Starting from Rowe's equation of motion we derive extended random phase approximation (ERPA) equations for excitation energies. The ERPA matrix elements are expressed in terms of the correlated ground state one- and two-electron reduced density matrices, 1- and 2-RDM, respectively. Three ways of obtaining approximate 2-RDM are considered: linearization of the ERPA equations, obtaining 2-RDM from density matrix functionals, and employing 2-RDM corresponding to an antisymmetrized product of strongly orthogonal geminals (APSG) ansatz. Applying the ERPA equations with the exact 2-RDM to a hydrogen molecule reveals that the resulting (1)Σ(g)(+) excitation energies are not exact. A correction to the ERPA excitation operator involving some double excitations is proposed leading to the ERPA2 approach, which employs the APSG one- and two-electron reduced density matrices. For two-electron systems ERPA2 satisfies a consistency condition and yields exact singlet excitations. It is shown that 2-RDM corresponding to the APSG theory employed in the ERPA2 equations yields excellent singlet excitation energies for Be and LiH systems, and for the N(2) molecule the quality of the potential energy curves is at the coupled cluster singles and doubles level. ERPA2 nearly satisfies the consistency condition for small molecules that partially explains its good performance.

We present a second-order formulation of multi-reference algebraic diagrammatic construction theory [Sokolov, A. Yu. J. Chem. Phys. 2018, 149, 204113] for simulating photoelectron spectra of strongly correlated systems (MR-ADC(2)). The MR-ADC(2) method uses second-order multi-reference perturbation theory (MRPT2) to efficiently obtain ionization energies and spectral densities for many photoelectron transitions in a single computation. In contrast to conventional MRPT2 methods, MR-ADC(2) provides information about ionization of electrons in all orbitals (i.e., core and active) and allows to compute transition properties in straightforward and efficient way. Although equations of MR-ADC(2) depend on four-particle reduced density matrices, we demonstrate that computation of these large matrices can be completely avoided without introducing any approximations. The resulting MR-ADC(2) implementation has a lower computational scaling compared to conventional MRPT2 methods. We present results of MR-ADC(2) for photoelectron spectra of small molecules, carbon dimer, and equally-spaced hydrogen chains (H 10 and H 30 ) and outline directions for future developments.

We report a new implementation of multireference algebraic diagrammatic construction theory (MR-ADC) for simulations of electron attachment and ionization in strongly correlated molecular systems (EA/IP-MR-ADC). Following our recent work on IP-MR-ADC [J. Chem. Theory Comput. 2019, 15, 5908], we present the first implementation of the second-order MR-ADC method for electron attachment (EA-MR-ADC(2)) and two extended second-order approximations (EA- and IP-MR-ADC(2)-X) that incorporate a partial treatment of third-order electron correlation effects. Introducing a small approximation for the second-order amplitudes of the effective Hamiltonian, our implementation of EA- and IP-MR-ADC(2)-X has a low computational scaling with the basis set size M. Additionally, we describe an efficient algorithm for solving the first-order amplitude equations in MR-ADC and partially contracted second-order N-electron valence perturbation theory (NEVPT2) which completely avoids computation of the four-particle reduced density matrices without introducing any approximations or imaginary-time propagation. For a benchmark set of eight small molecules, a carbon dimer, and a twisted ethylene, we demonstrate that EA- and IP-MR-ADC(2)-X achieve an accuracy similar to that of strongly contracted NEVPT2 while having a lower computational scaling with the active space size and providing efficient access to transition properties.

Articles you may be interested inPerformance of the antisymmetrized product of strongly orthogonal geminal (APSG) ansatz in describing ground states of molecules has been extensively explored in the recent years. Not much is known, however, about possibilities of obtaining excitation energies from methods that would rely on the APSG ansatz. In the paper we investigate the recently proposed extended random phase approximations, ERPA and ERPA2, that employ APSG reduced density matrices. We also propose a time-dependent linear response APSG method (TD-APSG). Its relation to the recently proposed phase including natural orbital theory is elucidated. The methods are applied to Li 2 , BH, H 2 O, and CH 2 O molecules at equilibrium geometries and in the dissociating limits. It is shown that ERPA2 and TD-APSG perform better in describing double excitations than ERPA due to inclusion of the so-called diagonal double elements. Analysis of the potential energy curves of Li 2 , BH, and H 2 O reveals that ERPA2 and TD-APSG describe correctly excitation energies of dissociating molecules if orbitals involved in breaking bonds are involved. For single excitations of molecules at equilibrium geometries the accuracy of the APSG-based methods approaches that of the time-dependent Hartree-Fock method with the increase of the system size. A possibility of improving the accuracy of the TD-APSG method for single excitations by splitting the electron-electron interaction operator into the long-and short-range terms and employing density functionals to treat the latter is presented.