Thermodynamics of system composed of three possible isomeric dideuteriocyclobutadienes has been studied based on the best available theoretical structural and vibrational parameters. Particular attention is paid to the recently raised question of applicability of the conventional (one term proportional to T3/2) expression for the rotational part of partition functions of the isotopomers at low temperatures T in comparison with more sophisticated approximations viz. containing an additional term proportional to T1/2 or even a correction proportional to T–1/2. Mutual relative stabilities of the isomeric isotopomers are evaluated as well as the isomerism contributions to the system thermodynamics. The three approaches are proved to yield very close results even at very low temperatures. Consequences for structure interplay in isomeric isotopomer sets are discussed.
A search for conditions leading to the highest possible difference between equilibrium association (clustering) degree in the H and D steam has been carried out and related optimal steam pressures evaluated. The difference decreases with increasing temperature but still is a few per cent at moderate temperatures.
Zero-point vibration energy differences for all possible 12 isotopomers of the water dimer have been evaluated using various modifications of MCY potential combined with the intramolecular force field of free water molecule. In agreement with observation, in isomeric pairs of H- and D-bonded dimers the latter have been proved, both through computation and partly also by a general reasoning, to be more stable.
Equilibrium constants of H2O/g/ and D2O/g/ associations to clusters /H2O/n/g/ and /D2O/n/g/ have been calculated on the basis of the ab initio SCF CI MCY-B water-water pair potential. Populations of the components of equilibrium cluster mixtures have been evaluated at various temperatures and pressures for both isotopomeric series. Differences between the H and D steam are pointed out and possible consequences are discussed.
Harmonic vibrational analysis is carried out for the water dimer (1H or natural isotopic mixture) and its2D and3T isotopomers in the gas phase, using the recently designed flexible potential energy functions. The results represent the most complete and reliable theoretical evaluation of the vibrational frequencies, directly applicable to various observation interpretations. The complete data set can also be useful for a more general isotopomeric reasoning.
Evaluation has been carried out of the component of the second virial coefficient of steam related to the formation of dimers. The necessary equilibrium constants of dimerization have been evaluated within the MCY-B water pair interaction potential. The calculated isotopic difference in the second virial coefficient reflects the qualitative features found by observation but, nevertheless, the calculation quite distinctly overestimates the value of this isotopic difference as compared with the observation. The nature of these differences and the relation to the state behaviour of water are discussed.
Using 8 modifications of recently developed flexible water potentials, zeropoint energy differences between the isomeric water-dimer isotopomers differing in the hydrogen isotope involved in the hydrogen bond have been evaluated. In all the 18 possible pairs, the species bound through the heavier isotope is always lower in the energy term.
The current experimental and computational research in carbon clusters pointed out a need for enumeration of all possible12C/13C isotopoments of the C2v cyclic odd-numbered carbon clusters Cn. It is shown that the number of the isotopomers is given by 2k–1(2k–1+1) withk=(n+1)/2. Some illustrative computed structure and energy data for the clusters are reported, too.
Isotopic rules are studied for calculated vibrational frequencies of all possible 7212C/13C isotopomers of the C7 cluster of the C2v symmetry. The isotopomers can undergo 486 isomerizations which are decomposed into 27 subclasses using properties of sums of the squares of the vibrational frequencies.
The set of all 51 possible12C/13C isotopomers of a C8 cluster of D2d symmetry has been studied by means of the harmonic vibration analysis based on the force field resulting from the second order Møller-Plesset (MP2) perturbation treatment with the 6-31G* basis set. The isotopomers can undergo 200 isomerizations which can be classified into 5 distinct groups using the properties of sums of the squares of harmonic vibrational frequencies.