Density matrix excited state

Mavri, J., Berendsen, H.J.C. Calculation of the proton transfer rate using density matrix evolution and molecular dynamics simulations Inclusion of the proton excited states. J. Phys. Chem. 99 (1995) 12711-12717. 

DensilysCurrent Specifies that population analysis procedures use the excited state density matrix rather than the ground state SCF density. 

Here, po is time independent density matrix and can be defined for initial state I. The excitation of electrons caused by absorption of a single photon is regarded as a polarization of the electron density, which is measured by the linear polarizability = Tr p uj)6). The equation of motion for the... 

In the DC-biased structures considered here, the dynamics are dominated by electronic states in the conduction band [1]. A simplified version of the theory assumes that the excitation occurs only at zone center. This reduces the problem to an n-level system (where n is approximately equal to the number of wells in the structure), which can be solved using conventional first-order perturbation theory and wave-packet methods. A more advanced version of the theory includes all of the hole states and electron states subsumed by the bandwidth of the excitation laser, as well as the perpendicular k states. In this case, a density-matrix picture must be used, which requires a solution of the time-dependent Liouville equation. Substituting the Hamiltonian into the Liouville equation leads to a modified version of the optical Bloch equations [13,15]. These equations can be solved readily, if the k states are not coupled (i.e., in the absence of Coulomb interactions). 

The usual reactivity indices, such as elements of the first-order density matrix, are also incapable of distinguishing properly between singlet and triplet behavior. Recently, French authors 139,140) have discussed the problem and shown how electron repulsion terms can be introduced to obtain meaningful results. The particular case of interest to them was excited state basicity, but their arguments have general applicability. In particular, the PMO approach, which loses much of its potential appeal because of its inability to distinguish between singlet and triplet behavior 25,121) coui(j profit considerably from an extension in this direction. 119,122)... 

Time-dependent response theory concerns the response of a system initially in a stationary state, generally taken to be the ground state, to a perturbation turned on slowly, beginning some time in the distant past. The assumption that the perturbation is turned on slowly, i.e. the adiabatic approximation, enables us to consider the perturbation to be of first order. In TD-DFT the density response dp, i.e. the density change which results from the perturbation dveff, enables direct determination of the excitation energies as the poles of the response function dP (the linear response of the KS density matrix in the basis of the unperturbed molecular orbitals) without formally having to calculate a(co). 

For a 1, the Hamiltonian Hf is independent of i. For any other value of a, the adiabatic Hamiltonian depends on i and we have different Hamiltonians for different excited states. Thus the noninteracting Hamiltonian (a 0) is different for different excited states. If there are several external potentials V =0 leading to the same density we select that potential for which the one-particle density matrix is closest to the interacting one-particle density matrix. 

Note that in the present case the matrix elements depend on the final density p . Moreover, because this density is obtained from the transformed wavefunction, they also depend on the expansion coefficients. For this reason, Eq. (177) must be solved iteratively. Such a procedure has been applied - in a sample calculation - to the 2 S excited state of the helium atom. The upper-bound character of the energy corresponding to the energy functional for the transformed wavefunction [ p( r,- ) with respect to the exact energy is guaranteed by... 

M. Rosina and M. V. Mihailovic, The determination of the particle—hole excited states by using the variational approach to the ground state two-body density matrix, in International Conference on Properties of Nuclear States, Montreal 1969, Les Presses de I Universite de Montreal, 1969. 

M. Rosina, The calculation of excited states in the particle-hole space using the two-body density matrix of the ground state, in Proceedings the International Corferenee on Nuclear Structure and Spectroscopy, Vol. 1 (H. P. Blok and A. E. L. Dieperink, eds.), North-Holland, Amsterdam, 1974. 

M. Nakata, M. Ehara, K. Yasuda, and H. Nakatsuji, Direct determination of second-order density matrix open-shell system and excited state. J. Chem. Phys. 112, 8772 (2000). 

M. Rosina, Application of 2-body density matrix of ground-state for calculations of some excited-states. hit. J. Quantum Chem. 13, 737 (1978). 

D. A. Mazziotti, Extraction of electronic excited states from the ground-state two-particle reduced density matrix. Phys. Rev. A 68, 052501 (2003). 

Figure 6.6 Two-state quantum system driven on resonance by an intense ultrashort (broadband) laser pulse. The power spectral density (PSD) is plotted on the left-hand side. The ground state 11) is assumed to have s-symmetry as indicated by the spherically symmetric spatial electron distribution on the right-hand side. The excited state 12) is ap-state allowing for electric dipole transitions. Both states are coupled by the dipole matrix element. The dipole coupling between the shaped laser field and the system is described by the Rabi frequency Qji (6 = f 2i mod(6Iti-...

Equation (40) is a generalized eigenvalue equation. The eigenvalue j is interpreted as the excitation energy from the ground state to the Jth excited state. The vectors Xj and Yj are the first-order correction to the density matrix at an excitation and describe the transition density between the ground state and the excited state J. 

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