The confirmation of accurate combination of functional and basis set for transition‐metal dimers: Fe2, Co2, Ni2, Ru2, Rh2, Pd2, Os2, Ir2, and Pt2

Eight kinds of density functionals named B3LYP, PBE1PBE, B1B95, BLYP, BP86, G96PW91, mPWPW91, and SVWN along with two different valence basis sets (LANL2DZ and CEP‐121g) are employed to study the transition‐metal dimers for the elements of group VIII. By comparing the equilibrium bond distances, vibrational frequencies, and dissociation energies of the ground state of these dimers with the available experimental values and theoretical data, we show that the “pure” DFT methods (G96PW91, BLYP, and BP86) with great‐gradient approximation always give better results relative to the hybrid HF/DFT schemes (B3LYP, PBE1PBE, and B1B95). The striking case found by us is that the G96PW91 functional, which is not tested in previous systemic studies, always predicts the dissociation energy to be well. The Ru₂ and Os₂ dimers are sensitive to not only the functionals employed but also the valence basis sets adopted. The natural bond orbital population is analyzed, and the molecular orbitals of the unpaired electrons are determined. Furthermore, our results indicate that the s and d orbitals of these dimers always hybridize with each other except for Rh₂ and Pt₂ molecules. And by analyzing the electron configuration of the bonding atom, the dissociation limit of the ground state is obtained. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Consistent Gaussian basis sets of triple‐zeta valence with polarization quality for solid‐state calculations

Consistent basis sets of triple‐zeta valence with polarization quality for main group elements and transition metals from row one to three have been derived for periodic quantum‐chemical solid‐state calculations with the crystalline‐orbital program CRYSTAL. They are based on the def2‐TZVP basis sets developed for molecules by the Ahlrichs group. Orbital exponents and contraction coefficients have been modified and reoptimized, to provide robust and stable self‐consistant field (SCF) convergence for a wide range of different compounds. We compare results on crystal structures, cohesive energies, and solid‐state reaction enthalpies with the modified basis sets, denoted as pob‐TZVP, with selected standard basis sets available from the CRYSTAL basis set database. The average deviation of calculated lattice parameters obtained with a selected density functional, the hybrid method PW1PW, from experimental reference is smaller with pob‐TZVP than with standard basis sets, in particular for metallic systems. The effects of basis set expansion by diffuse and polarization functions were investigated for selected systems. © 2012 Wiley Periodicals, Inc.     

Consistent gaussian basis sets of double‐ and triple‐zeta valence with polarization quality of the fifth period for solid‐state calculations

Consistent basis sets of double‐ and triple‐zeta valence with polarization quality for the fifth period have been derived for periodic quantum‐chemical solid‐state calculations with the crystalline‐orbital program CRYSTAL. They are an extension of the pob‐TZVP basis sets, and are based on the full‐relativistic effective core potentials (ECPs) of the Stuttgart/Cologne group and on the def2‐SVP and def2‐TZVP valence basis of the Ahlrichs group. We optimized orbital exponents and contraction coefficients to supply robust and stable self‐consistent field (SCF) convergence for a wide range of different compounds. The computed crystal structures are compared to those obtained with standard basis sets available from the CRYSTAL basis set database. For the applied hybrid density functional PW1PW, the average deviations of calculated lattice constants from experimental references are smaller with pob‐DZVP and pob‐TZVP than with standard basis sets. © 2018 Wiley Periodicals, Inc.     

The performance of different density functional methods in the calculation of molecular structures and vibrational spectra of platinum(II) antitumor drugs: cisplatin and carboplatin

A comparison of eight density functional models for predicting the molecular structures, vibrational frequencies, infrared intensities, and Raman scattering activities of platinum(II) antitumor drugs, cisplatin and carboplatin, is reported. Methods examined include the pure density functional protocols (G96LYP, G96PW91, modified mPWPW and original PW91PW91), one‐parameter hybrid approaches (mPW1PW and mPW1LYP), and three‐parameter hybrid models (B3LYP and B3PW91), as well as the HF and MP2 levels of theory. Different effective core potentials (ECPs) and several basis sets are considered. The theoretical results are discussed and compared with the experimental data. It is remarkable that the mPW1PW protocol introduced by Adamo and Barone [J Chem Phys 1998, 108, 664], is clearly superior to all the remaining density functional methods (including B3LYP). The geometry and vibrational frequencies of cisplatin and carboplatin calculated with the mPW1PW method, and the ECP of Hay and Wadt (LanL2DZ basis set) are in better agreement with experiment than those obtained with the MP2 method. The use of more elaborated ECP and the enlargements of basis sets do not significantly improve the results. A clear‐cut assignments of the platinum‐ligand vibrations in cisplatin and carboplatin are presented. It is concluded that mPW1PW is the new reliable method, which can be used in predicting molecular structures and vibrational spectra of large coordination compounds containing platinum(II). © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 901–912, 2001     

Reliable structures and energetics for two new delocalized pi...pi prototypes: cyanogen dimer and diacetylene dimer

Two new prototype delocalized pi[dot dot dot]pi complexes are introduced: the dimers of cyanogen, (N[triple bond]C-C[triple bond]N)(2), and diacetylene, (HC[triple bond]C-C[triple bond]CH)(2). These dimers have properties similar to larger delocalized pi...pi systems such as benzene dimer but are small enough that they can be probed in far greater detail with high accuracy electronic structure methods. Parallel-slipped and T-shaped structures of both cyanogen dimer and diacetylene dimer have been optimized with 15 different procedures. The effects of basis set size, theoretical method, counterpoise correction, and the rigid monomer approximation on the structure and energetics of each dimer have been examined. MP2 and CCSD(T) optimized geometries for all four dimer structures are reported, as well as estimates of the CCSD(T) complete basis set (CBS) interaction energy for every optimized geometry. The data reported here suggest that future optimizations of delocalized pi[dot dot dot]pi clusters should be carried out with basis sets of triple-zeta quality. Larger basis sets and the expensive counterpoise correction to the molecular geometry are not necessary. The rigid monomer approximation has very little effect on structure and energetics of these dimers and may be used without consequence. Due to a consistent cancellation of errors, optimization with the MP2 method leads to CCSD(T)/CBS interaction energies that are within 0.2 kcal mol(-1) of those for structures optimized with the CCSD(T) method. Future studies that aim to resolve structures separated by a few tenths of a kcal mol(-1) should consider the effects of optimization with the CCSD(T) method.     

Medium-size polarized basis sets for high-level-correlated calculations of molecular electric properties

Summary The basis set polarization approach is employed for the generation of medium-size polarized GTO/CGTO basis sets for calculations of molecular dipole moments and polarizabilities. The excellent performance of the [13.10.4/7.5.2] GTO/CGTO polarized basis sets derived for Si through Cl is illustrated by the atomic polarizability results and SCF and MBPT data for dipole moments and polarizabilities of the second-row atom hydrides. The possible applications of the electric-property oriented polarized basis sets are discussed. The basis set data for Si through Cl are those for H and C through F append the paper.     

Ab initio investigation of structure and cohesive energy of crystalline urea

The structure and cohesive energy of crystalline urea have been investigated at the ab initio level of calculation. The performance of different Hamiltonians in dealing with a hydrogen-bonded molecular crystal as crystalline urea is assessed. Detailed calculations carried out by adopting both HF and some of the most popular DFT methods in solid-state chemistry are reported. Local, gradient-corrected, and hybrid functionals have been adopted: SVWN, PW91, PBE, B3LYP, and PBE0. First, a 6-31G(d,p) basis set has been adopted, and then the basis set dependence of computed results has been investigated at the B3LYP level. All calculations were carried out by using a development version of the periodic ab initio code CRYSTAL06, which allows full optimization of lattice parameters and atomic coordinates. With the 6-31G(d,p) basis set, structural features are well reproduced by hybrid methods and GGA. LDA gives lattice parameters and hydrogen-bond distances that are too small relative to experiment, while at the HF level the opposite trend is observed. Results show that hybrid methods are more accurate than HF and both LDA and GGA functionals, with a trend in the computed properties similar to that of hydrogen-bonded molecular complexes. When BSSE and ZPE are taken into account, all methods, except LDA, give computed cohesive energies that are underestimated with respect to the experimental sublimation enthalpy. Dispersion energy, not properly taken into account by DFT methods, plays a crucial role. Such a deficiency also affects dramatically the computed crystalline structure, especially when large basis sets are adopted. We show that this is an artifact due to the BSSE. Indeed, with small basis sets the BSSE gives an extra-binding that compensates for the missing dispersion forces, thus yielding structures in fortuitous agreement with experiment.     

Intermolecular potentials of the silane dimer calculated with Hartree-Fock theory, Møller-Plesset perturbation theory, and density functional theory

We have calculated the intermolecular interaction potentials of the silane dimer at the D3d conformation using the Hartree-Fock (HF) self-consistent theory, the correlation-corrected second-order M?ller-Plesset (MP2) perturbation theory, and the density functional theory (DFT) with 108 functionals chosen from the combinations of 9 exchange and 12 correlation functionals. Single-point coupled cluster [CCSD(T)] calculations have also been carried out to calibrate the correlation effect. The HF calculations yield unbound potentials largely because of the exchange-repulsion interaction. In the MP2 calculations, the basis set effects on the repulsion exponent, the equilibrium bond length, the binding energy, and the asymptotic behavior of the calculated intermolecular potentials have been thoroughly studied. We have employed basis sets from the Slater type orbitals fitted with Gaussian functions (STO-nG, n = 3 approximately 6), Pople's medium size basis sets [up to 6-311++G(3df,3pd)], to Dunning's correlation consistent basis sets (cc-pVXZ and aug-cc-pVXZ, X = D, T, Q). With increasing basis size, the repulsion exponent and the equilibrium bond length converge at the 6-31G** basis set and the 6-311++G(3d,3p) basis set, respectively, while a large basis set (aug-cc-pVTZ) is required to converge the binding energy at a chemical accuracy ( approximately 0.05 kcal/mol). Up to the largest basis set used, the asymptotic dispersion coefficient has not converged to the expected C6 value from molecular polarizability calculations. We attribute the slow convergence partly to the inefficacy of using the MP2 calculations with Gaussian type functions to model the asymptotic behavior. Both the basis set superposition error (BSSE) corrected and uncorrected results are presented to emphasize the importance of including such corrections. Only the BSSE corrected results systematically converge to the expected potential curve with increasing basis size. The DFT calculations generate a wide range of interaction patterns, from purely unbound to strongly bound, underestimating or overestimating the binding energy. The binding energies calculated using the OPTXHCTH147, PBEVP86, PBEP86, PW91TPSS, PW91PBE, and PW91PW91 functionals and the equilibrium bond lengths calculated using the MPWHCTH93, TPSSHCTH, PBEVP86, PBEP86, PW91TPSS, PW91PBE, and PW91PW91 functionals are close to the MP2 results using the 6-311++G(3df,3pd) basis set. A correlation between the calculated DFT potentials and the exchange and correlation enhancement factors at the low-density region has been elucidated. The asymptotic behaviors of the DFT potentials are also analyzed.     

Importance of the basis set for the spin-state energetics of iron complexes

We have performed a systematic investigation of the influence of the basis set on relative spin-state energies for a number of iron compounds. In principle, with an infinitely large basis set, both Slater-type orbital (STO) and Gaussian-type orbital (GTO) series should converge to the same final answer, which is indeed what we observe for both vertical and relaxed spin-state splittings. However, we see throughout the paper that the STO basis sets give consistent and rapidly converging results, while the convergence with respect to the basis set size is much slower for the GTO basis sets. For example, the large GTO basis sets that give good results for the vertical spin-state splittings of compounds 1-3 (6-311+G**, Ahlrichs VTZ2D2P) fail for the relaxed spin-state splittings of compound 4 (where 1 is Fe-(PyPepS)2 (PyPepSH 2 = N-(2-mercaptophenyl)-2-pyridinecarboxamide), 2 is Fe(tsalen)Cl (tsalen = N, N'-ethylenebis-(thiosalicylideneiminato)), 3 is Fe(N(CH2-o-C6H4S) 3)(1-Me-imidazole), and 4 is FeFHOH). Very demanding GTO basis sets like Dunning's correlation-consistent (cc-pVTZ, cc-pVQZ) basis sets are needed to achieve good results for these relaxed spin states. The use of popular (Pople-type) GTO, effective core potentials basis set (ECPB), or mixed ECPB(Fe):GTO(rest) basis sets is shown to lead to substantial deviations (2-10 kcal/mol, 14-24 kcal/mol for 3-21G), in particular for the high spin states that are typically placed at too low energy. Moreover, the use of an effective core potential in the ECPB basis sets results in spin-state splittings that are systematically different from the STO-GTO results.     

Differences in structure, energy, and spectrum between neutral, protonated, and deprotonated phenol dimers: comparison of various density functionals with ab initio theory

We have carried out extensive calculations for neutral, cationic protonated, anionic deprotonated phenol dimers. The structures and energetics of this system are determined by the delicate competition between H-bonding, H-π interaction and π-π interaction. Thus, the structures, binding energies and frequencies of the dimers are studied by using a variety of functionals of density functional theory (DFT) and M?ller-Plesset second order perturbation theory (MP2) with medium and extended basis sets. The binding energies are compared with those of highly reliable coupled cluster theory with single, double, and perturbative triple excitations (CCSD(T)) at the complete basis set (CBS) limit. The neutral phenol dimer is unique in the sense that its experimental rotational constants have been measured. The geometry of the neutral phenol dimer is governed by the hydrogen bond formed by two hydroxyl groups and the H-π interaction between two aromatic rings, while the structure of the protonated/deprotonated phenol dimers is additionally governed by the electrostatic and induction effects due to the short strong hydrogen bond (SSHB) and the charges populated in the aromatic rings in the ionic systems. Our salient finding is the substantial differences in structure between neutral, protonated, and deprotonated phenol dimers. This is because the neutral dimer involves in both H(π)···O and H(π)···π interactions, the protonated dimer involves in H(π)···π interactions, and the deprotonated dimer involves in a strong H(π)···O interaction. It is important to compare the reliability of diverse computational approaches employed in quantum chemistry on the basis of the calculational results of this system. MP2 calculations using a small cc-pVDZ basis set give reasonable structures, but those using extended basis sets predict wrong π-stacked structures due to the overestimation of the dispersion energies of the π-π interactions. A few new DFT functionals with the empirical dispersion give reliable results consistent with the CCSD(T)/CBS results. The binding energies of the neutral, cationic protonated, and anionic deprotonated phenol dimers are estimated to be more than 28.5, 118.2, and 118.3 kJ mol(-1), respectively. The energy components of the intermolecular interactions for the neutral, protonated and deprotonated dimers are analyzed.     

Medium-size polarized basis sets for high-level-correlated calculations of molecular electric properties

Summary The basis set polarization method is used to derive the first-order polarized basis sets for Ge through Br for calculations of atomic and molecular electric properties. The performance of the [15.12.9/9.7.4] GTO/CGTO basis sets generated in this study is verified in calculations of atomic dipole polarizabilities and dipole moments and polarizabilities of the third-row atom hydrides. Whenever accurate reference data are available for comparison, the excellent performance of the derived first-order polarized basis sets is demonstrated. The role of the core polarization and relativistic contributions to atomic and molecular is also investigated. The detailed basis set data for Ge through Br are given in Appendix.     

Density functional theory calculations on the molecular structures and vibration spectra of platinum(II) antitumor drugs

A comparison of six density functional theory (DFT) methods and six basis sets for predicting the molecular structures and vibration spectra of cisplatin is reported. The theoretical results are discussed and compared with the experimental data. It is remarkable that LSDA/SDD level is clearly superior to all the remaining density functional methods (including mPW1PW) in predicting the structures of cisplatin. Mean deviation between the calculated harmonic and observed fundamental vibration frequencies for each method is also calculated. The results indicate that PBE1PBE/SDD is the best method to predict all frequencies on average for cisplatin molecule in DFT methods.     

Computational Study of Cage Like (ZnO)12 Cluster Using Hybrid and Hybrid Meta Functionals

Density Functional Theory employing hybrid and M06 functionals in combination with three different basis sets is used to calculate the ground state of a cage like (ZnO)₁₂ nanocluster which has been consistently reported as the more stable cluster for its particular size. B3LYP and B3PW91 hybrid functionals combined with 6‐31+G*, Lanl2dz and SDD basis sets are employed to treat the ZnO molecular system. Alternatively, three M06 functionals in combination with three basis sets are employed in the nanostructure calculations. Results obtained by treating ZnO sodalite cage nanocluster with M06 functionals demonstrated comparable quality to results obtained with hybrid functionals. Within this study, efficient theoretical DFT methods with the widely known hybrid and the recently created M06 meta‐hybrid functionals are employed to study nanostructured ZnO. Our resulting parameters provide a fresh approach performance wise on the different theoretical methods to treat transition metal nanostructures, particularly, ZnO nanoclusters geometry and electronic structure.     

Odd liquid crystalline dimers can be linear

The crystal and molecular structures of two liquid crystalline symmetric dimers containing the mesogenic group α,α′‐dimethylbenzalazine and flexible polymethylenic spacers of different parity (even and odd) are reported. They show nematic phases with strong odd–even effects. The unusual result we have found is that the odd dimer crystallizes adopting a molecular conformation in which the two mesogenic groups are aligned with respect to each other, as for the even dimer. The crystal packing of the two dimers is also analogous.     

Systematic study of the performance of density functional theory methods for prediction of energies and geometries of organoselenium compounds

A variety of density functional theory (DFT) methods are paired with Pople basis sets of varying sizes and evaluated for use with organoselenium compounds. The ability of each method to predict reliable geometries and energies is determined through comparison with quadratic configuration interaction with single and double excitations (QCISD) results. The recommended procedure for accurate prediction of energies and geometries is to use the B3PW91 functional with the 6-311G(2df,p) basis set. The B3PW91/6-31G(d,p) level of theory gives almost identical geometries as larger basis sets, so geometries can be predicted at this level for computational efficiency.     

Intermolecular potentials of the methane dimer calculated with Møller-Plesset perturbation theory and density functional theory

We have calculated the intermolecular interaction potentials of the methane dimer at the minimum-energy D(3d) conformation using the Hartree-Fock (HF) self-consistent theory, the correlation-corrected second-order M?ller-Plesset (MP2) perturbation theory, and the density functional theory (DFT) with the Perdew-Wang (PW91) functional as the exchange or the correlation part. The HF calculations yield unbound potentials largely due to the exchange-repulsion interaction. In the MP2 calculations, the basis set effects on the repulsion exponent, the equilibrium bond length, the binding energy, and the asymptotic behavior of the calculated intermolecular potentials have been thoroughly studied. We have employed basis sets from the Slater-type orbitals fitted with Gaussian functions (STO-nG) (n=3-6) [Quantum Theory of Molecular and Solids: The Self-Consistent Field for Molecular and Solids (McGraw-Hill, New York, 1974), Vol. 4], Pople's medium size basis sets of Krishnan et al. [J. Chem. Phys. 72, 650 (1980)] [up to 6-311++G(3df,3pd)] to Dunning's correlation consistent basis sets [J. Chem. Phys. 90, 1007 (1989)] (cc-pVXZ and aug-cc-pVXZ) (X=D, T, and Q). With increasing basis size, the repulsion exponent and the equilibrium bond length converge at the 6-31G** basis set and the 6-311++G(2d,2p) basis set, respectively, while a large basis set (aug-cc-pVTZ) is required to converge the binding energy at a chemical accuracy (approximately 0.01 kcal/mol). Up to the largest basis set used, the asymptotic dispersion coefficient has not converged to the destined C6 value from molecular polarizability calculations. The slow convergence could indicate the inefficacy of using the MP2 calculations with Gaussian-type functions to model the asymptotic behavior. Both the basis set superposition error (BSSE) corrected and uncorrected results are presented to emphasize the importance of including such corrections. Only the BSSE corrected results systematically converge to the destined potential curve with increasing basis size. The DFT calculations generate a wide range of interaction patterns, from purely unbound to strongly bound, underestimating or overestimating the binding energy. The binding energy calculated using the PW91PW91 functional and the equilibrium bond length calculated using the PW91VP86 functional are close to the MP2 results at the basis set limit.     

Group 12 Dihalides: Structural Predilections from Gases to Solids

Connections between the structures of Group 12 dihalides in their vapor and crystal phases are sought and discussed. The molecular structures of all monomers and dimers (MX₂: M=Zn, Cd, Hg and X=F, Cl, Br, I) were calculated at the density functional B3PW91 and MP2 computational levels. All the monomers are linear, with the mercury dihalide molecules having shorter bonds than their cadmium analogues; the ZnX₂ and CdX₂ structures are similar. The shorter Hg? X distances are traced back to relativistic effects. For the dimers, many possible geometrical arrangements were considered. The zinc and cadmium dihalide dimers have the usual D_2h‐symmetry geometry, whereas the mercury dihalide dimers are loosely‐bound units with C_2h symmetry. The origins of this C_2h structure are discussed from different points of view, including frontier orbital interactions. The crystals of Group 12 dihalides span a wide range of structure types, from three‐dimensional extended solids to molecular crystals. There is an obvious connection between the structures and characteristics of monomers, their dimers, and the crystals they form. The similarities as well as startling differences from the Group 2 dihalides are analyzed.     

Density functional theory optimized basis sets for gradient corrected functionals: 3d transition metal systems

Density functional theory optimized basis sets for gradient corrected functionals for 3d transition metal atoms are presented. Double zeta valence polarization and triple zeta valence polarization basis sets are optimized with the PW86 functional. The performance of the newly optimized basis sets is tested in atomic and molecular calculations. Excitation energies of 3d transition metal atoms, as well as electronic configurations, structural parameters, dissociation energies, and harmonic vibrational frequencies of a large number of molecules containing 3d transition metal elements, are presented. The obtained results are compared with available experimental data as well as with other theoretical data from the literature.     

An evaluation of various computational methods for the treatment of organoselenium compounds

A reliable computational method for the prediction of organoselenium geometries and bond dissociation energies (BDEs) has been determined on the basis of the performance of density functional theory (DFT: B3LYP and B3PW91) and ab initio molecular orbital procedures (Hartree-Fock (HF)) in conjunction with various Pople basis sets including (but not limited to) the 6-31G(d), 6-31G(d,p), 6-311G(d), 6-311G(d,p), 6-311G(2df,p), and 6-311G(3df,3pd) sets. Predicted geometries and BDEs are compared with available experimental data and quadratic configuration interaction including single and double substitutions (QCISD) results. The B3PW91/6-311G(2df,p) level of theory is recommended for the prediction of the geometries and energetics of organoselenium compounds.     

Role of long-range intermolecular forces in the formation of inorganic nanoparticle clusters

An understanding of the role played by intermolecular forces in terms of the electron density distribution is fundamental to the understanding of the self-assembly of molecules in the formation of a molecular crystal. Using ab initio methods capable of describing both short-range intramolecular interactions and long-range London dispersion interactions arising from electron correlation, analyses of inorganic dimers of As(4)S(4) and As(4)O(6) molecules cut from the structures of realgar and arsenolite, respectively, reveal that the molecules adopt a configuration that closely matches that observed for the crystal. Decomposition of the interaction energies using symmetry-adapted perturbation theory reveals that both model dimers feature significant stabilization from electrostatic forces as anticipated by a Lewis acid/Lewis base picture of the interaction. London dispersion forces also contribute significantly to the interaction, although they play a greater role in the realgar structure near equilibrium than in arsenolite.