Two methods for restricted configuration spaces within the multiconfiguration time-dependent Hartree-Fock method

The multiconfiguration time-dependent Hartree-Fock (MCTDHF) method has shown promise in calculating electronic dynamics in molecules driven by strong and high-energy lasers. It must incorporate restricted configuration spaces (meaning that a particular combination of Slater determinants is used, instead of full configuration interaction) to be applied to big systems. Two different Ansätze are used to determine the essential term in the equations. The first Ansatz is the Lagrangian variational principle. The explicit, complete MCTDHF equations of motion, satisfying that principle, for arbitrary configuration spaces, are given. The property that a restricted configuration list must satisfy in order for the Lagrangian and McLachlan variational principles to give different results is identified. The second Ansatz keeps the density matrix block diagonal among equivalent orbitals, in a generalization of the method of Worth [J. Chem. Phys. 112, 8322 (2000)]. The methods perform well in calculating the dynamics of Be and ${\mathrm{BC}}^{2+}$ subject to ultrafast, ultrastrong lasers in severely truncated Hilbert spaces, although they exhibit differing degrees of numerical stability as implemented.

Figure 1

Analysis of propagation for beryllium test case. The legend in the left panel applies to all of them.

Figure 2

Top panel: occupation of the least occupied (fifth) natural orbital for beryllium test case. Bottom panel: measure of off diagonality of the density matrix of Eq. (56). “Denmat FCI” refers to using the equation that would keep the density matrix block diagonal with full configuration interaction, as described at the end of Sec. 4.

Figure 3

Fourier transform of induced dipole moment for Be calculation obtained after propagation for 7.25 fs.

Figure 4

Analysis of propagation for ${\mathrm{BC}}^{2+}$ case.

Figure 5

Occupation of the least-occupied (sixth) natural orbital for ${\mathrm{BC}}^{2+}$ test case.

Figure 6

${\mathrm{BC}}^{2+}$ propagation with mean field time step 0.01 atomic units and different regularization parameters, as labeled.

Figure 7

${\mathrm{BC}}^{2+}$ propagation with mean field time step 0.05 atomic units and regularization parameter $10{}^{-6}$, for McLachlan [Eq. (46)], Lagrangian [Eq. (45)], and the least-norm-error simultaneous solution of the two equations in various ratios.