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We derive the explicit expression of the three self-energies that one encounters in many-body perturbation theory: the well-known GW self-energy, as well as the particle–particle and electron–hole T-matrix self-energies. Each of these can be easily computed via the eigenvalues and eigenvectors of a different random-phase approximation linear eigenvalue problem that completely defines their corresponding response function. For illustrative and comparative purposes, we report the principal ionization potentials of a set of small molecules computed at each level of theory. The performance of these schemes on strongly correlated systems (B2 and C2) is also discussed. [ABSTRACT FROM AUTHOR]

While the well-established GW approximation corresponds to a resummation of the direct ring diagrams and is particularly well suited for weakly correlated systems, the T-matrix approximation does sum ladder diagrams up to infinity and is supposedly more appropriate in the presence of strong correlation. Here, we derive and implement, for the first time, the static and dynamic Bethe–Salpeter equations when one considers T-matrix quasiparticle energies and a T-matrix-based kernel. The performance of the static scheme and its perturbative dynamical correction are assessed by computing the neutral excited states of molecular systems. A comparison with more conventional schemes as well as other wave function methods is also reported. Our results suggest that the T-matrix-based formalism performs best in few-electron systems where the electron density remains low. [ABSTRACT FROM AUTHOR]

Generalized coordinates are widely used in various analyses of the trajectories of polyatomic molecules from molecular dynamics simulations, such as normal mode analysis and force distribution analysis. Here, we presented detailed discussions on the properties of some specific sets of generalized coordinates, which separate translational, rotational, and vibrational motions of a molecule from one another once the trajectories of dynamical systems are known. Efficient methods were suggested for estimating the transformation matrix between generalized and Cartesian coordinates. Some properties of the well-known BAT coordinates (bond length, angle, and torsional coordinates) were discussed as well. [ABSTRACT FROM AUTHOR]

Absolute coagulation rate constants were determined by independently, instead of simultaneously, using static and dynamic light scattering with the requested optical factors calculated by T-matrix method. The aggregating suspensions of latex particles with diameters of 500, 700, and 900 nm, that are all beyond validity limit of the traditional Rayleigh-Debye-Gans approximation, were adopted. The results from independent static and dynamic light scattering measurements were compared with those by simultaneously using static and dynamic light scattering; and three of them show good consistency. We found, theoretically and experimentally, that for independent static light scattering measurements there are blind scattering angles at that the scattering measurements become impossible and the number of blind angles increases rapidly with particle size. For independent dynamic light scattering measurements, however, there is no such a blind angle at all. A possible explanation of the observed phenomena is also presented. [ABSTRACT FROM AUTHOR]

Using the Multi-Reference Configuration Interaction method, the adiabatic potential energy surfaces of Li3 are computed. The two lowest electronic states are bound and exhibit a conical intersection. By fitting the calculated potential energy surfaces to the cubic E ⊗ ε Jahn-Teller model we extract the effective Jahn-Teller parameters corresponding to Li3. These are used to set up the transformationmatrix which transforms from the adiabatic to a diabatic representation. This diabatization method gives a Hamiltonian for Li3 which is free from singular non-adiabatic couplings and should be accurate for large internuclear distances, and it thereby allows for bound dynamics in the vicinity of the conical intersection to be explored. [ABSTRACT FROM AUTHOR]

Using the Multi-Reference Configuration Interaction method, the adiabatic potential energy surfaces of Li3 are computed. The two lowest electronic states are bound and exhibit a conical intersection. By fitting the calculated potential energy surfaces to the cubic E ⊗ ε Jahn-Teller model we extract the effective Jahn-Teller parameters corresponding to Li3. These are used to set up the transformationmatrix which transforms from the adiabatic to a diabatic representation. This diabatization method gives a Hamiltonian for Li3 which is free from singular non-adiabatic couplings and should be accurate for large internuclear distances, and it thereby allows for bound dynamics in the vicinity of the conical intersection to be explored. [ABSTRACT FROM AUTHOR]

A procedure to determine optimal vibrational coordinates is developed on the basis of an earlier idea of Thompson and Truhlar [J. Chem. Phys. 77, 3031 (1982)]. For a given molecule, these coordinates are defined as the unitary transform of the normal coordinates that minimizes the energy of the vibrational self-consistent-field (VSCF) method for the ground state. They are justified by the fact that VSCF in these coordinates becomes exact in two limiting cases: harmonic oscillators, where the optimized coordinates are normal, and noninteracting anharmonic oscillators, in which the optimized coordinates are localized on individual oscillators. A robust and general optimization algorithm is developed, which decomposes the transformation matrix into a product of Jacobi matrices, determines the rotation angle of each Jacobi matrix that minimizes the energy, and iterates the process until a minimum in the whole high dimension is reached. It is shown that the optimized coordinates are neither entirely localized nor entirely delocalized (or normal) in any of the molecules (the water, water dimer, and ethylene molecules) examined (apart from the aforementioned limiting cases). Rather, high-frequency stretching modes tend to be localized, whereas low-frequency skeletal vibrations remain normal. On the basis of these coordinates, we introduce two new vibrational structure methods: optimized-coordinate VSCF (oc-VSCF) and optimized-coordinate vibrational configuration interaction (oc-VCI). For the modes that become localized, oc-VSCF is found to outperform VSCF, whereas, for both classes of modes, oc-VCI exhibits much more rapid convergence than VCI with respect to the rank of excitations. We propose a rational configuration selection for oc-VCI when the optimized coordinates are localized. The use of the optimized coordinates in VCI with this configuration selection scheme reduces the mean absolute errors in the frequencies of the fundamentals and the first overtones/combination tones from 104.7 (VCI) to 10.7 (oc-VCI) and from 132.4 (VCI) to 8.2 (oc-VCI) cm-1 for the water molecule and the water dimer, respectively. It is also shown that the degree of coupling in the potential for ethylene is reduced effectively from four modes to three modes by the transformation from the normal to optimized coordinates, which enhances the accuracy of oc-VCI with low-rank excitations. [ABSTRACT FROM AUTHOR]

Surface enhanced Raman scattering (SERS) enhancement factors G for nanoparticles consisting of a single Ag sphere or a dimer of Ag nanospheres are calculated using a T-matrix method that rigorously incorporates dipole reradiation (DR) effects. A comparison with the commonly used plane wave (PW) approximation, |Eloc(ω)|2|Eloc(ω′)|2, which for zero Stokes shift is |Eloc(ω)|4, is made so as to determine the error associated with using the PW enhancement factor instead of DR in modeling SERS intensities. Calculations for the single sphere are performed for various molecule locations, detector locations, and sphere sizes, while the dimer calculations consider the effects of molecule and detector locations for 50 nm diameter spheres with a 2 nm gap. In both the single sphere and dimer calculations, excellent agreement (<0.3%) is found between the PW approximation and DR calculations when the molecule is located along the incident field polarization direction and with the detector along an axis that is orthogonal both to the polarization and wave vector directions. The errors for other molecule locations, different detector locations, and larger sphere sizes can be considerably larger. A qualitative description of the nature of the errors is developed based on interferences between radiation emitted by the sphere and by the molecule and on quadrupole excitation in the metal spheres. An average over molecule and detector locations for both the single sphere and dimer results leads to DR enhancement factors that differ by factors of 2–3 (sometimes higher, sometimes lower) from the PW results. This indicates that for quantitative field enhancement factor calculations, the more rigorous DR result is important. [ABSTRACT FROM AUTHOR]