How accurate is the strongly orthogonal geminal theory in predicting excitation energies? Comparison of the extended random phase approximation and the linear response theory approaches

Abstract

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.

Reduced Density Matrix Functional Theory (RDMFT) and Linear Response Time-Dependent RDMFT (TD-RDMFT)

“…A confirmation of this statement has been delivered by the results for the H 2 and HeH + molecules, obtained within the adiabatic TD-PINO formalism with the PILS functional and the extended RPA results with the APSG density matrices. The latter approach has been shown to be equivalent to the adiabatic TD-PINO if the APSG functional is employed [165] and has been tested on several small molecules. Even though it recovers certain double excitations, its overall accuracy is not satisfactory.…”

“…However, the APSG wavefunction can also be used to construct a PINO functional (62). The adiabatic PINO response equations with the APSG functional are actually identical to those obtained by applying time-dependent response theory to the APSG wavefunction directly [165]. Calculations on small molecular systems have demonstrated that the lowest excitation energies for the APSG functional (62) are in very good agreement with more sophisticated approaches.…”

“…Higher excitation energies seem to be less reliable. Experiments using a range-separated version of the APSG functional indicate a shortcoming of the APSG functional rather than an inherent limitation of the adiabatic TD-PINO linear response equations [165]. However, more evidence needs to be gathered before we can make any conclusive statement.…”

“…A different route is also explored by combining features from the PINO response equations to the extended RPA equations [164,165] obtained from Rowe's equation of motion framework [166]. The advantage is that the response matrices are now formulated as partial contractions of the 1-RDM and 2-RDM instead of functional derivatives with respect to PINOs and occupation numbers.…”

Second-Order Exchange-Dispersion Energy Based on a Multireference Description of Monomers

“…The lack of double excitations in ERPA has much lesser effect on the E (2) disp component-errors with respect to FCI remain in the 8 − 30% range for the He· · · H 2 ( 1 Σ + u ) state of the dimer, and in the 7 − 12% range for the He· · · H 2 ( 1 Π u ) state (see Figure S1 and Table S2 in the Supporting Information). Taking into account that E (2) exch−disp is small in comparison to E (2) disp , and also the fact that the overall contribution from double excitations is expected to be less pronounced for many-electron systems than for the hydrogen molecule, 36 one can still expect that the proposed ERPA-based approximations will prove useful when applied to dispersion interactions in excited systems.…”