Analytic energy gradients for constrained DFT-configuration interaction

Benjamin Kaduk, Takashi Tsuchimochi, Troy Van Voorhis
2014 Journal of Chemical Physics  
The constrained density functional theory-configuration interaction (CDFT-CI) method has previously been used to calculate ground-state energies and barrier heights, and to describe electronic excited states, in particular conical intersections. However, the method has been limited to evaluating the electronic energy at just a single nuclear configuration, with the gradient of the energy being available only via finite difference. In this paper, we present analytic gradients of the CDFT-CI
more » ... of the CDFT-CI energy with respect to nuclear coordinates, which gives the potential for accurate geometry optimization and molecular dynamics on both the ground and excited electronic states, a realm which is currently quite challenging for electronic structure theory. We report the performance of CDFT-CI geometry optimization for representative reaction transition states as well as molecules in an excited state. The overall accuracy of CDFT-CI for computing barrier heights is essentially unchanged whether the energies are evaluated at geometries obtained from QCISD or CDFT-CI, indicating that CDFT-CI produces very good reaction transition states. These results open up tantalizing possibilities for future work on excited states. * tvan@mit.edu Electronic excited states are of interest in a great many chemical systems, being of relevance to photochemistry,[1-8] photodamage to DNA,[9-18] organic semiconductors,[19-23] and more.[24-26] Of particular interest is the dynamics on the excited state, after an excitation event has occurred. In order to study the geometric relaxation of electronic excited states, one requires the force experienced by the nuclei on the excited-state PES. This requirement limits the spectrum of electronic structure methods which are usable, with the field being limited to time-dependent density functional theory (TD-DFT),[27-35] configurationinteraction singles (CIS),[7, 31, 36-41] complete active space self-consistent field (CASSCF) and its second order perturbation theory (CASPT2)[42-48] (note that analytic gradients for CASPT2 have become available only recently[49]) equation-of-motion coupled-cluster singles and doubles (EOM-CCSD)[50-54] and its approximate form (EOM-CC2),[31, 55-61] and sometimes multi-reference configuration interaction (MRCI).[62-65] Even for EOM-CCSD, CASPT2, and MRCI, the computational expense will vary with the implementation and application, and such calculations become impractical for systems with more than 10 or 15 atoms. On the other hand, DFT methods gain a significant advantage of practicality as the system size increases. TD-DFT has seen broad use for electronic excited states in general, and excited-state dynamics and geometry optimization are no exception.[30-35] However, it still suffers from the deficiencies in describing multiple excitations and charge-transfer excitations which render it a less-than-general solution for vertical excitation energy calculations,[66-75] though recent developments show the state of affairs may be improving.[76-79] Restricted open-shell Kohn-Sham (ROKS) [80-82] is a state-specific method, and its gradients are easily available compared to TD-DFT.[83] However, ROKS consists of a two-determinant wave function, and therefore cannot describe electronic structures with multiple excitations. Constrained DFT (CDFT) is designed to directly construct charge-and spin-constrained states and as such can find charge-transfer states directly, using self-consistent ground state techniques. [84] [85] [86] The self-consistent nature of the solution means that nonlinear response of the density is included, and hence in principle permits the treatment of multiple excitations from the ground state. However, CDFT has limitations of its own; it is still a single-reference method (and thus suffers from the limitations of DFT in the face of strong
doi:10.1063/1.4862497 pmid:24832311 fatcat:xzpl2zvw2bfb5pupx422wgtdwu