Instead, the singularities are artifacts of the chosen basis of discontinuous functions. Though these singularities suggest that the exact molecular wave function may not have density at the conical intersection point, there is no physical basis for this constraint. In contrast to the well-known singularities in the first-derivative couplings at conical intersections, these singularities are non-integrable, resulting in undefined DBOC matrix elements. When the second-derivative nonadiabatic terms are added to the Hamiltonian, singularities in the diagonal BO corrections (DBOCs) of the individual BO states arise from these discontinuities. In order to construct a well-behaved molecular wave function that has density at a conical intersection, the individual BO vibronic states in the summation must be discontinuous. We demonstrate that though exact in principle, the expansion of the total molecular wave function as a sum over adiabatic Born-Oppenheimer (BO) vibronic states makes inclusion of the second-derivative nonadiabatic energy term near conical intersections practically problematic. Wave function continuity and the diagonal Born-Oppenheimer correction at conical intersections This feature permits pocket-calculator evaluation of the corrections within thermochemical accuracy (10(-1) mhartree or kcal/mol). An almost constant contribution per electron is identified, which converges with system size for specific series of organic molecules. Recent post-Hartree-Fock calculations of the diagonal-Born-Oppenheimer correction empirically show that it behaves quite similar to atomic nuclear mass corrections. Semiempirical evaluation of post-Hartree-Fock diagonal-Born-Oppenheimer corrections for organic molecules. The connection to adiabatic-to-diabatic transformations in non-adiabatic dynamics is explored and complications arising from biorthogonal nature of CC theory are identified. One of this agrees with the formula used in the current literature. On this basis, different computational schemes for evaluating DBOC using approximate CC wave-functions are derived. This is shown to lead to a biorthogonal version of SOS formula with similar properties. A biorthogonal formulation suitable for DBOC computations using standard unnormalised coupled-cluster (CC) wave-functions is presented. A sum-over-states (SOS) formula for DBOC which explicitly exhibits this invariance is derived. By viewing this freedom as a kind of gauge-freedom, it is shown that DBOC and the resulting associated mass-dependent adiabatic PES are gauge-invariant quantities. We examine how geometry-dependent normalisation freedom of electronic wave-functions affects extraction of a meaningful diagonal Born-Oppenheimer correction (DBOC) to the ground-state Born-Oppenheimer potential energy surface (PES). Copyright © 2010 John Wiley & Sons, Ltd.Diagonal Born-Oppenheimer correction for coupled-cluster wave-functions ![]() Thus, the proposed device is a reliable and suitable mass-carrying sliding system (MCSS) for dynamic testing using medium-size shaking tables. Measured dynamic friction coefficients, spectral accelerations and hysteresis loops show that friction developed in the LMGS did not add any significant amount of damping into the specimen response. Shaking table tests to collapse of reinforced concrete walls were used to evaluate the effectiveness of the proposed device. In order to drastically diminish the damping added to the specimen response when a friction device is used, the improved device employs a linear motion guide system (LMGS) with very low friction. Although friction devices for similar purposes have been developed using sliding bearings (Teflon pads or rollers), the measured coefficient of dynamic friction and the energy dissipated by friction have been very high. Therefore, to avoid the risk of lateral instability of models, to maintain the weight of test specimens within table payload, while maintaining the amount of mass needed, an external device for transmitting the inertia forces to the models using an improved sliding system is proposed. ![]() In these cases, to comply with modeling requirements, large amount of extra-mass should be added to the specimen. Because of the size and weight limitations of the tables, some approaches, like testing reduced-scale models or testing only the main structural components, are deemed necessary. Shaking tables are suitable facilities to assess and validate the behavior of structures and nonstructural components under actual seismic actions.
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