Search results for "partition function"
showing 10 items of 35 documents
Quantum-chemical determination of Born–Oppenheimer breakdown parameters for rotational constants: the open-shell species CN, CO+ and BO
2013
The quantum-chemical protocol for computing Born-Oppenheimer breakdown corrections to rotational constants in the case of diatomic molecules is extended to open-shell species. The deviation from the Born-Oppenheimer equilibrium rotational constant is obtained by considering three contributions: the adiabatic correction to the equilibrium bond distance, the electronic contribution to the moment of inertia requiring the computation of the rotational g-tensor, and the so-called Dunham correction. Values for the Born-Oppenheimer breakdown parameters of CN, CO+, and BO in their (2)sigma(+) electronic ground states are reported based on coupled-cluster calculations of the involved quantities and …
Gauge-origin independent calculation of magnetizabilities and rotational g tensors at the coupled-cluster level.
2007
An implementation of the gauge-origin independent calculation of magnetizabilities and rotational g tensors at the coupled-cluster (CC) level is presented. The properties of interest are obtained as second derivatives of the energy with respect to the external magnetic field (in the case of the magnetizability) or with respect to magnetic field and rotational angular momentum (in the case of the rotational g tensor), while gauge-origin independence and fast basis-set convergence are ensured by using gauge-including atomic orbitals (London atomic orbitals) as well as their extension to treat rotational perturbations (rotational London atomic orbitals). The implementation within our existing …
Thouless-Valatin Rotational Moment of Inertia from the Linear Response Theory
2017
Spontaneous breaking of continuous symmetries of a nuclear many-body system results in appearance of zero-energy restoration modes. Such modes introduce a non-physical contributions to the physical excitations called spurious Nambu-Goldstone modes. Since they represent a special case of collective motion, they are sources of important information about the Thouless-Valatin inertia. The main purpose of this work is to study the Thouless-Valatin rotational moment of inertia as extracted from the Nambu-Goldstone restoration mode that results from the zero-frequency response to the total angular momentum operator. We examine the role and effects of the pairing correlations on the rotational cha…
Anharmonic vibrational frequency calculations for solvated molecules in the B3LYP Kohn–Sham basis set limit
2012
Abstract The solvent dependence of harmonic and anharmonic vibrational wavenumbers of water, formaldehyde and formamide was studied using the B3LYP method. The results obtained with the hierarchy of Jensen's polarization-consistent basis sets were fitted with two-parameter formula toward the B3LYP Kohn–Sham complete basis set (CBS) limit. Anharmonic corrections have been obtained by a second order perturbation treatment (VPT2) and vibrational configuration interaction (VCI) method. The solvent environment was treated according to the self-consistent reaction field polarizable continuum model (SCRF PCM) approach.
The partition sum of methane at high temperature
2008
11 pages, 4 Tables, 3 Figures Computer code on line at http://icb.u-bourgogne.fr/JSP/TIPS.jsp; International audience; The total internal partition function of methane is revisited to provide reliable values at high temperature. A multi-resolution approach is used to perform a direct summation over all the rovibrational energy levels up to the dissociation limit. A computer code is executable on line at the URL : http://icb.u-bourgogne.fr/JSP/TIPS.jsp to allow the calculation of the partition sum of methane at temperatures up to 3000 K. It also provides detailed information on the density of states in the relevant spectral ranges. The recommended values include uncertainty estimates. It is …
Quantum and Classical Statistical Mechanics of the Non-Linear Schrödinger, Sinh-Gordon and Sine-Gordon Equations
1985
We are going to describe our work on the quantum and classical statistical mechanics of some exactly integrable non-linear one dimensional systems. The simplest is the non-linear Schrodinger equation (NLS) $$i{\psi _t} = - {\psi _{XX}} + 2c{\psi ^ + }\psi \psi $$ (1) where c, the coupling constant, is positive. The others are the sine- and sinh-Gordon equations (sG and shG) $${\phi _{xx}} - {\phi _{tt}} = {m^2}\sin \phi $$ (1.2) $${\phi _{xx}} - {\phi _{tt}} = {m^2}\sinh \phi $$ (1.3)
The pianigiani-yorke measure for topological markov chains
1997
We prove the existence of a Pianigiani-Yorke measure for a Markovian factor of a topological Markov chain. This measure induces a Gibbs measure in the limit set. The proof uses the contraction properties of the Ruelle-Perron-Frobenius operator.
Quantum-chemical calculation of Born–Oppenheimer breakdown parameters to rotational constants
2010
The paper describes how Born–Oppenheimer breakdown parameters for the rotational constants of diatomic molecules can be determined via quantum-chemical computations. The deviations from the Born–Oppenheimer equilibrium values are accounted for by considering the adiabatic correction to the equilibrium bond distances, the electronic contribution to the rotational constant via the rotational g tensor, and the so-called Dunham correction, which can be computed directly from a polynomial expansion of the potential curve around the equilibrium distance. Calculations for HCl, SiS, and HF demonstrate the accuracy that can be achieved in the theoretical treatment of the considered Born–Oppenheimer …
Calcium binding and ionic conduction in single conical nanopores with polyacid chains: model and experiments.
2012
Calcium binding to fixed charge groups confined over nanoscale regions is relevant to ion equilibrium and transport in the ionic channels of the cell membranes and artificial nanopores. We present an experimental and theoretical description of the dissociation equilibrium and transport in a single conical nanopore functionalized with pH-sensitive carboxylic acid groups and phosphonic acid chains. Different phenomena are simultaneously present in this basic problem of physical and biophysical chemistry: (i) the divalent nature of the phosphonic acid groups fixed to the pore walls and the influence of the pH and calcium on the reversible dissociation equilibrium of these groups; (ii) the asym…
Higher genera Catalan numbers and Hirota equations for extended nonlinear Schrödinger hierarchy
2021
We consider the Dubrovin--Frobenius manifold of rank $2$ whose genus expansion at a special point controls the enumeration of a higher genera generalization of the Catalan numbers, or, equivalently, the enumeration of maps on surfaces, ribbon graphs, Grothendieck's dessins d'enfants, strictly monotone Hurwitz numbers, or lattice points in the moduli spaces of curves. Liu, Zhang, and Zhou conjectured that the full partition function of this Dubrovin--Frobenius manifold is a tau-function of the extended nonlinear Schr\"odinger hierarchy, an extension of a particular rational reduction of the Kadomtsev--Petviashvili hierarchy. We prove a version of their conjecture specializing the Givental--M…