Thermodynamics of Forming Water Clusters at Various Temperatures and Pressures by Gaussian-2, Gaussian-3, Complete Basis Set-QB3, and Complete Basis Set-APNO Model Chemistries; Implications for Atmospheric Chemistry

The Gaussian-2, Gaussian-3, complete basis set- (CBS-) QB3, and CBS-APNO methods have been used to calculate ΔH° and ΔG° values for neutral clusters of water, (H2O)n, where n = 2−6. The structures are similar to those determined from experiment and from previous high-level calculations. The thermodynamic calculations by the G2, G3, and CBS-APNO methods compare well against the estimated MP2(CBS) limit. The cyclic pentamer and hexamer structures release the most heat per hydrogen bond formed of any of the clusters. While the cage and prism forms of the hexamer are the lowest energy structures at very low temperatures, as temperature is increased the cyclic structure is favored. The free energies of cluster formation at different temperatures reveal interesting insights, the most striking being that the cyclic trimer, cyclic tetramer, and cyclic pentamer, like the dimer, should be detectable in the lower troposphere. We predict water dimer concentrations of 9 × 1014 molecules/cm3, water trimer concentrations of 2.6 × 1012 molecules/cm3, tetramer concentrations of approximately 5.8 × 1011 molecules/cm3, and pentamer concentrations of approximately 3.5 × 1010 molecules/cm3 in saturated air at 298 K. These results have important implications for understanding the gas-phase chemistry of the lower troposphere.

Experimentation with different thermodynamic cycles used for pKa calculations on carboxylic acids using Complete Basis Set and Gaussian-n Models combined with CPCM Continuum Solvation Methods

Complete basis set and Gaussian-n methods were combined with Barone and Cossi's implementation of the polarizable conductor model (CPCM) continuum solvation methods to calculate pKa values for six carboxylic acids. Four different thermodynamic cycles were considered in this work. An experimental value of −264.61 kcal/mol for the free energy of solvation of H+, ΔGs(H+), was combined with a value for Ggas(H+) of −6.28 kcal/mol, to calculate pKa values with cycle 1. The complete basis set gas-phase methods used to calculate gas-phase free energies are very accurate, with mean unsigned errors of 0.3 kcal/mol and standard deviations of 0.4 kcal/mol. The CPCM solvation calculations used to calculate condensed-phase free energies are slightly less accurate than the gas-phase models, and the best method has a mean unsigned error and standard deviation of 0.4 and 0.5 kcal/mol, respectively. Thermodynamic cycles that include an explicit water in the cycle are not accurate when the free energy of solvation of a water molecule is used, but appear to become accurate when the experimental free energy of vaporization of water is used. This apparent improvement is an artifact of the standard state used in the calculation. Geometry relaxation in solution does not improve the results when using these later cycles. The use of cycle 1 and the complete basis set models combined with the CPCM solvation methods yielded pKa values accurate to less than half a pKa unit. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001

Accurate pKa Calculations for Carboxylic Acids Using Complete Basis Set and Gaussian-n Models Combined with CPCM Continuum Solvation Methods”

Complete Basis Set and Gaussian-n methods were combined with CPCM continuum solvation methods to calculate pKa values for six carboxylic acids. An experimental value of −264.61 kcal/mol for the free energy of solvation of H+, ΔGs(H+), was combined with a value for Ggas(H+) of −6.28 kcal/mol to calculate pKa values with Cycle 1. The Complete Basis Set gas-phase methods used to calculate gas-phase free energies are very accurate, with mean unsigned errors of 0.3 kcal/mol and standard deviations of 0.4 kcal/mol. The CPCM solvation calculations used to calculate condensed-phase free energies are slightly less accurate than the gas-phase models, and the best method has a mean unsigned error and standard deviation of 0.4 and 0.5 kcal/mol, respectively. The use of Cycle 1 and the Complete Basis Set models combined with the CPCM solvation methods yielded pKa values accurate to less than half a pKa unit.

Accurate relative pKa calculations for carboxylic acids using complete basis set and Gaussian-n models combined with continuum solvation methods

The complete basis set methods CBS-4, CBS-QB3, and CBS-APNO, and the Gaussian methods G2 and G3 were used to calculate the gas phase energy differences between six different carboxylic acids and their respective anions. Two different continuum methods, SM5.42R and CPCM, were used to calculate the free energy differences of solvation for the acids and their anions. Relative pKa values were calculated for each acid using one of the acids as a reference point. The CBS-QB3 and CBS-APNO gas phase calculations, combined with the CPCM/HF/6-31+G(d)//HF/6-31G(d) or CPCM/HF/6-31+G(d)//HF/6-31+G(d) continuum solvation calculations on the lowest energy gas phase conformer, and with the conformationally averaged values, give results accurate to ½ pKa unit. © 2001 American Institute of Physics.

Implementation and application of basis set superposition error-correction schemes to the theoretical modeling of weak intermolecular interactions

This thesis deals with the so-called Basis Set Superposition Error (BSSE) from both a methodological and a practical point of view. The purpose of the present thesis is twofold: (a) to contribute step ahead in the correct characterization of weakly bound complexes and, (b) to shed light the understanding of the actual implications of the basis set extension effects in the ab intio calculations and contribute to the BSSE debate. The existing BSSE-correction procedures are deeply analyzed, compared, validated and, if necessary, improved. A new interpretation of the counterpoise (CP) method is used in order to define counterpoise-corrected descriptions of the molecular complexes. This novel point of view allows for a study of the BSSE-effects not only in the interaction energy but also on the potential energy surface and, in general, in any property derived from the molecular energy and its derivatives A program has been developed for the calculation of CP-corrected geometry optimizations and vibrational frequencies, also using several counterpoise schemes for the case of molecular clusters. The method has also been implemented in Gaussian98 revA10 package. The Chemical Hamiltonian Approach (CHA) methodology has been also implemented at the RHF and UHF levels of theory for an arbitrary number interacting systems using an algorithm based on block-diagonal matrices. Along with the methodological development, the effects of the BSSE on the properties of molecular complexes have been discussed in detail. The CP and CHA methodologies are used for the determination of BSSE-corrected molecular complexes properties related to the Potential Energy Surfaces and molecular wavefunction, respectively. First, the behaviour of both BSSE-correction schemes are systematically compared at different levels of theory and basis sets for a number of hydrogen-bonded complexes. The Complete Basis Set (CBS) limit of both uncorrected and CP-corrected molecular properties like stabilization energies and intermolecular distances has also been determined, showing the capital importance of the BSSE correction. Several controversial topics of the BSSE correction are addressed as well. The application of the counterpoise method is applied to internal rotational barriers. The importance of the nuclear relaxation term is also pointed out. The viability of the CP method for dealing with charged complexes and the BSSE effects on the double-well PES blue-shifted hydrogen bonds is also studied in detail. In the case of the molecular clusters the effect of high-order BSSE effects introduced with the hierarchical counterpoise scheme is also determined. The effect of the BSSE on the electron density-related properties is also addressed. The first-order electron density obtained with the CHA/F and CHA/DFT methodologies was used to assess, both graphically and numerically, the redistribution of the charge density upon BSSE-correction. Several tools like the Atoms in Molecules topologycal analysis, density difference maps, Quantum Molecular Similarity, and Chemical Energy Component Analysis were used to deeply analyze, for the first time, the BSSE effects on the electron density of several hydrogen bonded complexes of increasing size. The indirect effect of the BSSE on intermolecular perturbation theory results is also pointed out It is shown that for a BSSE-free SAPT study of hydrogen fluoride clusters, the use of a counterpoise-corrected PES is essential in order to determine the proper molecular geometry to perform the SAPT analysis.

The ability of the Gaussian-2, Gaussian-3, Complete Basis Set–QB3, and Complete Basis Set–APNO model chemistries to model the geometries of small water clusters

The Gaussian-2, Gaussian-3, Complete Basis Set-QB3, and Complete Basis Set-APNO methods have been used to calculate geometries of neutral clusters of water, (H2O)n, where n = 2–6. The structures are in excellent agreement with those determined from experiment and those predicted from previous high-level calculations. These methods also provide excellent thermochemical predictions for water clusters, and thus can be used with confidence in evaluating the structures and thermochemistry of water clusters.

Comparison of the experimental, semi-experimental and ab initio equilibrium structures of acetylene: Influence of relativisitic effects and of the diagonal Born-Oppenheimer corrections

The equilibrium structure of acetylene (also named ethyne) has been reinvestigated to resolve the small discrepancies noted between different determinations. The size of the system as well as the large amount of available experimental data provides the quite unique opportunity to check the magnitude and relevance of various contributions to equilibrium structure as well as to verify the accuracy of experimental results. With respect to pure theoretical investigation, quantum-chemical calculations at the coupled-cluster level have been employed together with extrapolation to the basis set limit, consideration of higher excitations in the cluster operator, inclusion of core correlation effects as well as relativistic and diagonal Born-Oppenheimer corrections. In particular, it is found that the extrapolation to the complete basis set limit, the inclusion of higher excitations in the electronic-correlation treatment and the relativistic corrections are of the same order of magnitude. It also appears that a basis set as large as a core-valence quintuple-zeta set is required for accurately accounting for the inner-shell correlation contribution. From a pure experimental point of view, the equilibrium structure has been determined using very accurate rotational constants recently obtained by a global analysis (that is to say that all non-negligible interactions are explicitely included in the Hamiltonian matrix) of rovibrational spectra. Finally, a semi-experimental equilibrium structure (where the equilibrium rotational constants are obtained from the experimental ground state rotational constants and computed rovibrational corrections) has been obtained from the available experimental ground-state rotational constants for ten isotopic species corrected for computed vibrational corrections. Such a determination led to the revision of the ground-state rotational constants of two isotopologues, thus showing that structural determination is a good method to identify errors in experimental rotational constants. The three structures are found in a very good agreement, and our recommended values are rCC 120.2958(7) pm and rCH 106.164(1) pm. © 2011 American Institute of Physics.

Prediction of the formation and stabilities of energetic salts and ionic liquids based on ab initio electronic structure calculations

A computational approach to predict the thermodynamics for forming a variety of imidazolium-based salts and ionic liquids from typical starting materials is described. The gas-phase proton and methyl cation acidities of several protonating and methylating agents, as well as the proton and methyl cation affinities of many important methyl-, nitro-, and cyano- substituted imidazoles, have been calculated reliably by using the computationally feasible DFT (B3LYP) and MP2 (extrapolated to the complete basis set limit) methods. These accurately calculated proton and methyl cation affinities of neutrals and anions are used in conjunction with an empirical approach based on molecular volumes to estimate the lattice enthalpies and entropies of ionic liquids, organic solids, and organic liquids. These quantities were used to construct a thermodynamic cycle for salt formation to reliably predict the ability to synthesize a variety of salts including ones with potentially high energetic densities. An adjustment of the gas phase thermodynamic cycle to account for solid- and liquid-phase chemistries provides the best overall assessment of salt formation and stability. This has been applied to imidazoles (the cation to be formed) with alkyl, nitro, and cyano substituents. The proton and methyl cation donors studied were as follows: HCl, HBr, HI, (HO)(2)SO2, HSO3CF3 (TfOH), and HSO3(C6H4)CH3 (TsOH); CH3Cl, CH3Br, CH3I, (CH3O)(2)SO2, CH3SO3CF3 (TfOCH3) and CH3SO3(C6H4)CH3 (TsOCH3). As substitution of the cation with electron-withdrawing groups increases, the triflate reagents appear to be the best overall choice as protonating and methylating agents. Even stronger alkylating agents should be considered to enhance the chances of synthetic success. When using the enthalpies of reaction for the gas-phase reactants (eq 6) to form a salt, a cutoff value of - 13 kcal mol(-1) or lower (more negative) should be used as the minimum value for predicting whether a salt can be synthesized.

Structural and spectroscopic properties of the diazocarbene radical (CNN) and its ions CNN(+) and CNN(-): a high-level theoretical investigation

The diazocarbene radical, CNN, and the ions CNN(+) and CNN(-) were investigated at a high level of theory. Very accurate structural parameters for the states X(3)Sigma(-) and A(3)Pi of CNN, and X(2)Pi of both CNN(+) and CNN(-) were obtained with the UCCSD(T) method using correlated-consistent basis functions with extrapolations to the complete basis set limit, with valence only and also with all electrons correlated. Harmonic and anharmonic frequencies were obtained for all species and the Renner parameter and average frequencies evaluated for the Pi states. At the UCCSD(T)/CBS(T-5) level of theory, Delta(f)H(0 K) = 138.89 kcal/mol and Delta(f)H(298 K) = 139.65 kcal/mol were obtained for diazocarbene; for the ionization potential and the electron affinity of CNN, 10.969 eV (252.95 kcal/mol), and 1.743 eV (40.19 kcal/mol), respectively, are predicted. Geometry optimization was also carried out with the CASSCF/MRCI/CBS(T-5) approach for the states X(3)Sigma(-) A(3)Pi, and a(1)Delta of CNN, and with the CASSCF/MRSDCI/aug-cc-pVTZ approach for the states b(1)Sigma(+), c(1)Pi, d(1)Sigma(-), and B(3)Sigma(-), and excitation energies (T(e)) evaluated. Vertical energies were calculated for 15 electronic states, thus improving on the accuracy of the five transitions already described, and allowing for a reliable overview of a manifold of other states, which is expected to guide future spectroscopic experiments. This study corroborates the experimental assignment for the vertical transition X (3)Sigma(-) <- E (3)Pi.

Isomers on the [H, S(2), Cl] potential energy surface: A high level investigation

This study reports a systematic state-of-the-art characterization of new sulfur-chlorine species on the [H, S(2), Cl] potential energy surface. Coupled cluster theory singles and doubles with perturbative contributions of connected triples, using the series of correlation consistent basis sets with extrapolations to the complete basis set limit (CBS), were employed to quantify the energetic quantities involved in the isomerization processes on this surface. The structures and vibrational frequencies are unique for some species and represent the most accurate investigation to date. These molecules are potentially a new route of coupling the sulfur and chlorine chemistries in the atmosphere, and conditions of high concentration of H(2)S (HS) like in volcanic eruptions might contribute to their formation. Also an assessment of the MP2/CBS approach relative to CCSD(T)/CBS provides insights on the expected performance of MP2/CBS on the characterization of polysulfides, and also of more complex systems containing disulfide bridges. (C) 2009 Elsevier B.V. All rights reserved.

Theoretical study of the XP3 (X = Al, B, Ga) clusters

The lowest singlet and triplet states of AlP3, GaP3 and BP3 molecules with C-s, C-2v and C-3v symmetries were characterized using the B3LYP functional and the aug-cc-pVTZ and aug-cc-pVQZ correlated consistent basis sets. Geometrical parameters and vibrational frequencies were calculated and compared to existent experimental and theoretical data. Relative energies were obtained with single point CCSD(T) calculations using the aug-cc-pVTZ, aug-cc-pVQZ and aug-cc-pV5Z basis sets, and then extrapolating to the complete basis set (CBS) limit. (C) 2011 Elsevier B.V. All rights reserved.

Benchmark Structures and Binding Energies of Small Water Clusters with Anharmonicity Corrections

For (H2O)n where n = 1–10, we used a scheme combining molecular dynamics sampling with high level ab initio calculations to locate the global and many low lying local minima for each cluster. For each isomer, we extrapolated the RI-MP2 energies to their complete basis set limit, included a CCSD(T) correction using a smaller basis set and added finite temperature corrections within the rigid-rotor-harmonic-oscillator (RRHO) model using scaled and unscaled harmonic vibrational frequencies. The vibrational scaling factors were determined specifically for water clusters by comparing harmonic frequencies with VPT2 fundamental frequencies. We find the CCSD(T) correction to the RI-MP2 binding energy to be small (<1%) but still important in determining accurate conformational energies. Anharmonic corrections are found to be non-negligble; they do not alter the energetic ordering of isomers, but they do lower the free energies of formation of the water clusters by as much as 4 kcal/mol at 298.15 K.

Benchmark Structures and Binding Energies of Small Water Clusters with Anharmonicity Corrections

For (H2O)n where n = 1–10, we used a scheme combining molecular dynamics sampling with high level ab initio calculations to locate the global and many low lying local minima for each cluster. For each isomer, we extrapolated the RI-MP2 energies to their complete basis set limit, included a CCSD(T) correction using a smaller basis set and added finite temperature corrections within the rigid-rotor-harmonic-oscillator (RRHO) model using scaled and unscaled harmonic vibrational frequencies. The vibrational scaling factors were determined specifically for water clusters by comparing harmonic frequencies with VPT2 fundamental frequencies. We find the CCSD(T) correction to the RI-MP2 binding energy to be small (

Accurate Treatment of Large Supramolecular Complexes by Double-Hybrid Density Functionals Coupled with Nonlocal van der Waals Corrections

In this work, we present a thorough assessment of the performance of some representative double-hybrid density functionals (revPBE0-DH-NL and B2PLYP-NL) as well as their parent hybrid and GGA counterparts, in combination with the most modern version of the nonlocal (NL) van der Waals correction to describe very large weakly interacting molecular systems dominated by noncovalent interactions. Prior to the assessment, an accurate and homogeneous set of reference interaction energies was computed for the supramolecular complexes constituting the L7 and S12L data sets by using the novel, precise, and efficient DLPNO-CCSD(T) method at the complete basis set limit (CBS). The correction of the basis set superposition error and the inclusion of the deformation energies (for the S12L set) have been crucial for obtaining precise DLPNO-CCSD(T)/CBS interaction energies. Among the density functionals evaluated, the double-hybrid revPBE0-DH-NL and B2PLYP-NL with the three-body dispersion correction provide remarkably accurate association energies very close to the chemical accuracy. Overall, the NL van der Waals approach combined with proper density functionals can be seen as an accurate and affordable computational tool for the modeling of large weakly bonded supramolecular systems.

Intramolecular hydrogen bond: Can it be part of the basis set of valence internal coordinates in normal mode analysis?

It has been shown earlier1] that the relaxed force constants (RFCs) could be used as a measure of bond strength only when the bonds form a part of the complete valence internal coordinates (VIC) basis. However, if the bond is not a part of the complete VIC basis, its RFC is not necessarily a measure of bond strength. Sometimes, it is possible to have a complete VIC basis that does not contain the intramolecular hydrogen bond (IMHB) as part of the basis. This means the RFC of IMHB is not necessarily a measure of bond strength. However, we know that IMHB is a weak bond and hence its RFC has to be a measure of bond strength. We resolve this problem of IMHB not being part of the complete basis by postulating `equivalent' basis sets where IMHB is part of the basis at least in one of the equivalent sets of VIC. As long as a given IMHB appears in one of the equivalent complete VIC basis sets, its RFC could be used as a measure of bond strength parameter.