Equations-of-motion method including renormalization and double-excitation mixing

The equations‐of‐motion method is discussed as an approach to calculating excitation energies and transition moments directly. The proposed solution [T. Shibuya and V. McKoy, Phys. Rev. A 2, 2208 (1970)] of these equations is extended in two ways. First we include the proper renormalization of the equations with respect to the ground state particle‐hole densities. We then show how to include the effects of two‐particle‐hole components in excited states which are primarily single‐particle‐hole states. This is seen to be equivalent to a single‐particle‐hole theory with a normalized interaction. Applications to various diatomic and polyatomic molecules indicate that the theory can predict excitation energies and transition moments accurately and economically

Electronic excitations of benzene from the equations of motion method

We have used the equations of motion method to calculate the excitation energies and intensities of several transitions in benzene. The ordering of the singlet and triplet states of B_(2u), B_(1u), and E_(1u) symmetry agrees with experiment and the error in the calculated frequencies ranges from 3% to 25%. This error range is reasonable considering the relatively small basis set used. The most extensive calculation included 10 hole and 28 particle states and shows the effect of changes in the sigma core for each transition. The calculated transition moment of 1.74 a.u. for the ^1A_(1g)→^1E_(1u) transition agrees well with the experimental value of 1.61 a.u

Higher Random-Phase Approximation as an Approximation to the Equations of Motion

Starting from the equations of motion expressed as ground-state expectation values, we have derived a higher-order random-phase approximation (RPA) for excitation frequencies of low-lying states. The matrix elements in the expectation value are obtained up to terms linear in the ground-state correlation coefficients. We represent the ground state as eU|HF〉, where U is a linear combination of two particle-hole operators, and |HF〉 is the Hartree-Fock ground state. We then retain terms only up to those linear in the correlation coefficients in the equation determining the ground state. This equation and that for the excitation energy are then solved self-consistently. We do not make the quasiboson approximation in this procedure, and explicitly discuss the overcounting characteristics of this approximation. The resulting equations have the same form as those of the RPA, but this higher RPA removes many deficiencies of the RPA

Application of a higher RPA to a model pi-electron system

We have applied a proposed higher-order random phase approximation (RPA) to the simple model system of two pi electrons in the double bond of ethylene. The higher-order RPA removes some difficulties involved in the usual RPA, but retains the form of the RPA equations. To derive the higher RPA we retain all terms linear in the ground state correlation coefficients in the equations of motion for the excitation energy and in the equation determining the ground state. These equations are solved self-consistently and are simpler to handle than a configuration interaction solution in a realistic example. We do not use the quasiboson approximation

Travel and activity time allocation: An empirical comparison between eight cities in Europe

A study of daily time allocation to travel and out-of-home activity is conducted across eight European cities over three countries: France (Lyon, Grenoble, Strasbourg and Rennes), Switzerland (Geneva, Bern and Zurich) and Belgium (Brussels), based on individual travel survey data collected between 1997 and 2006. The effects of socio-demographic, spatial context, transport availability and city-specific variables are investigated thanks to the Cox proportional hazard model. The results indicate that socio-demographic characteristics and city (or country) specific effect play a major role while residential density and proximity to high level road or public transport networks have a very limited impact on time budgets for travel and out-of-home activities.Travel ; Activity ; Time allocation ; Cities ; Europe ; Duration model

Application of the equations-of-motion method to the excited states of N2, CO, and C2H4

We have used the equations-of-motion method to study various states of N2, CO, and ethylene. In this approach one attempts to calculate excitation energies directly as opposed to solving Schrödinger's equation separately for the absolute energies and wavefunctions. We have found that by including both single particle-hole and two particle-hole components in the excitation operators we can predict the excitation frequencies of all the low-lying states of these three molecules to within about 10% of the observed values and the typical error is only half this. The calculated oscillator strengths are also in good agreement with experiment. The method is economical, requiring far less computation time than alternative procedures

The Myth of Creditor Sabotage

Since credit derivatives began to substantially influence financial markets a decade ago, rumors have circulated about so-called “net-short” creditors who seek to damage promising, albeit financially distressed, companies. A recent episode pitting the hedge fund Aurelius against broadband provider Windstream is widely supposed to be a case in point and has at once fueled calls for law reform and yielded an effigy of ostensible Wall Street predation. This Article argues that creditor sabotage is a myth. Net-short strategies work, if at all, by in effect burning money. When an activist creditor shows its cards, as all activists must eventually do, it also reveals an opportunity for others to profit by thwarting the activist’s plans and saving threatened surplus. We discuss three sources of liquidity that targeted firms could tap to block a saboteur—“net-long” derivatives speculators, the target’s own investors, and bankruptcy. We conclude that it is exceedingly difficult for creditors to make money hobbling debtors and that there is little reason to believe anyone tries. We then examine the Windstream case and find, consistent with our theory, that the strongest reason for thinking Aurelius aimed at sabotage—namely that everyone says so—is weak indeed. Our analysis suggests that calls for law reform are addressed to a nonexistent or, at worst, self-correcting problem. Precisely for this reason, however, the persistent appeal of the sabotage myth is a lesson in political rhetoric. A story needn’t be true for some to find it useful

Equations-of-motion method: Potential energy curves for N2, CO, and C2H4

We have applied the equations-of-motion method to various states of N2, CO, and ethylene at nuclear configurations slightly distorted from the ground equilibrium geometry. This approach attempts to calculate energy differences instead of absolute energies and is thus relatively insensitive to the accuracy of the assumed ground state wavefunction. By using the experimental behavior of the ground state on distortion, we can generate accurate potential energy curves for the excited states in the region of spectroscopic interest. These curves confirm the spectroscopic behavior of the 1∑+ states of N2 and the 1∑+ states of CO where valence and Rydberg states of the same symmetry interact. The results for the T and V states of ethylene agree with experiment and show that the V state is predominantly a highly correlated valence state. Oscillator strengths across an absorption band are also accurately determined in this method. We report the dependence of the transition moment on bond length for the X1∑+→A1II transition in CO, which is in excellent agreement with experiment