TY - JOUR

T1 - Adiabatic approximation of time-dependent density matrix functional response theory

AU - Pernal, K.D.

AU - Giesbertz, K.J.H.

AU - Gritsenko, O.V.

AU - Baerends, E.J.

PY - 2007

Y1 - 2007

N2 - Time-dependent density matrix functional theory can be formulated in terms of coupled-perturbed response equations, in which a coupling matrix K (ω) features, analogous to the well-known time-dependent density functional theory (TDDFT) case. An adiabatic approximation is needed to solve these equations, but the adiabatic approximation is much more critical since there is not a good "zero order" as in TDDFT, in which the virtual-occupied Kohn-Sham orbital energy differences serve this purpose. We discuss a simple approximation proposed earlier which uses only results from static calculations, called the static approximation (SA), and show that it is deficient, since it leads to zero response of the natural orbital occupation numbers. This leads to wrong behavior in the ω→0 limit. An improved adiabatic approximation (AA) is formulated. The two-electron system affords a derivation of exact coupled-perturbed equations for the density matrix response, permitting analytical comparison of the adiabatic approximation with the exact equations. For the two-electron system also, the exact density matrix functional (2-matrix in terms of 1-matrix) is known, enabling testing of the static and adiabatic approximations unobscured by approximations in the functional. The two-electron He H+ molecule shows that at the equilibrium distance, SA consistently underestimates the frequency-dependent polarizability α (ω), the adiabatic TDDFT overestimates α (ω), while AA improves upon SA and, indeed, AA produces the correct α (0). For stretched He H+, adiabatic density matrix functional theory corrects the too low first excitation energy and overpolarization of adiabatic TDDFT methods and exhibits excellent agreement with high-quality CCSD ("exact") results over a large ω range. © 2007 American Institute of Physics.

AB - Time-dependent density matrix functional theory can be formulated in terms of coupled-perturbed response equations, in which a coupling matrix K (ω) features, analogous to the well-known time-dependent density functional theory (TDDFT) case. An adiabatic approximation is needed to solve these equations, but the adiabatic approximation is much more critical since there is not a good "zero order" as in TDDFT, in which the virtual-occupied Kohn-Sham orbital energy differences serve this purpose. We discuss a simple approximation proposed earlier which uses only results from static calculations, called the static approximation (SA), and show that it is deficient, since it leads to zero response of the natural orbital occupation numbers. This leads to wrong behavior in the ω→0 limit. An improved adiabatic approximation (AA) is formulated. The two-electron system affords a derivation of exact coupled-perturbed equations for the density matrix response, permitting analytical comparison of the adiabatic approximation with the exact equations. For the two-electron system also, the exact density matrix functional (2-matrix in terms of 1-matrix) is known, enabling testing of the static and adiabatic approximations unobscured by approximations in the functional. The two-electron He H+ molecule shows that at the equilibrium distance, SA consistently underestimates the frequency-dependent polarizability α (ω), the adiabatic TDDFT overestimates α (ω), while AA improves upon SA and, indeed, AA produces the correct α (0). For stretched He H+, adiabatic density matrix functional theory corrects the too low first excitation energy and overpolarization of adiabatic TDDFT methods and exhibits excellent agreement with high-quality CCSD ("exact") results over a large ω range. © 2007 American Institute of Physics.

U2 - 10.1063/1.2800016

DO - 10.1063/1.2800016

M3 - Article

SN - 0021-9606

VL - 127

SP - 214101

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

IS - 21

ER -