Density matrix excitation

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). 

A final study that must be mentioned is a study by Hartmann et al. [249] on the ultrafast spectroscopy of the Na3F2 cluster. They derived an expression for the calculation of a pump-probe signal using a Wigner-type density matrix approach, which requires a time-dependent ensemble to be calculated after the initial excitation. This ensemble was obtained using fewest switches surface hopping, with trajectories initially sampled from the thermalized vibronic Wigner function vertically excited onto the upper surface. 

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)... 

The analytic evaluation of the density matrix requires the diagonalization of Hi, which can be easily performed for the two extreme cases, a>r( Qg. Indeed, in the case of a low rf-field, only off-diagonal terms related to the CT are retained in the H Hamiltonian (39), which thus behaves like a fictitious spin-1/2 operator, affecting only the CT coherences /1 io- These coherences are thus selectively excited with the nutation frequency ... 

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. 

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). 

This volume in Advances in Chemical Physics provides a broad yet detailed survey of the recent advances and applications of reduced-density-matrix mechanics in chemistry and physics. With advances in theory and optimization, Coulson s challenge for the direct calculation of the 2-RDM has been answered. While significant progress has been made, as evident from the many contributions to this book, there remain many open questions and exciting opportunities for further development of 2-RDM methods and applications. It is the hope of the editor and the contributors that this book will serve as a guide for many further advenmres and advancements in RDM mechanics. 

Ramasesha, S., Pati, S.K., Krishnamurthy, H.R., Shuai, Z., Bredas, J.L. Low-lying electronic excitations and nonlinear optic properties of polymers via symmetrized density matrix renormalization group method. Synth. Met. 1997, 85(1-3), 1019. 

Raghu, C., Anusooya Pati, Y., Ramasesha, S. Density-matrix renormalization-group study of low-lying excitations of polyacene within a Pariser-Parr-Pople model. Phys. Rev. B 2002, 66(3), 035116. 

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. 

In Ref. [4] we have studied an intense chirped pulse excitation of a molecule coupled with a dissipative environment taking into account electronic coherence effects. We considered a two state electronic system with relaxation treated as diffusion on electronic potential energy surfaces with respect to the generalized coordinate a. We solved numerically equations for the density matrix of a molecular system under the action of chirped pulses of carrier frequency a> with temporal variation of phase [Pg.131]

This is the quantum M-equation for the density matrix of the system S by itself. It can be used to compute averages. For instance, the average excitation number of S obeys... 

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