B3LYP Potential Research Articles

Comprehensive Benchmark Results for the Accuracy of Basis Sets for Anharmonic Molecular Vibrations.

The accuracy and convergence of a series of commonly used split-valence electronic basis sets are systematically investigated for the anharmonic molecular vibrational spectroscopic calculations using the second-order perturbative corrected vibrational self-consistent field theory. A series of 18 split-valence basis sets with increasing flexibility is assessed in conjunction with MP2 and density functional theory (DFT)-based dispersion-corrected B3LYP potentials and applied to a set of molecular systems with different electronic and vibrational characteristics. The computed fundamental transitions and intensities are compared with the experimental values to assess the accuracy of different basis sets. Comparisons with high levels of Dunning basis sets, aug-cc-pVQZ along with def2-TZVPP and aug-pc-2 type basis sets, are also tested to check the convergence. A full statistical error analysis has been performed, assessing the success and failure of each basis set in terms of both accuracy and precision. The general statement "the bigger the basis, the better the results" is not strictly followed for bigger basis sets that are nearly converged to the adiabatic ab initio limit. It is found that the basis set hierarchy holds good for minimal basis sets up to polarized double-ζ basis sets. Beyond that, the improvements in comparison to experimental results or with very high end aug-cc-pVQZ and others are found rather slow. Finally, a prescription regarding the choice of a basis set for a suitable balance between accuracy and the computational time is given, which can be further used to investigate specific normal modes and large molecules as a blackbox.

Estimating the activation energy of the displacement of Mg atoms in the channels of B25C4Mg1.42 crystals

The activation energy of displacement of Mg atoms through channels of B25C4Mg1.42 crystals is estimated using quantum chemical calculations (DFT (B3LYP potential), RHF, and UHF methods, 3-21G basis set) of the element of the structure modeling the channel and location of Mg atoms in it. The changes in the activation energy at the replacement of Mg atoms by Na and Li atoms were estimated. The greatest decreasing in the activation energy was detected for Li atoms. The obtained results can be regarded as a theoretical background for development of conducting systems based on B25C4Mg1.42 crystals.

Infrared Spectrum of Toluene: Comparison of Anharmonic Isolated-Molecule Calculations and Experiments in Liquid Phase and in a Ne Matrix

First-principles anharmonic calculations are carried out for the CH stretching vibrations of isolated toluene and compared with the experimental infrared spectra of isotopologues of toluene in a Ne matrix at 3 K and of liquid toluene at room temperature. The calculations use the vibrational self-consistent field method and the B3LYP potential surface. In general, good agreement is found between the calculations and experiments. However, the spectrum of toluene in a Ne matrix is more complicated than that predicted theoretically. This distinction is discussed in terms of matrix-site and resonance effects. Interestingly, the strongest peak in the CH stretching spectrum has similar widths in the liquid phase and in a Ne matrix, despite the very different temperatures. Implications of this observation to the broadening mechanism are discussed. Finally, our results show that the B3LYP potential offers a good description of the anharmonic CH stretching band in toluene, but a proper description of matrix-site and resonance effects remains a challenge.

Spontaneous resolution of heterometallic complex: cis-[Co(NH3)4(H2O)2][Fe(ox)3]·2H2O – A rare example for labile iron(III) complex

The new conglomerate forming compound of the formula cis-[Co(NH3)4(H2O)2][Fe(ox)3]·2H2O (1) (ox=C2O42−) was synthesized and structurally, spectroscopically and magnetically characterized revealing weak antiferromagnetic couplings. Two forms of (1) crystallizing in hexagonal enantiomorphic space groups, P6522 and P6122, were identified proving that spontaneous resolution of the racemic mixture occurred at the crystallization stage, because chiral (1a) and (1b), respectively, were obtained from the same synthesis using racemic K3[Fe(ox)3]·3H2O substrate. It is rare example of conglomerate formation with labile Fe(III) ion as a coordination center. In packing along z axis for (1a) and (1b) structures we observe pattern with iron and cobalt complexes as well as water molecules arranged in separated helices, left-handed for (1a) and right-handed for (1b). Analysis of the intermolecular contacts formed by the “false block” with inverted chirality placed in the homochiral network revealed steric hindrance as well as disruption of approximately 50% of hydrogen bonds inside a helix and between adjacent helices. This analysis was supported by calculations performed using gaussian-03 run with DFT B3LYP potential using 6–31+G(d,p) basis. They revealed significantly more stable structure for the true block due to disruption of several hydrogen bonds and steric hindrance introduced by the false block. Hence, the helices imposed by chiral [Fe(ox)3]3− blocks are a template for supramolecular structure, which reveals achiral water molecules and Co(III) moieties forming helices of the same handedness as iron blocks. These Fe(III) moieties are trapped inside tightly packed crystal network, which is maintained by the robust hydrogen bond network. In this structure Co(III) blocks transmit interactions between adjacent helices. Analysis of intermolecular interactions network allows also for deeper insight into a nature of light- and/or time-catalyzed degradation as well as spontaneous resolution processes.

First Principle Calculations of the Electronic and Vibrational Properties of the 3-(1,1-Dicyanoethenyl)-1-phenyl-4,5-dihydro-1H-pyrazole Molecule

Results of first principle quantum chemical calculations of electronic and vibrational properties of the push-pull 3-(1,1-dicyanoethenyl)-1-phenyl-4,5-dihydro-1H-pyrazole (DCNP) molecule are reported and discussed. The structure of DCNP was optimized with HF/6-311G methodology and found to be planar. On the basis of obtained geometry, infrared absorption and Raman spectra were computed within the HF/6-311++G** formalism. They allow to conclude that the changes of molecule dipole moment and variation of its polarizability appear at the same vibrational mode and affect the optical properties of the DCNP. Four different methodologies: time-dependent HF and time-dependent DFT method with B3LYP, LC-BLYP, and CAM-B3LYP potentials were used to compute the optical absorption spectra of DCNP. Influence of solvent on molecular electronic structure was studied within the C-PCM model. It predicts the DFT/B3LYP methodology as the best one to compute the NLO properties of the DCNP. The computed HOMO and LUMO orbitals show evidence that the ground state of the molecule is located at its aromatic part. The discussion of charge transfer during the excitation process for the transition S0-S1 was performed. The charge transfer parameter calculated in vacuum and in solvent gives the evidence that the solvent environment weakly enhance the molecular charge transfer. It confirms the tendency of an occurrence of the intermolecular charge transfer in DCNP which is crucial for its hyperpolarizability magnitude. It was proved that the second-order susceptibility corresponding to SHG may be calculated for host-guest polymer/DCNP composite using the simple oriented gas model and the rigorous local field approach should not necessarily be applied.

Density functional theory calculation of refractive indices of the highly polar compounds

Refractive indices of the highly polar compounds are evaluated by computation from first principles combined with molecular dynamics simulation. The molecular polarisability is obtained by density functional theory (DFT) using the B3LYP potential; the equilibrium density in the liquid phase is calculated utilising the GROMOS force field simultaneously. This combination of method is shown to provide an economical methodology for estimating the refractive indices of a wide range of polar species. All the evaluation data for the considered highly polar compounds are good agreement to the available data based on the standard of experiment.

Approximate first-principles anharmonic calculations of polyatomic spectra using MP2 and B3LYP potentials: comparisons with experiment.

Anharmonic vibrational spectroscopy calculations using MP2 and B3LYP computed potential surfaces are carried out for a series of molecules, and frequencies and intensities are compared with those from experiment. The vibrational self-consistent field with second-order perturbation correction (VSCF-PT2) is used in computing the spectra. The test calculations have been performed for the molecules HNO3, C2H4, C2H4O, H2SO4, CH3COOH, glycine, and alanine. Both MP2 and B3LYP give results in good accord with experimental frequencies, though, on the whole, MP2 gives very slightly better agreement. A statistical analysis of deviations in frequencies from experiment is carried out that gives interesting insights. The most probable percentage deviation from experimental frequencies is about -2% (to the red of the experiment) for B3LYP and +2% (to the blue of the experiment) for MP2. There is a higher probability for relatively large percentage deviations when B3LYP is used. The calculated intensities are also found to be in good accord with experiment, but the percentage deviations are much larger than those for frequencies. The results show that both MP2 and B3LYP potentials, used in VSCF-PT2 calculations, account well for anharmonic effects in the spectroscopy of molecules of the types considered.

The Triplet-Singlet Gap in the m-Xylylene Radical: A Not So Simple One.

Meta-benzoquinodimethane (MBQDM) or m-xylylene provides a model for larger organic diradicals, the triplet-singlet gap being the key property. In the present work this energy difference has been the object of a systematic study by means of several density functional theory-based methods including B3LYP, M06, M06-2X, HSE and LC-ωPBE potentials and a variety of wave function-based methods such as complete active space self consistent field (CASSCF), Multireference second-order Møller-Plesset (MRMP), difference dedicated configuration interaction (DDCI), and Multireference configuration interaction (MRCI). In each case various basis sets of increasing quality have been explored, and the effect of the molecular geometry is also analyzed. The use of the triplet and broken symmetry (BS) solutions for the corresponding optimized geometries obtained from B3LYP and especially M06-2X functionals provide the value of the adiabatic triplet-singlet gap closer to experiment when compared to the reported value of Wenthold, Kim, and Lineberger, (J. Am. Chem. Soc. 1997, 119, 1354) and also for the electron affinity. The agreement further improves using the full π-valence CASSCF(8,8) optimized geometry as an attempt to correct for the spin contamination effects on the geometry of the BS state. The CASSCF, MRMP, and MRCI, even with the full π valence CAS(8,8) as reference and relatively large basis set, systematically overestimate the experimental value indicating either that an accurate description must go beyond this level of theory, including σ electrons and higher order polarization functions, or perhaps that the measured value is affected by the experimental conditions.

Complexes of prodigiosin (a naturally occurring pyrrolylpyrromethene) with H+, Cl−, [formula omitted] and CO2: A computational study

Prodigiosin (a naturally occurring pyrrolylpyrromethene) is a red pigment which can be isolated from the marine bacterium serratia and has potent immunosuppressive and anticancer activities. It has recently been shown to function as an anion exchanger for Cl− and HCO3- across lipid cell membranes. It possesses three N(H) groups arranged in an arc. These groups generate a convergent set of H-bonds (directed toward a common point) on a rigid scaffold which allow prodigiosin to bind strongly to anions like HCO3-. It may therefore also provide a means for sensing HCO3- or capturing HCO3- from solution.We have carried out quantum mechanical calculations on the structures, energetics, UV–visible spectra and NMR spectra of prodigiosin and its complexes with H+, Cl−, HCO3-, (HCO3-)2 and CO2. Geometry optimizations and energetic calculations have been performed at the 6-311G(d,p) B3LYP level with proper accounting for vibrational contributions to the free energy, corrections for basis set superposition error, and corrections for solvation effects using a polarizable continuum model. Comparison of the energetics for formation of complexes with HCO3- shows that the protonated prodigiosin forms the most stable complex. Our calculated geometry for the prodigiosinH+⋯Cl− complex is in good agreement with the experimentally determined structure for a close analog. The calculated stability of the complexes is strongly influenced by the polarity of the solvent. The UV–visible spectrum of neutral prodigiosin calculated at the TD DFT level, with the B3LYP potential, is also in good agreement with experiment. The lowest energy spectral peak is dominated by a HOMO to LUMO transition involving orbitals localized on the ring system of the molecule. Calculated changes in the UV–visible spectra produced by protonation and complex formation are small.

Migration and chemical reaction of H+ in protonated β-galactose

Equilibrium structures for a proton on β-D-galactose and transition states for proton hopping are computed. Also, Ab Initio Molecular Dynamics (AIMD) simulations are carried out. All calculations used B3LYP potentials with dispersion. At 40 K, proton hopping between sites is of near microsecond timescale. At 300 K, the proton migrates across the sugar on a sub-picosecond timescale. At 500 K, the proton reacts with the sugar to produce H(2)O. Implications for sugar chemistry are discussed.

Refractive indices of liquid-forming organic compounds by density functional theory

Refractive indices of typical liquid-forming organic materials are calculated by computation from first principles in conjunction with molecular dynamics simulation. The molecular polarizability is obtained by density functional theory using the B3LYP potential, while the equilibrium density in the liquid phase is calculated utilizing the COMPASS force field. This combination of procedures is shown to provide an economical methodology for estimating the refractive indices of a wide range of organic species. By the standard of experiment, both the trends and the magnitudes of the available data are reproduced with good accuracy.

Matrix-isolation study of cluster formation in methanol: O–H stretching region

The process of hydrogen-bonded cluster formation in methyl alcohol was investigated by FTIR spectroscopy using a matrix-isolation technique. Temperature dependence of the registered spectra of methanol trapped in an Ar matrix in the frequency region of O–H stretch fundamental was analyzed. The transformation of the FTIR bands of free O–H groups (3600–3800 cm − 1 ) into diffuse bands (3000–3600 cm − 1 ), which were assigned to the vibrations of the H-bonded hydroxyl groups in various clusters, was monitored in its initial stage at matrix heating from 10 K to 50 K. For the interpretation of the obtained experimental data the results of quantum-chemical simulation were used. The ab initio calculation was carried out at the DFT level of theory using the Gaussian 03 program with B3LYP potential and 6-31G(d) basis functions set. The similarity of the registered spectra of methanol trapped in the Ar matrix at 10–20 K to the gas-phase spectra of methanol and their gradual transformation with matrix heating to the ones similar to the spectra of liquid methanol (at 40–50 K) allows making the conclusion that such experiments may be considered as the proof of structural transformations in methyl alcohol during the phase transition from gas to liquid.

An Investigation of KS-DFT Electron Densities used in Atoms-in-Molecules Studies of Energetic Molecules

The atoms-in-molecules (AIM) theory has been proposed as a method to understand chemical stability through stationary properties of the electron density. To assess the applicability of this method for establishing such correlations with various performance and vulnerability properties of energetic materials, we calculated the Kohn-Sham density functional theory (KS-DFT) wavefunctions and their subsequent AIM data for representative materials, including hexanitrobenzene (HNB), pentaerythritol tetranitrate (PETN), pentanitroaniline (PNA), 1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX), ethylenedinitramine (EDNA), 1,1-diamino-2,2-dinitroethylene (FOX-7), 3-nitro-1,2,4-triazol-5-one (NTO), nitroguanidine (NQ), 1,3,5-triamino-2,4,6-trinitrobenzene (TATB), and the TATB dimer using the B3LYP, PBE, and PW91 potentials as well as Hartree-Fock (HF). For the HNB and HMX molecules and the TATB dimer, the number of critical points in the low-density regions of the density gradient vector field varied, sometimes dramatically, with basis set and potential even at their individually optimized geometries. Adding ghost atoms in the low-density regions also affected the existence of critical points. The variation was seen in results generated with three separate AIM software packages, AIMPAC, AIMAll, and InteGriTy. This inconsistency implies that KS-DFT wave-functions can have significant variation in the topology of the electron density to such an extent that these calculations cannot be used to justify the existence or absence of low-density critical points. Therefore, predictions of the stability of a molecule based solely on properties of low-density bond critical points generated from a single DFT calculation are questionable.

Comment on “About the calculation of exchange coupling constants using density-functional theory: The role of the self-interaction error” [J. Chem. Phys. 123, 164110 (2005)

The use of density functional theory to obtain energy differences related to magnetic coupling constants is debated with special emphasis to the claims by Ruiz et al. [J. Chem. Phys.123, 164110 (2005)] that good agreement with experiment using the B3LYP potential is obtained by ignoring spin symmetry in case self-interaction error cannot be removed.

Metastable Lanthanide Complex Formation and their Thermal Behavior in the Solid State with Alkylcyanobiphenyls

ABSTRACT The formation of two metastable complexes (M/L = 1/2 and 1/1) is shown for low temperature co-condensates of europium and samarium vapors with mesogenic ligand 4-penthyl-4′-cyanobiphenyl (5CB). The DFT-calculations based on hybrid B3LYP potential have been carried out to study the equilibrium structures of complexes. The model structures including one and two metal atoms with antiparallel disposition of ligand molecules are considered. The spectral shifts for ligand CN-group stretching vibrations and the relative thermal stability of the complexes are discussed.

Absorption and Fluorescence of 3-Methylindole: A Theoretical Study, Including H2O Interactions

The paper presents a computational study of the ground and excited states of 3-methylindole. The ground-state geometry is optimized using the DFT B3LYP potential in conjunction with a 6-31+G(d) basis set. In addition the ground and first and second excited singlet states are optimized, for the first time, using the CASSCF method with an ANO−S basis set. The results are compared with experiment and with the experimental and theoretical literature data for the parent indole. The calculated excitations are in agreement with the absorption data. The comparison also shows that the 3-methylindole relaxation of the second excited-state terminates in an avoided crossing. The relaxed geometry of the second excited 3-methylindole state is therefore of mixed 1La/1Lb nature. The interaction of 3-methylindole with water is also examined, revealing three stable chromophore−water complexes. The calculations are extended to the more stable chromophore−(water)2 complexes. The excitation energies of these complexes are calculated using the CASPT2 method (ANO−S type basis). Calculations using ESP-charges instead of water molecules demonstrate the usefulness of such approximation for the calculation of excitation energy shifts. Analogous results are obtained using Amber5.0 point charges.

Reduced basis set for the gold atom in cluster complexes.

To extend the metal cluster size used in interfacing between bulk metals and molecules in ab initio studies of molecular electronics and chemisorption, a reduced size atomic orbital basis set for the gold atom has been generated. Based on the SKBJ relativistic effective core potential set, the three component 5d Gaussian orbital basis set is completely contracted. Comparisons between the full and reduced basis set in Au atom clusters and cluster complexes for geometry, bond distances, dipole moments, atomic charges, spin, bond dissociation energies, lowest energy harmonic frequencies, electron affinities, ionization energies, and density of states distributions show the contracted set to be a viable replacement for the full basis set. This result is obtained using both the B3LYP and BPW91 exchange-correlation potentials in density functional theory.

AlTiNi Ternary Alloy Clusters: Molecular Dynamics Simulations and Density Functional Theory Calculations

Structural and electronic properties of AlkTilNim (k + l + m = 4) clusters have been investigated by performing molecular dynamics (MD) simulations and density functional theory (DFT) calculations (within the B3LYP and effective core potential level). After an empirical potential energy function (PEF) was parametrized for the AlTiNi ternary system, stable structures of the clusters were determined by MD simulations. The possible dissociation channels and electronic properties of the obtained clusters were calculated by the DFT method. The energetics of the clusters at 1 and 300 K are also discussed.

Accuracy of geometries: influence of basis set, exchange?correlation potential, inclusion of core electrons, and relativistic corrections

The geometries of a set of small molecules were optimized using eight different exchange–correlation (xc) potentials in a few different basis sets of Slater-type orbitals, ranging from a minimal basis (I) to a triple-zeta valence basis plus double polarization functions (VII). This enables a comparison of the accuracy of the xc potentials in a certain basis set, which can be related to the accuracies of wavefunction-based methods such as Hartree–Fock and coupled cluster. Four different checks are done on the accuracy by looking at the mean error, standard deviation, mean absolute error and maximum error. It is shown that the mean absolute error decreases with increasing basis set size, and reaches a basis set limit at basis VI. With this basis set, the mean absolute errors of the xc potentials are of the order of 0.7–1.3 pm. This is comparable to the accuracy obtained with CCSD and MP2/MP3 methods, but is still larger than the accuracy of the CCSD(T) method (0.2 pm). The best performing xc potentials are found to be Becke–Perdew, PBE and PW91, which perform as well as the hybrid B3LYP potential. In the second part of this paper, we report the optimization of the geometries of five metallocenes with the same potentials and basis sets, either in a nonrelativistic or a scalar relativistic calculation using the zeroth-order regular approximation approach. For the first-row transition-metal complexes, the relativistic corrections have a negligible effect on the optimized structures, but for ruthenocene they improve the optimized Ru–ring distance by some 1.4–2.2 pm. In the largest basis set used, the absolute mean error is again of the order of 1.0 pm. As the wavefunction-based methods either give a poor performance for metallocenes (Hartree–Fock, MP2), or the size of the system makes a treatment with accurate methods such as CCSD(T) in a reasonable basis set cumbersome, the good performance of density functional theory calculations for these molecules is very promising; even more so as density functional theory is an efficient method that can be used without problems on systems of this size, or larger.

Time-dependent density functional theory calculations of the photoabsorption of fluorinated alkanes

Time-dependent density functional theory (TD-DFT) calculations of the transition energies and oscillator strengths of fluorinated alkanes have been performed. The TD-DFT method with the non-local B3LYP potential yields transition energies for the methanes, which are smaller by about 10% as compared to the experimental values. An empirical linear correlation was found between the calculated and experimental transition energies both at the B3LYP/DZ+Ryd(C, F) and B3LYP/cc-pVTZ+Ryd(C, F, H) levels for a total of 19 transitions of the fluorinated methanes with linear correlation coefficients of 0.987 for the former and 0.988 for the latter. This empirical correlation for fluorinated methane molecules is found to agree well with the previously obtained empirical correlations between calculated and experimental values for non-fluorinated molecules. The results show that a single empirical-correlation relationship can be used for both non-fluorinated and fluorinated molecules to predict transition energies. This linear relationship is then used to predict the photoabsorption spectra of ethane, propane, butane, and partially and fully fluorinated derivatives. A key result of these calculations is the dominance of Rydberg transitions in the spectral region of interest.