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The paper describes methods and fast computational algorithm for building effective Hamiltonians in molecular physics using perturbative approach. Separations of fast and slow variables are considered in the framework of contact transformations (CT). The particular focus is on a systematic derivation of effective models for rovibrational spectroscopy from ab initio-based potential energy surfaces with an exhaustive review of previous studies in this field. We consider applications to several types of polyads coupled by Fermi, Coriolis, Darling-Dennison and other types of resonance interactions with examples for asymmetric top, symmetric top and spherical top molecules. A flexible choice of the modelling operator accounts for strong couplings of various types of nuclear motion in molecules among closely lying levels including vibrational resonance schemes (2:1:2...), (2:1:2:1), (4:2:6:3), (3:2:1:2:1:1), etc. that occur for C2v, C3v and Td molecules and their isotopic species. The method is implemented in the MOL_CT programme suite, which offers a complementary tool to variational methods in terms of convergence and computational time. The range of applications is also different. The goal of the CT method is providing mathematical models for analyses of molecular spectra with the high-resolution accuracy using physically meaningful parameters derived from ab initio functions. [ABSTRACT FROM AUTHOR]

A variant of coupled-cluster theory is described here, wherein the degrees of freedom are fluctuations of fragments between internally correlated states. The effects of intra-fragment correlation on the inter-fragment interaction are pre-computed and permanently folded into an effective Hamiltonian, thus avoiding redundant evaluations of local relaxations associated with coupled fluctuations. A companion article shows that a low-scaling step may be used to cast the electronic Hamiltonians of real systems into the form required. Two proof-of-principle demonstrations are presented here for non-covalent interactions. One uses harmonic oscillators, for which accuracy and algorithm structure can be carefully controlled in comparisons. The other uses small electronic systems (Be atoms) to demonstrate compelling accuracy and efficiency, also when inter-fragment electron exchange and charge transfer must be handled. Since the cost of the global calculation does not depend directly on the correlation models used for the fragments, this should provide a way to incorporate difficult electronic structure problems into large systems. This framework opens a promising path for building tunable, systematically improvable methods to capture properties of systems interacting with a large number of other systems. The extension to excited states is also straightforward. [ABSTRACT FROM AUTHOR]

We show here that the Hamiltonian for an electronic system may be written exactly in terms of fluctuation operators that transition constituent fragments between internally correlated states, accounting rigorously for inter-fragment electron exchange and charge transfer. Familiar electronic structure approaches can be applied to the renormalised Hamiltonian. For efficiency, the basis for each fragment can be truncated, removing high-energy local arrangements of electrons from consideration, and effectively defining collective coordinates for the fragments. For a large number of problems (especially for non-covalently interacting fragments), this has the potential to fold the majority of electron correlation into the effective Hamiltonian, and it should provide a robust approach to incorporating difficult electronic structure problems into large systems. The number of terms in the exactly transformed Hamiltonian formally scales quartically with system size, but this can be reduced to quadratic in the mesoscopic regime, to within an arbitrary error tolerance. Finally, all but a linear-scaling number of these terms may be efficiently decomposed in terms of electrostatic interactions between a linear-scaling number of pre-computed transition densities. In a companion article, this formalism is applied to an excitonic variant of coupled-cluster theory. [ABSTRACT FROM AUTHOR]

Optimal control theory has been employed to populate separately two dark states of the acetylene polyad,Ns= 1 andNr = 5, by indirect coupling via the ground state. Relevant level energies and transition dipole moments are extracted from the experimental literature. The optimal pulses are rather simple. The evolution of the population is shown for the duration of the control process and also for the field-free evolution that follows the control. One of the dark states appears to be a potential target for realistic experimental investigation because the average population of the Rabi oscillation remains high and decoherence is expected to be weak. [ABSTRACT FROM AUTHOR]

The absorption spectrum of acetylene has been recorded at room temperature (297 K) using high-sensitivity cavity ring-down spectroscopy (αmin∼ 5×10−11cm−1) in the 5851 and 6341 cm−1interval corresponding to a region of very weak absorption. A list of about 10,700 absorption features with estimated absolute line intensities was constructed. The smallest intensities are of the order of 5×10−29cm molecule−1. The line list includes about 2500 absorption lines of ethylene present at the ppm level in the acetylene sample and identified on the basis of a high-resolution Fourier transform spectrum specifically recorded. A total of more than 2700 lines of12C2H2were rovibrationally assigned in comparison with accurate predictions provided by a global effective operator model. Overall, the present effort adds about 2260 new assignments to the set of about 500 assigned transitions available in the literature. The new assignments correspond to 45 new bands and 17 already-known bands, for which additionalJlines were assigned. Spectroscopic parameters were derived for the upper vibrational levels from a band by band fit of the line positions (typical root mean square deviation values are of the order of 0.001 cm−1). A few of the analysed bands were found to be affected by rovibrational perturbations, which are discussed. The new data will be valuable to refine the parameters of the global effective Hamiltonian and dipole moments of12C2H2. [ABSTRACT FROM PUBLISHER]

The vibration–rotation dynamics of acetylene are computed from a spectroscopic Hamiltonian with 468 parameters fit to 19,582 vibration–rotation transitions up to 13,000 cm−1 of vibrational energy. In this energy range, both the bending and the CH stretching vibrations can reach large amplitudes, but the maximum energy remains below the threshold for isomerization to vinylidene. In contrast to the behavior at energies below 5000 cm−1 [Mol. Phys. 108, 1115 (2010)], excitation of single bright states leads, in almost all cases, to computed intramolecular vibrational redistribution (IVR) that is irreversible on the timescales investigated. Hierarchies of IVR processes on timescales ranging from 20 fs to 20 ps result when different bright states are excited. Different parts of the vibrational quantum number space are explored as a result of the four different classes of coupling terms: vibrational l-type resonance, anharmonic resonances, the rotational l-type resonance, and Coriolis couplings. The initial IVR rates are very different depending on whether the bright states are bending states or stretching states, normal modes or local modes, edge states or interior states. However, the rates of the rotationally mediated couplings do not depend substantially on these distinctions. [ABSTRACT FROM AUTHOR]

We study the influence of wetting films on (density-density) correlations for a fluid in a slit-like geometry near capillary condensation. We show that, for systems with short-ranged forces, the interaction between the wetting films strongly enhances the amplitude of the exponential decay of correlations and, unlike the interfacial roughness, is independent of a high-momentum cut-off. The correlation function shows scaling behaviour near condensation arising from the equality of two characteristic length scales: the parallel correlation length (associated with the complete wetting films) and a length scale related to the non-local interaction between the wetting films on either side of the slit. We introduce a dimensionless amplitude ratio associated with the decay of correlations which allows us to distinguish between local and non-local effective Hamiltonian theories. Only the latter is fully consistent with microscopic density functional descriptions of correlation functions. The influence of long-ranged intermolecular forces and fluctuation effects in two dimensions is also discussed. [ABSTRACT FROM AUTHOR]

We apply the method of moments to the multireference (MR) coupled cluster (CC) formalism representing the continuous transition between the Brillouin-Wigner-type and Rayleigh-Schrodinger-type theories based on the Jeziorski-Monkhorst wave function ansatz and derive the formula for the noniterative energy corrections to the corresponding MRCC energies that recover the exact, full configuration interaction energies in the general model space case, including complete and incomplete model spaces. We also extend the relationship between the generalised moments of the state-universal (SU) MRCC equations within the Jeziorski-Monkhorst and Kucharski-Bartlett formulations of the SUMRCC theory to the general model space case. Finally, we argue that in the complete model space case, the relationship between moments of the SUMRCC equations corresponding to the Jeziorski-Monkhorst and Kucharski-Bartlett formulations of the SUMRCC theory, derived in this work, implies an equivalence of these two formulations of the SUMRCC approach, provided that the disconnected linked terms are included in the Kucharski-Bartlett formulation, and verify this statement numerically. [ABSTRACT FROM AUTHOR]

The construction of an effective Hamiltonian which accurately accounts for the short-time dynamics at a conical intersection in high-dimensional systems [Phys. Rev. Lett. 94, 113003 (2005)] is discussed and extended to include topological considerations. A set of three topology-adapted, orthogonal coordinates is introduced, two of which span the branching space at the conical intersection. The new coordinates are at the same time characteristic dynamical and topological coordinates. This description is compared with the characteristic (g,h,s) vectors of the adiabatic representation. The dynamics induced by the effective Hamiltonian is discussed for a 22-dimensional model system related to the D 1 –D 0 conical intersection in the butatriene cation. [ABSTRACT FROM AUTHOR]

We describe a multi-reference Brillouin–Wigner coupled-cluster (BWCC) method that employs a general model space (GMS) by relying on the recently introduced C-conditions [X. Li, J. Paldus. J. chem. Phys. , 119 , 5320 (2003).] This generalization preserves all the essential features of the standard complete model space (CMS) BWCC method. This makes it possible to substantially reduce the dimension of the model space employed by keeping only important configurations and thus to minimize the computational cost. We also present the results of a preliminary numerical test using the cc-pVDZ model of the LiH molecule. [ABSTRACT FROM AUTHOR]