Triple Zeta Valence Quality Research Articles

All-electron ZORA triple zeta basis sets for the elements Cs–La and Hf–Rn

Segmented all-electron basis set of triple zeta valence quality plus polarization functions (TZP) for the elements of the fifth row to be used together with the zero-order regular approximation (ZORA) is carefully constructed. To correctly describe electrons distant from atomic nuclei, the basis set is augmented with diffuse functions giving rise to a set designated as ATZP-ZORA. At the ZORA-B3LYP theoretical level, these sets are used to calculate the ionization energy and mean dipole polarizability of some atoms, bond length, dissociation energy, and harmonic vibrational frequency of diatomic molecules. Then, these results are compared with the theoretical and experimental data found in the literature. Even considering that our sets are relatively compact, they are sufficiently accurate and reliable to perform property calculations involving simultaneously electrons from the inner shell and outer shell. The performances of the ZORA and second-order Douglas–Kroll–Hess Hamiltonians are evaluated and the results are also discussed.

All-electron triple zeta basis sets for ZORA calculations: Application in studies of atoms and molecules

Segmented all-electron basis set of triple zeta valence quality plus polarization functions for the elements from H to Xe to be used together with the ZORA Hamiltonian is developed. This set was augmented with diffuse functions in order to properly describe electrons distant from the nuclei. At the ZORA-CCSD(T) level of theory, ionization energies and mean dipole polarizabilities of some atoms as well as bond lengths, dissociation energies, and harmonic vibrational frequencies of a set of molecules are calculated. Scalar relativistic effects are estimated for all properties. The performances of the ZORA and DKH2 Hamiltonians are also assessed.

All-electron segmented contraction basis sets of triple zeta valence quality for the fifth-row elements

All-electron contracted Gaussian basis set of triple zeta valence quality plus polarisation functions (TZP) for the elements Cs, Ba, La, and from Hf to Rn is presented. Douglas–Kroll–Hess (DKH) basis set for fifth-row elements is also reported. We have recontracted the original TZP basis set, i.e., the values of the contraction coefficients are re-optimised using the second-order DKH Hamiltonian. By addition of diffuse functions (s, p, d, f, and g symmetries), which are optimised for the anion ground states, an augmented TZP basis set is constructed. Using the B3LYP hybrid functional, the performance of the TZP–DKH basis set is assessed for predicting atomic ionisation energy as well as spectroscopy constants of some compounds. Despite its compact size, this set demonstrates consistent, efficient, and reliable performance and will be especially useful in calculations of molecular properties that require explicit treatment of the core electrons.

Gaussian basis set of triple zeta valence quality for the atoms from K to Kr: Application in DFT and CCSD(T) calculations of molecular properties

A contracted basis set of triple zeta (TZ) valence quality for the atoms from K to Kr was constructed from fully-optimized Gaussian basis sets generated in this work. Gaussian polarization functions (d, f, and g symmetries), which were optimized at the second-order Mφller–Plesset level, were added to the TZ set. This extends earlier work on segmented contracted TZ basis set for atoms H-Ar. This set along with the BP86 non-hybrid and B3LYP hybrid functionals were used to calculate geometric parameters, dissociation energy, harmonic vibrational frequency, and electric dipole moment of a sample of molecules and, then, comparison with results obtained with other basis sets and with experimental data reported in the literature is done. CCSD(T) atomic excitation energies and bond lengths, dissociation energies, and harmonic vibrational frequencies of some diatomics were also evaluated. Using density functional theory and gauge-including atomic orbitals, 57Fe and 77Se nuclear magnetic resonance chemical shifts in Fe(C5H5)2, H2Se, (CH3)SeH, CSe2, SeCO, H2CSe, and SeF6 were calculated. Comparison with theoretical and experimental values previously published in the literature was done. It is verified that in general these results give good agreement with experimental and benchmark values.

A vibrational and DFT study of M(diimine)(dithiolate) complexes and their complexation route

A complete vibrational spectra analysis of the Pd(phen)(bdt), the free ligands, where phen = 1,10-phenanthroline and bdt = 1,2-benzenedithiolate and the starting material of its synthesis, Pd(phen)Cl 2, is performed in this paper. The molecular geometry, binding and spectroscopic properties for the aforementioned compounds are studied in detail by FT-IR, Raman and DFT methods using B3LYP functional together with basis sets of valence triple-zeta quality. Further, changes in FT-IR and Raman spectra during complexation are monitored revealing the electron delocalization over ligands. They are also consistent with π-back donation theory.

Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracy

Gaussian basis sets of quadruple zeta valence quality for Rb-Rn are presented, as well as bases of split valence and triple zeta valence quality for H-Rn. The latter were obtained by (partly) modifying bases developed previously. A large set of more than 300 molecules representing (nearly) all elements-except lanthanides-in their common oxidation states was used to assess the quality of the bases all across the periodic table. Quantities investigated were atomization energies, dipole moments and structure parameters for Hartree-Fock, density functional theory and correlated methods, for which we had chosen Møller-Plesset perturbation theory as an example. Finally recommendations are given which type of basis set is used best for a certain level of theory and a desired quality of results.

Quantum chemical calculations of linear cumulene chains

The molecular geometry of cumulene chains H 2C n H 2 have been optimized using LCAO-SCF MO method (contracted Gaussian basis set of triple zeta valence quality TZVP and the more extended Dunning's correlation consistent basis set aug-cc-PVDZ), density functional theory at different basis set levels, and the highly parametrized MNDO(PM3) method. The bond lengths have no remarkable alternation within the chain and converge to the asymptotic limit as the value of n is getting larger. The total charges calculated by Mulliken population analysis yield unrealistic values if the split valence basis set was employed. In contrast, using NBO analysis the net charges of the individual atoms converge very rapidly to their asymptotic limits with almost zero charges on central atoms. The comparison of the different basis set results to test the reliability of proton affinities calculated from the differences in molecular enthalpies of the parent chain and the corresponding anions was carried out. The increase of the number of C C bonds in the chain decreases these differences asymptotically. The concept of ‘terminal charge repulsion’ is developed for the explanation of energy effects in long chains. The role of this concept in explanation of dependence of proton affinities on the chain length was discussed. The studied compounds are the best available building blocks in bimetallic compounds with useful properties in molecular electronics and nonlinear optics.

Systematic quantum chemical study of DNA-base tautomers.

The relative energies of the energetically low-lying tautomers of pyridone, cytosine, uracil, thymine, guanine, and iso-cytosine are studied by a variety of different quantum chemical methods. In particular, we employ density functional theory (DFT) using the six functionals HCTH407, PBE, BP86, B-LYP, B3-LYP, and BH-LYP, and the ab initio methods Hartree-Fock (HF), standard second-order Møller-Plesset perturbation theory (MP2), an improved version of it (SCS-MP2), and quadratic configuration interaction including single and double excitations (QCISD) and perturbative triple corrections [QCISD(T)]. A detailed basis set study is performed for the formamide/formamidic acid tautomeric pair. In general, large AO basis sets of at least valence triple-zeta quality including f-functions (TZV) are employed, which are found to be necessary for an accurate energetic description of the various structures. The performance of the more approximate methods is evaluated with QCISD(T)/TZV(2df,2dp) data taken as reference. In general it is found that DFT is not an appropriate method for the problem. For the tautomers of pyridone and cytosine, most density functionals, including the popular B3-LYP hybrid, predict a wrong energetic order, and only for guanine, the correct sequence of tautomers is obtained with all functionals. Out of the density functionals tested, BH-LYP, which includes a rather large fraction of HF exchange, performs best. A consistent description of the nonaromatic versus aromatic tautomers seems to be a general problem especially for pure, nonhybrid functionals. Tentatively, this could be assigned to the exchange potentials used while the functional itself, including the correlation part, seems to be appropriate. Out of the ab initio methods tested, the new SCS-MP2 approach seems to perform best because it effectively reduces some outliers obtained with standard MP2. It outperforms the much more costly QCISD method and seems to be a very good compromise between computational effort and accuracy.

Thermodynamic Properties of PaCl5 and PaF5 Based on Quantum Chemical Calculations.

Abstract Quantum chemical calculations using the Becke–Perdew (BP86) and Becke3–Lee–Yang–Parr (B3LYP) exchange-correlation density functionals in conjunction with basis sets of polarised valence triple-zeta quality have been performed for PaCl 5 and PaF 5 . The two methods consistently gave the trigonal bipyramid ( D 3h ) structure as the global minimum on the potential energy surface, being 4–6 kJ mol −1 more stable than the tetragonal pyramid ( C 4v ) structure. The geometrical parameters and vibrational frequencies of the D 3h structures computed by the two methods are in good agreement. The results have been used to calculate the thermodynamic functions of the molecules. In combination with literature data the enthalpies of formation have been evaluated.

Optimized Slater-type basis sets for the elements 1-118.

Seven different types of Slater type basis sets for the elements H (Z = 1) up to E118 (Z = 118), ranging from a double zeta valence quality up to a quadruple zeta valence quality, are tested in their performance in neutral atomic and diatomic oxide calculations. The exponents of the Slater type functions are optimized for the use in (scalar relativistic) zeroth-order regular approximated (ZORA) equations. Atomic tests reveal that, on average, the absolute basis set error of 0.03 kcal/mol in the density functional calculation of the valence spinor energies of the neutral atoms with the largest all electron basis set of quadruple zeta quality is lower than the average absolute difference of 0.16 kcal/mol in these valence spinor energies if one compares the results of ZORA equation with those of the fully relativistic Dirac equation. This average absolute basis set error increases to about 1 kcal/mol for the all electron basis sets of triple zeta valence quality, and to approximately 4 kcal/mol for the all electron basis sets of double zeta quality. The molecular tests reveal that, on average, the calculated atomization energies of 118 neutral diatomic oxides MO, where the nuclear charge Z of M ranges from Z = 1-118, with the all electron basis sets of triple zeta quality with two polarization functions added are within 1-2 kcal/mol of the benchmark results with the much larger all electron basis sets, which are of quadruple zeta valence quality with four polarization functions added. The accuracy is reduced to about 4-5 kcal/mol if only one polarization function is used in the triple zeta basis sets, and further reduced to approximately 20 kcal/mol if the all electron basis sets of double zeta quality are used. The inclusion of g-type STOs to the large benchmark basis sets had an effect of less than 1 kcal/mol in the calculation of the atomization energies of the group 2 and group 14 diatomic oxides. The basis sets that are optimized for calculations using the frozen core approximation (frozen core basis sets) have a restricted basis set in the core region compared to the all electron basis sets. On average, the use of these frozen core basis sets give atomic basis set errors that are approximately twice as large as the corresponding all electron basis set errors and molecular atomization energies that are close to the corresponding all electron results. Only if spin-orbit coupling is included in the frozen core calculations larger errors are found, especially for the heavier elements, due to the additional approximation that is made that the basis functions are orthogonalized on scalar relativistic core orbitals.

Ground state rotational spectrum, K = 3 splittings, ab initio anharmonic force field and equilibrium structure of trifluoroamine

The submillimetre-wave spectrum of 14NF3 has been measured and the ground state rotational spectrum has been reanalysed, including the K=3 splittings. The quadratic, cubic and semidiagonal quartic force field has been calculated at the CCSD(T) level of theory employing a basis set of at least polarized valence triple-zeta quality. This force field has been used to predict the spectroscopic constants, including the parameters specific to the doubly degenerate vibrational states. The calculated values are found to be in good agreement with the available experimental data. The equilibrium structure has been derived from the experimental ground state rotational constants and either the ab initio or the experimental rovibrational interaction parameters. These experimental and semiexperimental structures are in excellent agreement with the ab initio equilibrium geometry.

Millimeter-wave and high-resolution FTIR spectroscopy of [formula omitted]: the ground and [formula omitted] states

The first high-resolution infrared spectroscopic study of the ν 4 band at 322.85 cm - 1 of SiH 2 F 2 is reported, and millimeter-wave spectra in the 350–471 GHz range of the ground and the v 4 = 1 excited states are presented. These data have been combined with existing microwave measurements and substantially improved ground state parameters, and molecular constants of the v 4 = 1 state, have been determined. The quadratic, cubic, and semidiagonal quartic force field of difluorosilane has been calculated at the MP2 level of theory employing a basis set of polarized valence triple-zeta quality. The spectroscopic constants derived from the force field are in excellent agreement with experiment. The equilibrium structure has been derived from experimental ground state rotational constants and ab initio rovibrational interaction parameters. This semiexperimental structure is in perfect agreement with the ab initio equilibrium geometry calculated at the CCSD(T) level of theory.

Thermodynamic properties of PaCl 5 and PaF 5 based on quantum chemical calculations

Quantum chemical calculations using the Becke–Perdew (BP86) and Becke3–Lee–Yang–Parr (B3LYP) exchange-correlation density functionals in conjunction with basis sets of polarised valence triple-zeta quality have been performed for PaCl 5 and PaF 5. The two methods consistently gave the trigonal bipyramid ( D 3h) structure as the global minimum on the potential energy surface, being 4–6 kJ mol −1 more stable than the tetragonal pyramid ( C 4v) structure. The geometrical parameters and vibrational frequencies of the D 3h structures computed by the two methods are in good agreement. The results have been used to calculate the thermodynamic functions of the molecules. In combination with literature data the enthalpies of formation have been evaluated.

DFT and HF–DFT calculations of [formula omitted] quadrupole coupling constants in molecules

The efficacy of several DFT and HF–DFT methods for the calculation of 14 N quadrupole coupling constants in molecules has been investigated. Valence triple-zeta quality Pople and Dunning correlation consistent type bases were used. Assessment of the different methods was made by linear regression analysis of the calculated efg's versus the experimental nqcc's. The HF–DFT methods were found superior to the DFT methods. The least residual standard deviation was obtained with the B3PW91/6-311+G(df,pd) model. For 39 molecules containing 45 nitrogen sites, the standard deviation is 30 kHz (1.3%). Regarding the Dunning type aug-cc-pVTZ basis, it was found that the addition to nitrogen of core–valence correlation functions significantly improves the results.

Ab initio anharmonic force field, spectroscopic parameters and equilibrium structure of trifluorosilane

The quadratic, cubic and semidiagonal quartic force field of trifluorosilane has been calculated at the MP2 level of theory employing a basis set of polarized valence triple-zeta quality. This force field has been used to predict the spectroscopic constants, including the parameters specific of the double degenerate vibrational states. The calculated values are found to be in good agreement with the available experimental data, and explanations are offered for discrepancies. This confirms the accuracy of the ab initio force field and the validity of the theory of the reduction of the rovibrational Hamiltonian of a doubly degenerate vibrational state. The equilibrium structure has been derived from the experimental rotational constants and the ab initio rovibrational interaction parameters. This semiexperimental structure is in excellent agreement with the ab initio equilibrium geometry.

Density functional study of hydrogen-bonded systems: Energetic and vibrational features of some gas-phase adducts of hydrogen fluoride

A series of detailed density functional calculations on hydrogen-bonded gas-phase adducts of the FH molecule for which both experiments and calculations based on traditional approaches were available have been carried out. The adducts were: (FH) 2, FH/CO and FH/NH 3. The adopted methods were: SCF, MP2, S-VWN, B-LYP, B-P86 and B3-LYP. Basis sets were: 6-31G(d,p), 6-31+G(d,p), 6-311++G(d,p), 6-311+G(2d,2p), 6-311+G(3df,2pd), DZ(d,p), cc-pVDZ, aug-cc-pVDZ, cc-pVTZ, and aug-cc-pVTZ. Computed properties were: geometries, harmonic vibrations, binding energies and intensity of the F–H stretching mode of the donor. A detailed analysis of the anharmonicity associated with the F–H stretching mode was also carried out by numerically solving the nuclear Schrödinger equation associated with the F–H mode for both the FH/NH 3 and FH/CO cases. Comparison with previous studies as well as with available experimental data shows that heats of formation computed with the gradient corrected DF methods are as accurate as MP2 or better, when a basis set of at least triple-zeta valence quality with a double set of polarization functions is chosen. All functionals are able to give the correct order of stability for the FH/CO adduct, i.e. the carbon-bound structure as the more stable one, in agreement with MP2 studies. The Pople basis set 6-311+G(2d,2p) appears as good as the correlation-consistent basis set proposed by Dunning, namely aug-cc-pVDZ. Some care should be taken when adopting the 6-31G(d,p) basis set, as for instance in the case of (FH) 2 where spurious interactions stabilize cyclic structures with respect to open ones. All DF methods overestimate the shifts in the F–H stretching mode due to the hydrogen-bond interaction, calculated at the harmonic level, and no improvement is brought about by anharmonicity. The increase in the infrared intensity of the FH donor molecule is correctly accounted for. DF methods based on local electron density overestimate both the binding energies and the shifts in the F–H stretching mode showing their unrealiability for studying hydrogen-bonding interactions.

Fully optimized contracted Gaussian basis sets of triple zeta valence quality for atoms Li to Kr

Contracted Gaussian basis sets of triple zeta valence (TZV) quality are presented for Li to Kr. The TZV bases are characterized by typically including a single contraction to describe inner shells and three basis functions for valence shells. All parameters—orbital exponents and contraction coefficients—have been determined by minimization of atomic self-consistent field ground state energies. Advantages and necessary modifications of TZV basis sets are discussed for simple test calculations of molecular energies and nuclear magnetic resonance (NMR) chemical shieldings in treatments with and without inclusion of electron correlation.

6-311G is not of valence triple-zeta quality

We have discovered a weakness in the construction of the 6-311G basis set. The second set of three contracted s-functions is, in fact, not a valence orbital but is instead a 1s function. Thus in the s space this basis set is better represented as 63-11. Coupled with an earlier observation that additional diffuse p functions are required to yield results comparable to those of the Huzinaga–Dunning (10s6p/5s3p) triple-zeta basis set in certain cases, this suggests that greater caution should be exercised in the use of the 6-311G basis set.

Theoretical characterization of the minimum energy path for the reaction H+O2→HO2*→HO+O

The potential energy surface for the reaction H+O2→HO*2 →HO+O has been characterized in the vicinity of the minimum energy path using CASSCF/contracted CI calculations with a basis set which is triple zeta valence quality plus three sets of polarization functions. CASSCF/CI calculations were carried out along the CCI minimum energy path. The latter calculation shows essentially no barrier for addition of an H atom to O2, in agreement with predictions made in earlier studies. The potential surface for recombination of OH and O is complicated by a crossing, at rOO ≈5.5a0, between the surface for electrostatic (OH dipole–O quadrupole) interaction and that for the formation of an O–O chemical bond. This surface crossing results in a small (≈0.5 kcal/mol) barrier.