Linear and Nonlinear Optical Properties from TDOMP2 Theory

Abstract

We present a derivation of real-time (RT) time-dependent orbital-optimized Møller–Plesset (TDOMP2) theory and its biorthogonal companion, time-dependent non-orthogonal OMP2 theory, starting from the time-dependent bivariational principle and a parametrization based on the exponential orbital-rotation operator formulation commonly used in the time-independent molecular electronic structure theory. We apply the TDOMP2 method to extract absorption spectra and frequency-dependent polarizabilities and first hyperpolarizabilities from RT simulations, comparing the results with those obtained from conventional time-dependent coupled-cluster singles and doubles (TDCCSD) simulations and from its second-order approximation, TDCC2. We also compare our results with those from CCSD and CC2 linear and quadratic response theories. Our results indicate that while TDOMP2 absorption spectra are of the same quality as TDCC2 spectra, including core excitations where optimized orbitals might be particularly important, frequency-dependent polarizabilities and hyperpolarizabilities from TDOMP2 simulations are significantly closer to TDCCSD results than those from TDCC2 simulations.

Transient spectroscopy from time-dependent electronic-structure theory without multipole expansions

“…The orbital-adaptive methods yield roughly the same intensity profiles as their static-orbital counterparts, but the transition frequencies are blue-shifted: ∼ 0.5 eV for TDOMP2 versus TDCC2 and ∼ 2 eV for OATDCCD versus TDCCSD. As has been observed previously [58], these blue-shifts are insignificant compared with other sources of error such as basis-set incompleteness and higher-order correlation effects. Electron-correlation effects are significantly more important than the orbital relaxation provided by dynamic orbitals, as seen in Fig.…”

“…The orbital expansion coefficients are either kept constant (static orbitals) at the groundstate Hartree-Fock (HF) level or allowed to vary in response to the external field (dynamic orbitals). Static orbitals are used in the time-dependent configuration interaction singles (TDCIS) [56], time-dependent secondorder approximate coupled-cluster singles-and-doubles (TDCC2) [57,58], and time-dependent coupled-cluster singles-and-doubles (TDCCSD) [59] methods. Dynamic orbitals are used in the time-dependent Hartree-Fock (TDHF) [56], time-dependent orbital-optimized secondorder Møller-Plesset (TDOMP2) [58,60], and orbitaladaptive time-dependent coupled-cluster doubles (OAT-DCCD) [61] methods.…”

“…Static orbitals are used in the time-dependent configuration interaction singles (TDCIS) [56], time-dependent secondorder approximate coupled-cluster singles-and-doubles (TDCC2) [57,58], and time-dependent coupled-cluster singles-and-doubles (TDCCSD) [59] methods. Dynamic orbitals are used in the time-dependent Hartree-Fock (TDHF) [56], time-dependent orbital-optimized secondorder Møller-Plesset (TDOMP2) [58,60], and orbitaladaptive time-dependent coupled-cluster doubles (OAT-DCCD) [61] methods. Only the methods using dynamic orbitals are gauge invariant (in the limit of complete basis set) [62][63][64][65].…”

Time-dependent multiconfiguration self-consistent-field and time-dependent optimized coupled-cluster methods for intense laser-driven multielectron dynamics

“…A similar approach using biorthogonal orbitals (TDNOMP2) has been also reported and assessed for linear and nonlinear optical properties. 33 Although TD-OMP2 is based on the perturbation theory, it can be applied to high-field phenomena because the orbitals variationally evolve over time and the external field is totally included in the unperturbed Hamiltonian . is the permutation operator), which is significantly simpler than the original TD-OCCD equations of 𝑝 𝑝𝑞 motion.…”

Time‐dependent coupled‐cluster theory

“…However, for frequency‐dependent polarizabilities and hyperpolarizabilities extracted from TDCC2, TDCCSD, and TDOMP2 simulations with ramped monochromatic continuous‐wave lasers as suggested by Ding et al, 14 Kristiansen et al 98 found that TDOMP2 theory outperforms the TDCC2 model, producing linear and nonlinear response functions much closer to the full TDCCSD results. While the linear absorption spectra were in perfect agreement with results from linear response theory (to within the resolution of the Fourier transformation), the TDCC2 and TDCCSD polarizabilities and hyperpolarizabilities were found to deviate slightly.…”