Composition of the Water Dimer and the Heterodimers of Water with N2 and O2 in Earth's Atmosphere.

The mole fractions χ and number concentrations n of the water dimer and the heterodimers H2O-N2 and H2O-O2 in Earth's atmosphere are reported up to 20 km. The water dimer data is obtained from published values of the equilibrium constant based on the water equation of state. The mixed equilibrium constants for the heterodimers are obtained from the respective second virial coefficients using an approach introduced by Stogryn and Hirschfelder that extracts the components pertaining to pairwise interactions producing bound and metastable dimers. From these calculations, χ and n for the water dimer and the (H2O)(N2) and (H2O)(O2) heterodimers at standard sea level are 1.79(6) × 10-5, 4.77(12) × 10-5 and 9.90(5) × 10-6 and 4.55(15) × 1014, 1.23(3) × 1016 and 2.56(1) × 1015, respectively. Analytical expressions are provided for these quantities for altitudes between 0-20 km and temperatures from 200-300 K. Sea level values of χ and n are given for two specific locations.

Thermodynamics of the van der Waals Dimers of O2, N2 and the Heterodimer (N2)(O2) and Their Presence in Earth's Atmosphere.

The dimerization thermodynamics of N2 and O2, the principal components of Earth's atmosphere, have been determined from the respective second virial coefficients of the bound and metastable dimers calculated using the method of Stogryn and Hirschfelder that utilizes the Lennard-Jones (LJ) potential to account for intermolecular interactions. In addition, the thermodynamic properties of the heterodimer (N2)(O2) have been obtained using the same approach, employing combining rules to construct the LJ potential. Thus, Keq, ΔH, and ΔS for the three dimers are reported between 80-120 K. Over this temperature range, the ranking of Keq is (N2)(O2) > (O2)(O2) > (N2)(N2). The same trend is found for the exoethalpicity of dimer formation. For example, at 100 K, the Keq values are, respectively, 0.0406(14), 0.0215(5), and 0.0181(10), and the corresponding ΔH values are -2401(5), -2344(7), and -2279(1) J/mol. The mole fraction composition of the dimers in the atmosphere was calculated for altitudes up to 20 km. These calculations show that in the troposphere and the lower stratosphere (up to 20 km), the three dimers rank fifth to seventh in abundance, between CO2 and Ne. In this region, the average mole fractions of (N2)(N2), (O2)(O2), and (N2)(O2) are calculated to be 3.4(2) × 10-4, 2.80(9) × 10-5, and 1.95(7) × 10-4, respectively.

Thermodynamic Properties of van der Waals Dimers and Trimers of Nonpolar Gases and Their Correlation with Lennard-Jones Potential Well Depths.

A method of unifying the equilibrium thermodynamic properties ΔHo and ΔGo relating to the van der Waals dimers and trimers of 15 nonpolar gases (He-Xe, H2, D2, CH4, CF4, ethene, ethane, CO2, SF6, propane, and neopentane) is described. Values of ΔHo and ΔGo, obtained at the reduced temperature Tr = 0.7, show good correlation with the respective Lennard-Jones pair potential well depth, calculated from the monomer critical temperature and the acentric factor. Such relationships present the opportunity to estimate the van der Waals dimer and trimer thermodynamic properties of other nonpolar molecules, and examples of seven such applications are given. It is found that the enthalpies of dimerization and trimerization of the 15 gases are about 21 and 29% of the respective condensation enthalpies, providing information about the thermodynamics of small clusters in relation to liquefaction.

Equilibrium Thermodynamics of the Dimers and Trimers of H2 and D2 and Their Heterodimer (H2)(D2).

The equilibrium thermochemical properties of the dimers and trimers of H2 and D2 are obtained from the equations of state (EOSs) of normal H2 and D2. The standard dimer and trimer equilibrium constants K D o and K T o and ΔH D, T o and ΔS D, T o are reported for these weakly bound van der Waals molecules between 25 and 45 K. Statistical thermodynamics (ST) calculations of H2 and D2 dimerization using Morse pair potentials to account for intermolecular interactions, obtained from recent experimental work, are in qualitative agreement with the EOS results. The entropies of the H2 and D2 dimers and trimers are calculated from the EOS ΔS o values and ST calculations of the monomer entropies.

Thermodynamics of Helium-4 Dimerization and Trimerization.

A new equation of state (EOS) for helium-4 is used to obtain the equilibrium thermochemical properties of helium-4 dimerization (24He ⇌ 4He2) and trimerization (34He ⇌ 4He3) between 3.0 and 10.0 K. It is shown that at sufficiently low temperatures there are appreciable populations of dimer and trimer. The calculations account only for monomer, dimer, and trimer. At 3.0 K, the respective KPo values for dimerization and trimerization are 0.4832 and 0.4876, respectively. The standard enthalpy changes at 3.0 K are -54.53 and -110.0 J/mol, and standard entropy changes are -24.22 and -42.97 J/mol-K. Statistical thermodynamic calculations provide results that are qualitatively consistent with those obtained from the EOS calculations.

Ab initio calculations of nitrogen oxide reactions: formation of N2O2, N2O3, N2O4, N2O5, and N4O2 from NO, NO2, NO3, and N2O.

Ab initio computational methods were used to obtain Delta(r)H(o), Delta(r)G(o), and Delta(r)S(o) for the reactions 2 NO <=> N(2)O(2) (I), NO+NO(2) <=> N(2)O(3) (II), 2 NO(2) <=> N(2)O(4) (III), NO(2)+NO(3) <=> N(2)O(5) (IV), and 2 N(2)O <=> N(4)O(2) (V) at 298.15 K. Optimized geometries and frequencies were obtained at the CCSD(T) level for all molecules except for NO, NO(2), and NO(3), for which UCCSD(T) was used. In all cases the aug-cc-pVDZ (avdz) basis set was employed. The electronic energies of all species were obtained from complete basis set extrapolations (to aug-cc-pV5Z) using five different extrapolation methods. The [U]CCSD(T)/avdz geometries and frequencies of the N(x)O(y) compounds are compared with literature values, and problems associated with the values and assignments of low-frequency modes are discussed. The standard entropies are compared with values cited in the NIST/JANAF tables [NIST-JANAF Thermochemical Tables, J. Phys. Chem. Ref. Data Monograph No. 9, 4th ed. edited by M. W. Chase, Jr. (American Chemical Society and American Institute of Physics, Woodbury, NY, 1988)]. With the exception of I, in which the dimer is weakly bound, and V, for which thermodynamic data appears to be lacking, the calculated standard thermodynamic functions of reaction are in good agreement with literature values obtained both from statistical mechanical and various equilibrium methods. A multireference-configuration interaction calculation (MRCI+Q) for I provides a D(e) value that is consistent with previous calculations. The combined uncertainties of the NIST/JANAF values for Delta(r)H(o), Delta(r)G(o), and Delta(r)S(o) of II, III, and IV are discussed. The potential surface for the dissociation of N(2)O(4) was explored using multireference methods. No evidence of a barrier to dissociation was found.

Ab initio study of the torsional potential energy surfaces of N2O3 and N2O4: origin of the torsional barriers.

Intrinsic reaction coordinate (IRC) torsional potentials were calculated for N(2)O(4) and N(2)O(3) based on optimized B3LYP/aug-cc-pVDZ geometries of the respective 90 degrees -twisted saddle points. These potentials were refined by obtaining CCSD(T)aug-cc-pVXZ energies [in the complete basis set (CBS) limit] of points along the IRC. A comparison is made between these ab initio potentials and an analytical form based on a two-term cosine expansion in terms of the N-N dihedral angle. The shapes of these two potential curves are in close agreement. The torsional barriers in N(2)O(4) and N(2)O(3) obtained from the CCSD(T)/CBS//B3LYP/aug-cc-pVDZ calculations are 2333 and 1704 cm(-1), respectively. For N(2)O(4) the torsion fundamental frequency from the IRC potential is 87.06 cm(-1), which is in good agreement with the experimentally reported value of 81.73 cm(-1). However, in the case of N(2)O(3) the torsional frequency found from the IRC potential, 144 cm(-1), is considerably larger than the reported experimental values 63-76 cm(-1). Consistent with this discrepancy, the torsional barrier obtained from several different calculations, 1417-1718 cm(-1), is higher than the value of 350 cm(-1) deduced from experimental studies. It is suggested that the assignment of the torsional mode in N(2)O(3) should be reexamined. N(2)O(4) and N(2)O(3) exhibit strong hyperconjugative interactions of in-plane O lone pairs with the central N-N sigma* antibond. Hyperconjugative stabilization is somewhat stronger at the planar geometries because 1,4 interactions of lone pairs on cis O atoms promote delocalization of electrons into the N-N antibond. Calculations therefore suggest that the torsional barriers in these molecules arise principally from a combination of 1,4 interactions and hyperconjugation.

Ab initio study of cyclobutane: molecular structure, ring-puckering potential, and origin of the inversion barrier.

The structure and ring-puckering properties of cyclobutane and its perdeuterated isotopomer are studied using high-level ab initio methods and complete basis set extrapolations. Calculations reveal significant coupling between the ring-puckering (theta) and CH(2)-rocking (alpha) motions, with equilibrium angles (theta(eq) = 29.59 degrees and alpha(eq) = 5.67 degrees) that are within the range of experimentally determined values. Our best estimate of the inversion barrier is 482 cm(-1), in excellent agreement with recent experimental determinations. Ring-inversion transition frequencies are evaluated from the eigenstates of the intrinsic reaction coordinate potentials for cyclobutane and cyclobutane-d(8). Natural bond orbital analysis shows that sigma(CC) --> sigma(CH)* and sigma(CH) --> sigma(CH)* hyperconjugative interactions are strengthened as cyclobutane puckers, thereby suggesting that inversion barriers in four-membered ring systems are a consequence of electronic delocalization rather than torsional strain.

An intrinsic reaction coordinate calculation of the torsion-internal rotation potential of hydrogen peroxide and its isotopomers.

Intrinsic reaction coordinate (IRC) calculations of the internal rotation (torsional) potentials for H(2)O(2) and its isotopomers HDO(2) and D(2)O(2) were carried out at the CCSD(T)/CBS//aug-cc-pVDZ level. Two extrapolation methods were used to obtain energies in the complete basis set (CBS) limit. The full IRC potential was constructed from scans from the C(2v) (cis) and C(2h) (trans) transition states to the equilibrium C(2) (gauche) structure. The IRC potential for H(2)O(2) was fit to a five-term Fourier function; coefficients were compared with values obtained from spectroscopic data. The twofold IRC torsional potentials were used to obtain torsional eigenvalues, which yielded values of the transitions between various ntau states. These results compare favorably with Raman and near-infrared data. Our calculations provide values of the cis and trans barriers of 2495 and 364 cm(-1), respectively, which are in good agreement with both previously calculated and experimentally derived values. It appears that coupling between torsional motion and other degrees of freedom is not significant in these molecules.