# Cumulant reconstruction of the three-electron reduced density matrix in the anti-Hermitian contracted SchrÃ¶dinger equation

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Linearly averaged position moment (LAPM) [Rk11Rk22Â·Â·Â· Rk3N3N] is defined as the linear (not quadratic) average of the position moment operator Rk11Rk22Â·Â·Â· Rk3N3N over the N-electron wave function Î¨({Rj}), where {Rj} are 3N Cartesian coordinates of electrons and {kj} are...

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The photoexcited reaction pathway from gauche-1,3-butadiene to bicyclobutane via a conical intersection is analyzed through the direct calculation of two-electron reduced density matrices (2-RDMs) from solutions to the anti-Hermitian contracted SchrÃ¶dinger equation (ACSE). The study utilizes...

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The power method for solving N-particle eigenvalue equations is contracted onto the two-particle space to produce a reduced â€œvariationalâ€ method for solving the contracted SchroÂ¨dinger equation (CSE), also known as the density equation. In contrast to the methods which solve a...

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We solve numerically the time-dependent SchrÃ¶dinger equation to study the behavior of a molecule interacting with two phase-locked ultrashort laser pulses. The two-dimensional model used in the calculations mimics the properties of the CH3ONO molecule. The two pulses are identical except for...

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A previously proposed [M. Piris, X. Lopez, F. RuipÃ©rez, J. M. Matxain, and J. M. Ugalde, J. Chem. Phys. 134, 164102 (2011)] formulation of the two-particle cumulant, based on an orbital-pairing scheme, is extended here for including more than two natural orbitals. This new approximation is...

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Contrary to the previous belief, it is found that the time dependent SchrÃ¶dinger equation is not always reduced to the Hamiltonâ€“Jacobi equation in the hâ†’0 limit. An explicit example is given.

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Hierarchies of nonlinear SchrÃ¶dinger equations were investigated for multiparticle systems, satisfying the separation property, i.e., where product wave functions evolve by the separate evolution of each factor. Such a hierarchy defines a nonlinear derivation on tensor products of the...