Polarized basis sets for accurate calculations of static and dynamic electric properties of molecules.

We report on the development and testing of large polarized basis sets (LPolX, where X is the element symbol) for accurate calculations of linear and nonlinear electric properties of molecules. The method used to generate LPolX sets is based on our studies of the analytic dependence of Gaussian functions on external time-independent and time-dependent electric fields. At variance with the earlier investigations of small, highly compact (ZPolX) basis sets for moderately accurate calculations of electric properties of large molecules, the present goal is to obtain basis sets that are nearly saturated with respect to the selected class of electric properties and can be used for accurate studies of interaction-induced properties. This saturation makes the LPolX sets also useful in calculations of optical properties for chiral molecules. In this article, the LPolX sets are generated for X = H, C, N, O, and F, and examined in calculations of linear and nonlinear electric properties of four standard test systems: HF, N(2), CO, and HCN. The study of the performance of LPolX basis sets has been carried out at different levels of approximation ranging from the SCF HF method to highly correlated CCSD(T) approach. The results obtained in this study compare favorably with accurate reference data and show a high level of saturation of LPolX basis sets with respect to the polarization effect due to external electric fields.

Model studies of the optical rotation, and theoretical determination of its sign for beta-pinene and trans-pinane.

We have carried out extensive studies on the basis set dependence of the calculated specific optical rotation (OR) in molecules at the level of the time-dependent Hartree-Fock and density functional approximations. To reach the limits of the basis set saturation, we have devised an artificial model, the asymmetrically deformed (chiral) methane (CM) molecule. This small system permits to use basis sets which are prohibitively large for real chiral molecules and yet shows all the important features of the basis set dependence of the OR values. The convergence of the OR has been studied with n-aug-cc-pVXZ basis sets of Dunning up to the 6-zeta. In a parallel series of calculations, we have used the recently developed large polarized (LPolX) basis sets. The relatively small LPolX sets have been shown to be competitive to very large n-aug-cc-pVXZ basis sets. The conclusions reached in calculations of OR in CM concerning the usefulness of LPolX basis sets have been further tested on (S)-methyloxirane and (S)-fluoro-oxirane. The smallest set of the LPolX family (LPol-ds) has been found to yield OR values of similar quality as those obtained with much larger Dunning's aug-cc-pVQZ basis set. These results have encouraged us to carry out the OR calculations with LPol-ds basis sets for systems as large as beta-pinene and trans-pinane. In both cases, our calculations have lead to the correct sign of the OR value in these molecules. This makes the relatively small LPol-ds basis sets likely to be useful in OR calculations for large molecules.

Thermodynamics and kinetics of intramolecular proton transfer in Guanine. Post Hartree-Fock study.

The most stable tautomers and rotamers of guanine are characterized by post Hartree-Fock ab initio calculations at the MP2 and CCSD(T) levels employing extended basis sets. Four of the lowest-energy structures (7H-oxo-amino- < 9H-oxo-amino- < 9H-syn-hydroxo-amino- < 9H-anti-hydroxo-amino-guanine) are found to lie within ca. 1 kcal/mol. The next form of guanine is established to lie more than 3 kcal/mol higher than the global minimum tautomer. The transition states of the following reversible reactions: 9H-oxo-amino-guanine right harpoon over left harpoon 9H-syn-hydroxo-amino-guanine right harpoon over left harpoon 9H-anti-hydroxo-amino-guanine have been studied. The calculated energy data were used to obtain thermodynamic parameters and to estimate the composition of the equilibrium mixture of conformers at 0 K and room temperature. The rate constants for the tautomerization of 9H-oxo-amino-guanine were determined by using the instanton approach. Their predicted values characterize an extremely slow chemical process, which is expected to reach the equilibrium in ca. 2500 h. Despite being so slow, we have shown that such a rate of the tautomerization describes a process that is much faster than the one characterized by the observed frequency of spontaneous point mutations. Therefore, additional stabilization factors, e.g., hydrations and interactions with enzymes are necessary to secure the known fidelity of DNA synthesis.

Blue-shifting intramolecular C-H...O interactions.

Two model systems, 3-methylacroleine and 3-(difluoromethyl)acroleine, are investigated computationally with respect to the character of the C-H...O interaction in their chelate-type (ZZ) conformers. By selecting the appropriate reference conformers, the C-H...O interaction is shown to result in the increase of the C-H stretching frequency (i.e., in the blue shift of the C-H stretching band). This is accompanied by the shortening of the C-H bond distance as compared to its values in reference molecules. Parallel to calculations of the C-H bond distance and stretching frequency, the energy contribution of the C-H...O interaction to the total energy (i.e., the energy associated with the C-H...O contact) is evaluated by using the methods proposed recently for the estimation of the energies of intramolecular hydrogen bonds. It is found that the C-H...O contact in the chelate-type forms of 3-methylacroleine and 3-(difluoromethyl)acroleine corresponds to the negative energy contribution and is repulsive. It is concluded that, despite the stability of the ZZ conformers of the two molecules and their deceptive structural shape, no hydrogen bond in the usual sense is formed between the C-H bond and the lone pair donor. The results are interpreted in terms of the steric compression, which leads to the dominance of the valence repulsion contribution in the C-H...O contact. This mechanism suggests that blue-shifting intramolecular interactions should not be that uncommon, although their recognition requires a careful consideration of the reference system.

Van der Waals complexes of Cu, Ag, and Au with hydrogen sulfide. The bonding character.

The electronic and structural features of the Cu...SH2, Ag...SH2, and Au...SH2 complexes are investigated by using the spin-adapted restricted open-shell HF coupled cluster CCSD(T) method combined with the second-order spin-free Douglas-Kroll-Hess (DKH) relativistic approach. M...SH2 complexes are nonplanar with bonding energies -5.99, -1.99, and -9.08 mHartree, respectively. Comparison with analogous M...OH2 and M...NH3 complexes allows us to establish general features of the bonding between coinage metal atoms and ligand molecules with the participation of their lone electron pairs. Consistent interpretation of the interaction effects can be obtained by using the molecular orbital picture of the M...L region. The bonding character is explained by stressing the importance of the charge transfer from the lone pair of the ligand to the metal atom. Relativistic changes of the metal element electron affinity and polarizability facilitate the understanding of major trends in the pattern of interactions between the coinage metal atoms and different lone pair donating ligands.

Estimates of the energy of intramolecular hydrogen bonds.

A method for the estimation of the energy of intramolecular hydrogen bonds in conjugated systems existing in a variety of conformations is presented. The method is applied to determine the intramolecular hydrogen bond energy in 3-aminopropenal and 3-aminopropenthial. According to the proposed estimation scheme, the intramolecular H-bond energies are found to be of the order of 5-7 kcal/mol. These results are compared with those obtained by using other estimation schemes as well as with the recent results by other authors. Also, the H-bond energies in dimers and trimers of the two molecules are calculated and compared with the corresponding data for internally hydrogen-bonded monomers. This comparison shows that the bond equalization effect is primarily due to proton donor-proton acceptor proximity. In comparison with intermolecular hydrogen bonds, the rigidity of the chelate skeleton enhances this proximity effect. The same effect can be seen in systems with intermolecular hydrogen bonds, although its magnitude is diminished because of the absence of additional forces which pull the proton donor and proton acceptor groups toward each other. No specific resonance-assisted origin of the intramolecular hydrogen bond energy seems to be needed to elucidate the energetics of these bonds.

The quadrupole moment of the Sb nucleus from molecular microwave data and calculated relativistic electric-field gradients.

The recently determined accurate values of the nuclear quadrupole coupling constant of the Sb nucleus in SbN, SbP, SbF, and SbCl and the calculated electric-field gradients at Sb in these molecules are used to obtain the nuclear quadrupole moment of 121Sb and 123Sb. The calculation of the electric-field gradient has been carried out by using the infinite-order two-component relativistic method in the scalar approximation. The accompanying change of picture of the electric-field gradient operator has been accounted for by employing the shifted nucleus model of nuclear quadrupoles. The electron correlation effects are calculated at the level of the coupled cluster approximation. The present calculations give the "molecular" value of the nuclear quadrupole moment of 121Sb equal to -556+/-24 mb which is considerably different from the old "recommended" value of -360+/-40 mb and also differs from the recent "solid-state" result (-669+/-15 mb). The validation of the present data is comprehensively discussed.

Reduced-size polarized basis sets for calculations of molecular electric properties. II. Simulation of the Raman spectra.

The accuracies of the calculated vibrational frequencies and Raman intensities given by two new, highly compact Pol-type basis sets, Z2PolX and Z3PolX, have been determined and compared to the 6-31G(d), PolX, and aug-cc-pVTZ basis sets. Calculation of accurate Raman intensities has previously required large basis sets, but the ZmPolX basis sets are smaller even than PolX, which are the most compact basis sets able to calculate accurate Raman intensities. For the largest compound studied, C5H10O2, Z3PolX required more than an order of magnitude less CPU time than PolX, which has been shown to be 10 times faster than aug-cc-pVTZ. Two sets of test molecules were studied: one was a series of small molecules for which experimental values for absolute Raman activities were available; the second was a series of medium-sized molecules (mainly common organic solvents) where only relative Raman band intensities were available. The accuracies of the Raman intensities given by both of the ZmPolX basis sets were good compared to those of the PolX and aug-cc-pVTZ sets, and much better than the 6-31G(d) values. The errors in even unscaled frequency values <2000 cm(-1) were also acceptable and were slightly lower for Z3PolX than Z2PolX (30 cm(-1) vs. 48 cm(-1)). The combination of good intensity and frequency data meant that for the medium-sized organic molecules there was a close correspondence between the simulated Raman spectra and experimental data, and that the observed bands could easily be assigned on the basis of these calculations. Achieving this level of accuracy in the simulations at modest computational cost should now allow computational methods to be combined with experimental Raman studies much more widely than is currently the case.

Reduced-size polarized basis sets for calculations of molecular electric properties. I. The basis set generation.

Following the recent studies of basis sets explicitly dependent on oscillatory external electric field we have investigated the possibility of some further truncation of the so-called polarized basis sets without any major deterioration of the computed data for molecular dipole moments, dipole polarizabilities, and related electric properties of molecules. It has been found that basis sets of contracted Gaussian functions of the form [3s1p] for H and [4s3p1d] for the first-row atoms can satisfy this requirement with particular choice of contractions in their polarization part. With m denoting the number of primitive GTOs in the contracted polarization function, the basis sets devised in this article will be referred to as the ZmPol sets. In comparison with earlier, medium-size polarized basis sets (PolX), these new ZmPol basis sets are reduced by 2/3 in their size and lead to the order of magnitude computing time savings for large molecules. Simultaneously, the dipole moment and polarizability data remain at almost the same level of accuracy as in the case of the PolX sets. Among a variety of possible applications in computational chemistry, the ZmPolX are also to be used for calculations of frequencies and intensities in the Raman spectra of large organic molecules (see Part II, this issue).

The quadrupole moment of the 3/2+ nuclear ground state of 197Au from electric field gradient relativistic coupled cluster and density-functional theory of small molecules and the solid state.

An attempt is made to improve the currently accepted muonic value for the 197Au nuclear quadrupole moment [+0.547(16)x10(-28) m2] for the 3/2+ nuclear ground state obtained by Powers et al. [Nucl. Phys. A230, 413 (1974)]. From both measured Mossbauer electric quadrupole splittings and solid-state density-functional calculations for a large number of gold compounds a nuclear quadrupole moment of +0.60x10(-28) m2 is obtained. Recent Fourier transform microwave measurements for gas-phase AuF, AuCl, AuBr, and AuI give accurate bond distances and nuclear quadrupole coupling constants for the 197Au isotope. However, four-component relativistic density-functional calculations for these molecules yield unreliable results for the 197Au nuclear quadrupole moment. Relativistic singles-doubles coupled cluster calculations including perturbative triples [CCSD(T) level of theory] for these diatomic systems are also inaccurate because of large cancellation effects between different field gradient contributions subsequently leading to very small field gradients. Here one needs very large basis sets and has to go beyond the standard CCSD(T) procedure to obtain any reliable field gradients for gold. From recent microwave experiments by Gerry and co-workers [Inorg. Chem. 40, 6123 (2001)] a significantly enhanced (197)Au nuclear quadrupole coupling constant in (CO)AuF compared to free AuF is observed. Here, these cancellation effects are less important, and relativistic CCSD(T) calculations finally give a nuclear quadrupole moment of +0.64x10(-28) m2 for 197Au. It is argued that it is currently very difficult to improve on the already published muonic value for the 197Au nuclear quadrupole moment.

Monomer basis-set truncation effects in calculations of interaction energies: A model study.

Supermolecular interaction energies are analyzed in terms of the symmetry-adapted perturbation theory and operators defining the inaccuracy of the monomer wave functions. The basis set truncation effects are shown to be of first order in the monomer inaccuracy operators. On the contrary, the usual counterpoise correction schemes are of second order in these operators. Recognition of this difference is used to suggest an approach to corrections for basis-set truncation effects. Also earlier claims--that dimer-centered basis sets may lead to interaction energies free of basis-set superposition effects--are shown to be misleading. According to the present study the basis-set truncation contributions, evaluated by means of the symmetry-adapted perturbation theory with monomer-centered basis sets, provide physically and mathematically justified corrections to supermolecular results for interaction energies.