Large-N expansions in quantum mechanics, atomic physics and some O(N) invariant systems

The highest frequency hydrogen bond fundamental of formic acid dimer, ν24 (Bu), is experimentally located at 264 cm−1. FTIR spectra of this in-plane bending mode of (HCOOH)2 and band centers of its symmetric D isotopologues (isotopomers) recorded in a supersonic slit jet expansion are presented. Comparison to earlier studies at room temperature reveals the large influence of thermal excitation on the band maximum. Together with three Bu combination states involving hydrogen bond fundamentals and with recent progress for the Raman-active modes, this brings into reach an accurate statistical thermodynamics treatment of the dimerization process up to room temperature. We obtain D0 = 59.5(5) kJ/mol as the best experimental estimate for the dimer dissociation energy at 0 K. Further improvements have to wait for a more consistent determination of the room temperature equilibrium constant.

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Communication: The highest frequency hydrogen bond vibration and an experimental value for the dissociation energy of formic acid dimer

Survey jet-cooled spectra of acetic acid have been recorded in the infrared region (200–4000 cm−1) over a wide range of expansion conditions. From the variations of the relative intensities of the signals, vibrational transitions have been assigned unambiguously to the trans-monomer and cyclic-dimer. The IR-active fundamental frequencies have been determined at the instrumental accuracy of 0.5 cm−1. This analysis of the jet-cooled spectra supported by electronic structure calculations permitted us to characterize the trans-monomer/cyclic-dimer equilibrium. From static cell spectra at 298 K, variations of the molar fractions ratio as a function of the total pressure were used to estimate the equilibrium constant and the Gibbs free energy of dimerization at 298 K. The very good agreement with the literature data shows that the present method is able to produce, from a single study, a free energy value as reliable as the one obtained from a large collection of data. In addition, the semi-empirical free energy value was used to estimate the accuracy of electronic structure calculations and in turn the accuracy of the derived useful information such as the dissociation energy of the complex (i.e. the strength of the hydrogen bonds) or the relative energies within the conformational landscape.

Standard free energy of the equilibrium between the trans-monomer and the cyclic-dimer of acetic acid in the gas phase from infrared spectroscopy

The association term of the nonrandom hydrogen bonding theory, which is an equation of state model, is extended to describe the dimerization of carboxylic acids in binary mixtures with inert solvents and in systems of two different acids. Subsequently, the model is applied to describe the excess enthalpies and the vapor-liquid equilibrium of relevant binary mixtures containing low molecular weight organic acids. The model sheds light on the interplay of intermolecular interactions through the calculation of the various contributions to the mixing enthalpies, namely from hydrogen bonding and non-hydrogen bonding (dipolar, induced polar or dispersive) interactions. According to model predictions, the acid molecules are so strongly associated that the addition of inert solvents to carboxylic acids with small carbon numbers at ambient temperature does not dramatically alter their degree of association. Consequently, the observed endothermic dissolution process is mainly attributed to the hindering of polar interactions. Furthermore, upon mixing of two carboxylic acids, the rearrangement of hydrogen bonds due to the formation of cross associating species results in an insignificant contribution to the heats of mixing due to the rather constant dimerization enthalpy that is revealed by the available experimental data for low molecular weight compounds.

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Dimerization of Carboxylic Acids: An Equation of State Approach.

By tuning the alkyl substituent of a carboxylic acid, the intermolecular modes in its hydrogen-bonded dimer can be reordered. These modes are detected at low vibrational congestion for formic, acetic, propiolic and pivalic acid using Raman jet spectroscopy. By probing the shock zone between the free jet and the background gas, a continuous evolution of the dimer spectra between cryogenic and ambient temperatures is achieved. Analysis of the dimer stretching mode within a pseudo-diatomic model quantifies substitution effects on the hydrogen-bond force constant. They do not correlate with effects on predicted overall dimer binding energies. The evolution of the spectra with increasing cluster size reveals the stacking structure of supra-dimeric aggregates.

Adding more weight to a molecular recognition unit: the low-frequency modes of carboxylic acid dimers

Squeezing and photon antibunching from a two-photon dicke model

A statistical mechanical model is used to critique vapor density experiments on acetic acid. The model suggests that the differences in the standard enthalpy of dissociation of acetic acid dimer reported in the literature lie mainly in the interpretation of the data and not in the data itself. If a uniform and plausible interpretative framework is adopted, the discrepancies largely disappear.

Acetic acid vapor: 2. A statistical mechanical critique of vapor density experiments.

Two statistical mechanical/quantum computational models are developed for the ideal acetic acid vapor. One describes the equilibrium of the cis-monomer and the ring dimer and the other the equilibrium of a mixture of oligomers. Ten quantum computational models of the acetic acid ring dimer have been compared in developing these models. The end product of this work is a critical tool for assessing experimental vapor density studies of acetic acid reported in the literature.

James B. Togeas

Papers

Squeezing and photon antibunching from a two-photon dicke model

Acetic acid vapor: 2. A statistical mechanical critique of vapor density experiments.

Acetic acid vapor: 1. Statistical/quantum mechanical models of the ideal vapor.

Large-N phase-integral approximation for SU(1,1) coherent states

Scaling variational approach to non-confining potentials: The gaussian well