Calculation Of Nonadiabatic Couplings Research Articles

Calculations of non-adiabatic couplings within equation-of-motion coupled-cluster framework: Theory, implementation, and validation against multi-reference methods.

We report an implementation of non-adiabatic coupling (NAC) forces within the equation-of-motion coupled-cluster with single and double excitations (EOM-CCSD) framework via the summed-state approach. Using illustrative examples, we compare NAC forces computed with EOM-CCSD and multi-reference (MR) wave functions (for selected cases, we also consider configuration interaction singles). In addition to the magnitude of the NAC vectors, we analyze their direction, which is important for the calculations of the rate of non-adiabatic transitions. Our benchmark set comprises three doublet radical-cations (hexatriene, cyclohexadiene, and uracil), neutral uracil, and sodium-doped ammonia clusters. When the characters of the states agree among different methods, we observe good agreement between the respective NAC vectors, both in the Franck-Condon region and away. In the cases of large discrepancies between the methods, the disagreement can be attributed to the difference in the states' character, which, in some cases, is very sensitive to electron correlation, both within single-reference and multi-reference frameworks. The numeric results confirm that the accuracy of NAC vectors depends critically on the quality of the underlying wave functions. Within their domain of applicability, EOM-CC methods provide a viable alternative to MR approaches.

Performance of Tamm-Dancoff approximation on nonadiabatic couplings by time-dependent density functional theory

The Tamm-Dancoff approximation (TDA), widely used in physics to decouple excitations and de-excitations, is well known to be good for the calculation of excitation energies but not for oscillator strengths. In particular, the sum rule is violated in the latter case. The same concern arises within the TDA in the calculation of nonadiabatic couplings (NACs) by time-dependent density functional theory (TDDFT), due to the similarities in the TDDFT formulations of NACs and oscillator strengths [C. Hu, H. Hirai, and O. Sugino, J. Chem. Phys. 127, 064103 (2007)]. In this study, we present a systematic evaluation of the performance of TDDFT/TDA for the calculation of NACs. In the cases we considered, including a variety of systems possessing Jahn-Teller and Renner-Teller intersections, as well as an example with accidental conical intersections, it is found that the TDDFT/TDA performs better than the full TDDFT, contrary to the conjecture that the TDA might cause the NAC results to deteriorate and violate the sum rule. The surprisingly good performance of the TDA for NACs is probably because the TDA can partially compensate for the local-density-approximation error and give better excitation energies in the vicinity of intersections of potential energy surfaces. Our study also shows that it is important to use the TDA based on the rigorous full-TDDFT formulation of NACs, instead of using it based on an alternative approximate formulation.

Nonadiabatic couplings from time-dependent density functional theory: Formulation by the Kohn-Sham derivative matrix within density functional perturbation theory

We present an improved method for accurately calculating nonadiabatic couplings (NACs) between the ground and excited states of electronic systems, using time-dependent density functional theory (TDDFT) within the plane-wave pseudopotential framework. Based on our previous work that the TDDFT formulation of NACs by the Kohn-Sham derivative matrix elements can avoid the accuracy problem caused by the nonlocal pseudopotentials, we extend the evaluation of these matrix elements to the analytical scheme, achieved by density functional perturbation theory (DFPT). As DFPT has been a standard implementation in many ab initio codes, our scheme requires little effort in the coding. Extensive calculations of NACs near various Jahn-Teller or Renner-Teller intersections show the good accuracy of our results. A comparison of our present and previous work has also clarified an important fact in the TDDFT computation of NACs, regarding the evaluation of the nuclear derivative of the many-body Hamiltonian after mapping to the Kohn-Sham system.

Calculation of nonadiabatic couplings with restricted open-shell Kohn-Sham density-functional theory

This paper generalizes the recently proposed approaches for calculating the derivative couplings between adiabatic states in density-functional theory (DFT) based on a Slater transition-state density to transitions such as singlet-singlet excitations, where a single-determinant ansatz is insufficient. The proposed approach is based on restricted open-shell Frank et al. [J. Chem. Phys. 108, 4060 (1998)] theory used to describe a spin-adapted Slater transition state. To treat the dependence of electron-electron interactions on the nuclear positions, variational linear-response density-functional perturbation theory is generalized to reference states with an orbital-dependent Kohn-Sham Hamiltonian and nontrivial occupation patterns. The methods proposed in this paper are not limited to the calculation of derivative coupling vectors, but can also be used for the calculation of other transition matrix elements. Moreover, they can be used to calculate the linear response of open-shell systems to arbitrary external perturbations in DFT.

Calculation of nonadiabatic couplings in density-functional theory

This paper proposes methods for calculating the derivative couplings between adiabatic states in density-functional theory (DFT) and compares them with each other and with multiconfigurational self-consistent field calculations. They are shown to be accurate and, as expected, the costs of their calculation scale more favorably with system size than post-Hartree-Fock calculations. The proposed methods are based on single-particle excitations and the associated Slater transition-state densities to overcome the problem of the unavailability of multielectron states in DFT which precludes a straightforward calculation of the matrix elements of the nuclear gradient operator. An iterative scheme employing linear-response theory was found to offer the best trade-off between accuracy and efficiency. The algorithms presented here have been implemented for doublet-doublet excitations within a plane-wave-basis and pseudopotential framework but are easily generalizable to other excitations and basis sets. Owing to their fundamental importance in cases where the Born-Oppenheimer separation of motions is not valid, these derivative couplings can facilitate, for example, the treatment of nonadiabatic charge transfers, of electron-phonon couplings, and of radiationless electronic transitions in DFT.

Multi-Partitioning QDPT and Difference-Dedicated CI Calculations of Non-Adiabatic Couplings: Application to Charge Transfer in LiF System

Potential energy and non-adiabatic coupling functions for the two lowest 1 Σ + states of LiF were calculated using the recently proposed perturbative approach, based on the multiple partitioning of the full Hamiltonian, and the difference-dedicated CI method. The results are compared with MRDCI and available full CI data for the same AO basis set. A high accuracy was achieved with a semiempirical perturbative scheme combining the direct calculations at second order with an approximate estimation of higher-order local contributions.