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Register a new userA time-dependent formulation of multi-reference perturbation theory
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We discuss the time-dependent formulation of perturbation theory in the context of the interacting zeroth-order Hamiltonians that appear in multi-reference situations. As an example, we present a time-dependent formulation and implementation of second-order n-electron valence perturbation theory. The resulting t-NEVPT2 method yields the fully uncontracted n-electron valence perturbation wavefunction and energy, but has a lower computational scaling than the usual contracted variants, and also avoids the construction of high-order density matrices and the diagonalization of metrics. We present results of t-NEVPT2 for the water, nitrogen, carbon, and chromium molecules, and outline directions for the future.
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We present a multi-reference generalization of the algebraic diagrammatic construction theory (ADC) [J. Schirmer, Phys. Rev. A 26, 2395 (1982)] for excited electronic states. The resulting multi-reference ADC approach (MR-ADC) can be efficiently and reliably applied to systems, which exhibit strong electron correlation in the ground or excited electronic states. In contrast to conventional multi-reference perturbation theories, MR-ADC describes electronic transitions involving all orbitals (core, active, and external) and enables efficient computation of spectroscopic properties, such as transition amplitudes and spectral densities. Our derivation of MR-ADC is based on the effective Liouvillean formalism of Mukherjee and Kutzelnigg [D. Mukherjee, W. Kutzelnigg, in Many-Body Methods in Quantum Chemistry (1989), pp. 257--274], which we generalize to multi-determinant reference states. We discuss a general formulation of MR-ADC, perform its perturbative analysis, and present an implementation of the first-order MR-ADC approximation, termed MR-ADC(1), as a first step in defining the MR-ADC hierarchy of methods. We show results of MR-ADC(1) for the excitation energies of the Be atom, an avoided crossing in LiF, doubly excited states in C2, and outline directions for our future developments.
We present a new release of the turboTDDFT code featuring an implementation of hybrid functionals, a recently introduced pseudo-Hermitian variant of the Liouville-Lanczos approach to time-dependent density-functional perturbation theory, and a newly developed Davidson-like algorithm to compute selected interior eigenvalues/vectors of the Liouvillian super-operator. Our implementation is thoroughly validated against benchmark calculations performed on the cyanin (C$_{21}$O$_{11}$H$_{21}$) molecule using the Gaussian09 and turboTDDFT 1.0 codes.
We calculate the high-harmonic generation (HHG) spectra, strong-field ionization, and time-dependent dipole-moment of Ne using explicitly time-dependent optimized second-order many-body perturbation method (TD-OMP2) where both orbitals and amplitudes are time-dependent. We consider near-infrared (800 nm) and mid-infrared (1200 nm) laser pulses with very high intensities ($5times10^{14}$, $8times10^{14}$ , and $1times10^{15}$ W/cm$^2$), required for strong-field experiments with the high-ionization potential (21.6 eV) atom. We compare the result of the TD-OMP2 method with the time-dependent complete-active-space self-consistent field method and the time-dependent Hartree-Fock method. Further, we report the implementation of the TD-CC2 method within the chosen active space, which is also a second-order approximation to the TD-CCSD method, and present results of time-dependent dipole-moment and HHG spectra with an intensity of $5times10^{13}$ W/cm$^2$ at a wavelength of 800 nm. It is found that the TD-CC2 method is not stable in the case with a higher laser intensity, and it does not provide a gauge-invariant description of the physical properties, which makes TD-OMP2 a superior choice to reach out to larger chemical systems, especially for the study of strong-field dynamics. The obtained results indicate that the TD-OMP2 method shows moderate performance, overestimating the response of Ne, while TDHF underestimates it. Nevertheless, it is remarkable that stable computation of such highly nonlinear nonperturbative phenomena is possible within the framework of time-dependent perturbation method, by virtue of the nonperturbative inclusion of the laser-electron interaction and time-dependent optimization of orbitals.
The accurate electronic structure calculation for strongly correlated chemical systems requires an adequate description for both static and dynamic electron correlation, and is a persistent challenge for quantum chemistry. In order to account for static and dynamic electron correlations accurately and efficiently, in this work we propose a new method by integrating the density matrix renormalization group (DMRG) method and multi-reference second-order Epstein-Nesbet perturbation theory (ENPT2) with a selected configuration interaction (SCI) approximation. Compared with previous DMRG-based dynamic correlation methods, the DMRG-ENPT2 method extends the range of applicability, allowing us to efficiently calculate systems with very large active space beyond 30 orbitals. We demonstrate this by performing calculations on H$_2$S with an active space of (16e, 15o), hexacene with an active space of (26e, 26o) and 2D H$_{64}$ square lattice with an active space of (42e, 42o).
The Kohn-Sham approach to time-dependent density-functional theory (TDDFT) can be formulated, in principle exactly, by invoking the force-balance equation for the density, which leads to an explicit expression for the exchange-correlation potential as an implicit density functional. It is shown that this suggests a reformulation of TDDFT in terms of the second time derivative of the density, rather than the density itself. The result is a time-local Kohn-Sham scheme of second order in time whose causal structure is more transparent than that of the usual Kohn-Sham formalism. The scheme can be used to construct new approximations at the exchange-only level and beyond, and it offers a straightforward definition of the exact adiabatic approximation.
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