Oscillator strengths of electronic excitations with response theory using phase including natural orbital functionals

Abstract

Articles you may be interested inExcitation energies with linear response density matrix functional theory along the dissociation coordinate of an electron-pair bond in N-electron systems J. Chem. Phys. 140, 024101 (2014); 10.1063/1.4852195Response calculations based on an independent particle system with the exact one-particle density matrix: Excitation energies J. Chem. Phys. 136, 094104 (2012) The key characteristics of electronic excitations of many-electron systems, the excitation energies ω α and the oscillator strengths f α , can be obtained from linear response theory. In one-electron models and within the adiabatic approximation, the zeros of the inverse response matrix, which occur at the excitation energies, can be obtained from a simple diagonalization. Particular cases are the eigenvalue equations of time-dependent density functional theory (TDDFT), time-dependent density matrix functional theory, and the recently developed phase-including natural orbital (PINO) functional theory. In this paper, an expression for the oscillator strengths f α of the electronic excitations is derived within adiabatic response PINO theory. The f α are expressed through the eigenvectors of the PINO inverse response matrix and the dipole integrals. They are calculated with the phaseincluding natural orbital functional for two-electron systems adapted from the work of Löwdin and Shull on two-electron systems (the phase-including Löwdin-Shull functional). The PINO calculations reproduce the reference f α values for all considered excitations and bond distances R of the prototype molecules H 2 and HeH + very well (perfectly, if the correct choice of the phases in the functional is made). Remarkably, the quality is still very good when the response matrices are severely restricted to almost TDDFT size, i.e., involving in addition to the occupied-virtual orbital pairs just (HOMO+1)-virtual pairs (R1) and possibly (HOMO+2)-virtual pairs (R2). The shape of the curves f α (R) is rationalized with a decomposition analysis of the transition dipole moments.

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

“…No reduction was made in δn(ω), because its full treatment turned out to be important for particle number conservation. Indeed, calculations with low values of k demonstrated that the polarizabilities [147], excitations [156], and oscillator strengths [157] are in excellent agreement with the exact results. Taking transitions from only the highest occupied PINO into account (k ¼ 1) gives reasonable results for the low lying excitations of the hydrogen molecule at its equilibrium.…”

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

“…(2) and (7) when it comes to ground state calculation. However, Giesbertz et al have recently formulated a timedependent formalism for PINO functionals 6,7,12 which can be readily applied to the APSG functional written in a PINO form, Eq. (7).…”

Spectrum for Nonmagnetic Mott Insulators from Power Functional within Reduced Density Matrix Functional Theory

“…In practice, however, the correlation energy is an unknown functional of the 1-RDM and must be approximated. Although there are several known approximations for the xc energy functional [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34], the most promising for extended systems is the power functional [14,15] where the xc energy reads…”