thought that they can be treated properly within the existing quantum formulation of dynamical processes. This was achieved by incorporating them in the Born-Oppenheimer (BO) treatment with time-dependent coefficients. The extension of the BO treatment to include the Fock states results in a formidable enhancement in numerical efforts expressed, in particular, in a significant increase in CPU time. In the present article we discuss an approach that yields an efficient and reliable approximation with only negligible losses in accuracy. The approximation is tested in detail for the dissociation process of H(2) (+) as caused by a laser field.

Space-time contours to treat intense field-dressed molecular states. I. Theory

A molecular system exposed to an intense external field is considered. The strength of the field is measured by the number L of electronic states that become populated during this process. In the present article the authors discuss a rigorous way, based on the recently introduced space-time contours [R. Baer, et al., J. Chem. Phys. 119, 6998 (2003)], to form N coupled Schrodinger equations where N<L, which maintains the effects due to the remaining (L-N) populated states. It is shown that whereas the size of L is unlimited, the main requirement concerning N is that the original group of N field-free states forms a Hilbert subspace in the spatial region of interest. From previous studies it is known that a group of states forms a Hilbert subspace if and only if the corresponding topological D matrix is diagonal [M. Baer, et al., Farad, Discuss 127, 337 (2004)].

Nonadiabatic effects in C–Br bond scission in the photodissociation of bromoacetyl chloride

Bromoacetyl chloride photodissociation has been interpreted as a paradigmatic example of a process in which nonadiabatic effects play a major role. In molecular beam experiments by Butler and co-workers [J. Chem. Phys. 95, 3848 (1991); J. Chem. Phys. 97, 355 (1992)], BrCH2C(O)Cl was prepared in its ground electronic state (S0) and excited with a laser at 248 nm to its first excited singlet state (S1). The two main ensuing photoreactions are the ruptures of the C-Cl bond and of the C-Br bond. A nonadiabatic model was proposed in which the C-Br scission is strongly suppressed due to nonadiabatic recrossing at the barrier formed by the avoided crossing between the S1 and S2 states. Recent reduced-dimensional dynamical studies lend support to this model. However, another interpretation that has been given for the experimental results is that the reduced probability of C-Br scission is a consequence of incomplete intramolecular energy redistribution. To provide further insight into this problem, we have studied the energetically lowest six singlet electronic states of bromoacetyl chloride by using an ab initio multiconfigurational perturbative electronic structure method. Stationary points (minima and saddle points) and minimum energy paths have been characterized on the S0 and S1 potential energy surfaces. The fourfold way diabatization method has been applied to transform five adiabatic excited electronic states to a diabatic representation. The diabatic potential energy matrix of the first five excited singlet states has been constructed along several cuts of the potential energy hypersurfaces. The thermochemistry of the photodissociation reactions and a comparison with experimental translational energy distributions strongly suggest that nonadiabatic effects dominate the C-Br scission, but that the reaction proceeds along the energetically allowed diabatic pathway to excited-state products instead of being nonadiabatically suppressed. This conclusion is also supported by the low values of the diabatic couplings on the C-Br scission reaction path. The methodology established in the present study will be used for the construction of global potential energy surfaces suitable for multidimensional dynamics simulations to test these preliminary interpretations.

Vibronic coupling and double excitations in linear response time-dependent density functional calculations: Dipole-allowed states of N2

The present study serves two purposes. First, we evaluate the ability of present time-dependent density functional response theory (TDDFRT) methods to deal with avoided crossings, i.e., vibronic coupling effects. In the second place, taking the vibronic coupling effects into account enables us, by comparison to the configuration analysis in a recent ab initio study [J. Chem. Phys. 115, 6438 (2001)], to identify the neglect of double excitations as the prime cause of limited accuracy of these linear response based TDDFRT calculations for specific states. The "statistical averaging of (model) orbital potentials (SAOP)" Kohn-Sham potential is used together with the standard adiabatic local-density approximation (ALDA) for the exchange-correlation kernel. We use the N2 molecule as prototype, since the TDDFRT/SAOP calculations have already been shown to be accurate for the vertical excitations, while this molecule has a well-studied, intricate vibronic structure as well as significant double excitation nature in the lowest 1Pi(u) state at elongated bond lengths. A simple diabatizing scheme is employed to obtain a diabatic potential energy matrix, from which we obtain the absorption spectrum of N2 including vibronic coupling effects. Considering the six lowest dipole allowed transitions of 1Sigma(u)+ and 1Pi(u) symmetry, we observe a good general agreement and conclude that avoided crossings and vibronic coupling can indeed be treated satisfactorily on the basis of TDDFRT excitation energies. However, there is one state for which the accuracy of TDDFRT/ALDA clearly breaks down. This is the state for which the ab initio calculations find significant double excitation character. To deal with double excitation character is an important challenge for time-dependent density functional theory.

A field theoretical approach to calculate electronic Born-Oppenheimer coupling terms

In this paper we suggest to consider the spatial distribution of the Born-Oppenheimer nonadiabatic coupling terms as fields which are created by sources, located at degeneracy points, and which can be derived using the ordinary mathematical tools of field theory. It is shown that the curl-divergence equations as formed within a given Hilbert space [M. Baer, Chem. Phys. Lett. 35, 112 (1975)] can be converted into a set of inhomogeneous coupled Poisson equations which are solved for a given set of boundary conditions. The method is applied to the three-state Hilbert subspace of the H(3) system. The numerical results are compared with ab initio calculations for which a very encouraging fit is found.