Density functional theory and post-Hartree-Fock studies on molecular structure and harmonic vibrational spectrum of formaldehyde

Density functional theory (DFT) with the Becke's three-parameter exchange correlation functional and the functional of Lee, Yang and Parr, gradient-corrected functionals of Perdew, and Perdew and Wang [the DFT(B3LYP), DFT(B3P86) and DFT(B3PW91) methods, respectively], and several levels of conventional ab initio post-Hartree-Fock theory (second- and fourth-order perturbation theory M?ller-Plesset MP2 and MP4(SDTQ), coupled cluster with the single and double excitations (CCSD), and CCSD with perturbative triple excitation [CCSD(T)], configuration interaction with the single and double excitations [CISD], and quadratic configuration interaction method [QCISD(T)], using several basis sets [ranging from a simple 6-31G(d,p) basis set to a 6-311+ +G(3df, 2pd) one], were applied to study of the molecular structure (geometrical parameters, rotational constants, dipole moment) and harmonized infrared (IR) spectrum of formaldehyde (CH₂O). High-level ab initio methods CCSD(T) and QCISD(T) with the 6-311+ +G(3df, 2pd) predict correctly molecular parameters, vibrational harmonic wavenumbers and the shifts of the harmonic IR spectrum of ¹²CH₂ ¹⁶O upon isotopic substitution. Received: 30 January 1997 / Accepted: 7 May 1997     

One‐bond 29Si‐1H spin‐spin coupling constants in the series of halosilanes: benchmark SOPPA and DFT calculations,relativistic effects,and vibrational corrections

A number of most representative second order polarization propagator approach (SOPPA) based wavefunction methods, SOPPA, SOPPA(CC2) and SOPPA(CCSD), and density functional theory (DFT) based methods, B3LYP, PBE0, KT2, and KT3, have been benchmarked in the calculation of the one‐bond ²⁹Si‐¹H spin‐spin coupling constants in the series of halosilanes SiH_nX_4?n (X = F, Cl, Br, I), both at the non‐relativistic and full four‐parameter Dirac's relativistic levels taking into account vibrational corrections. At the non‐relativistic level, the wavefunction methods showed much better results as compared with those of DFT. At the DFT level, out of four tested functionals, the Perdew, Burke, and Ernzerhof's PBE0 showed best performance. Taking into account, relativistic effects and vibrational corrections noticeably improves wavefunction methods results, but generally worsens DFT results. Copyright © 2013 John Wiley & Sons, Ltd.     

Which density functional is close to CCSD accuracy to describe geometry and interaction energy of small noncovalent dimers? A benchmark study using Gaussian09

A benchmark study on all possible density functional theory (DFT) methods in Gaussian09 is done to locate functionals that agree well with CCSD/aug‐cc‐pVTZ geometry and Ave‐CCSD(T)/(Q‐T) interaction energy (E_int) for small non‐covalently interacting molecular dimers in “dispersion‐dominated” (class 1), “dipole‐induced dipole” (class 2), and “dipole‐dipole” (class 3) classes. A DFT method is recommended acceptable if the geometry showed close agreement to CCSD result (RMSD < 0.045) and E_int was within 80–120% accuracy. Among 382 tested functionals, 1–46% gave good geometry, 13–44% gave good E_int, while 1–33% satisfied geometry and energy criteria. Further screening to locate the best performing functionals for all the three classes was made by counting the acceptable values of energy and geometry given by each functionals. The meta‐generalized gradient approximation (GGA) functional M06L was the best performer with total 14 hits; seven acceptable energies and seven acceptable geometries. This was the only functional “recommended” for at least two dimers in each class. The functionals M05, B2PLYPD, B971, mPW2PLYPD, PBEB95, and CAM‐B3LYP gave 11 hits while PBEhB95, PW91B95, Wb97x, BRxVP86, BRxP86, HSE2PBE, HSEh1PBE, PBE1PBE, PBEh1PBE, and PW91TPSS gave 10 hits. Among these, M05, B971, mPW2PLYPD, Wb97x, and PW91TPSS were among the “recommended” list of at least one dimer from each class. Long‐range correction (LC) of Hirao and coworkers to exchange‐correlation functionals showed massive improvement in geometry and E_int. The best performing LC‐functionals were LC‐G96KCIS and LC‐PKZBPKZB. Our results predict that M06L is the most trustworthy DFT method in Gaussian09 to study small non‐covalently interacting systems. © 2013 Wiley Periodicals, Inc.     

Allycyanide gauche revisited

The microwave spectrum of the ground state of the gauche rotamer of allylcyanide (CH₂=CHCH₂ CN) has been remeasured. The obtained rotational constants A = 19 707.9 ± 0.1, B = 2 619.74 ± 0.05 and C = 2 497.43 ± 0.05 (in MHz) were in good agreement with a structural model. The dipole moment components were also fitted as |μ_a| = 3.50 ± 0.05, |μ_b| = 1.70 ± 0.02 and |μ_c| = 0.19 ± 0.04 (in Debye). The results are in both cases in good agreement with a CCCC dihedral angle near the expected 120°.     

Theoretical study on the structures, isomerization and stability of SiC3H isomers

The calculations of the geometry optimizations, energies, dipole moments, vibrational spectra, rotational constants, and isomerization of doublet SiC₃H species were performed using density functional theory and ab initio methods. Four types of isomers, a total of 18 minima, connected by 16 interconversion transition states, were located on the potential energy surface (PES) at the B3LYP/6-311G (d, p) level. More accurate energies were obtained at the CCSD(T)/6-311G(2df, 2p), and G3(MP2) levels. With the highest isomerization barrier, the lowest lying structure, linear A1 possesses the largest kinetic stability. Besides, the isomerization barriers of A2, A4, C2, F1, F4 and F5 are over 10 kcal/mol, and these isomers are also considered to be higher kinetically stable. Other isomers cannot be kinetically stabilized with considerably low isomerization barriers. Investigation on the bonding properties and the computations of vibrational spectra, dipole moments, and rotational constants for SiC₃H isomers are helpful for understanding their structures and also valuable for their detections in the interstellar space and laboratory.     

Benchmarking of DFT functionals for the kinetics and mechanisms of atmospheric addition reactions of OH radicals with phenyl and substituted phenyl‐based organic pollutants

^•OH addition reactions play a pivotal role in the atmospheric transformation of a number of phenyl and substituted phenyl‐based persistent and toxic organic pollutants. Here, we screened appropriate DFT functionals to predict reaction mechanisms and rate constants (k_OH) of the ^•OH additions by taking benzene and substituted benzenes (C₆H₅F, C₆H₅Cl, C₆H₅Br, C₆H₅CH₃, C₆H₅OH) as model compounds. By comparing the k_OH values calculated with DFT methods to experimental values, we found that the ωB97 functional is the best among the 18 functionals considered (using the basis sets 6‐31 + G(d,p) for optimizations and 6‐311++G(3df,2pd) for single point energy calculations) in the temperature range of 230‐330 K. In addition, we found that some other functionals performed well in specific conditions, e.g., BMKD3 is good for benzene, halogenated benzenes and C₆H₅CH₃, and CAM‐B3LYP is good for the reaction of C₆H₅OH at room temperature. Based on the diversity of the electronic structures of the selected model compounds and the frequent occurrence of certain substituents ( CH₃,  OH,  F,  Cl, and  Br) in the target compounds, the functionals recommended here can be used for future study of the reaction mechanisms and k_OH values for ^•OH addition to phenyl and substituted phenyl‐based persistent and toxic organic pollutants.     

Investigation of electronic structure in chlorine-substituted methanes

The electronic structure, dipole moments, and nuclear magnetic resonance and nuclear quadrupole resonance constants of the CH₄, CCl₄, CHCl₃, CH₂Cl₂, and CH₃Cl molecules were calculated by the Parr-Pariser-Pople (PPP) and Wolfsberg-Helmholz (WH) methods, with self-consistency of the charges on the atoms. Conclusions were reached on the applicability limits of these methods. The calculated values were compared with experimental data.     

DFT Study of Solvent Effects for Some Organic Molecules Using a Polarizable Continuum Model

Forty ionic molecules are studied by DFT (B3LYP, B3P86), MP4 with different basis sets using the PCM/UAHF model within the self-consistent reaction-field method to assess solvent effects. For these molecules, the solvation free energies (ΔG _sol) in water and the dipole moments in vacuoas well as in water are obtained. By comparing the calculated values of ΔG _sol with experimental values and molecular simulation results, it is found that the ΔG _sol values generated by the DFT method are in better agreement with experimental values. Moreover, especially for the B3LYP/6-31+G_∗ level, the results of both ΔG _sol and dipole moments are more accurate considering the lower computational cost. It can be noted that the dipole moments of solutes in water show some increase relative to those in vacuo.     

What are the spectroscopic properties of HFC‐32? Answers from DFT

Although coupled cluster theory coupled to large basis sets can reach impressive accuracies for thermochemical and spectroscopic properties, it is still limited to small/medium sized molecules. Density functional theory (DFT) represents the working option for systems composed of hundreds to thousands heavy atoms. In this context, investigations are required aimed at characterizing the performances of the different density functionals (DF). This work focuses on the study of DFT performances in the prediction of spectroscopic properties, with particular attention to the vibrational problem, by focusing on the CH₂F₂ molecule as a test case. An extensive and systematic investigation is performed on several DFT model chemistries by testing their predictions of molecular constants and vibrational frequencies and intensities against CCSD(T)/aug‐cc‐pCVQZ data. B3LYP, B3PW91, B97‐1, PBE0, TPSSh, M05, M05‐2X, and B2PLYP DFs are used in conjunction with a variety of basis sets. Anharmonic frequencies are derived from the VPT2 treatment of anharmonic‐ and hybrid CCSD(T)/DFT‐force fields. A software for VPT2 computations is also presented. © 2014 Wiley Periodicals, Inc.     

DFT plus PCM calculation for pairing specificity of Watson–Crick‐type bases in aqueous solutions

This study is aimed at explaining the preference for AT and CG pairings and the possible insertion of other tautomeric DNA base pairs such as G_enolT, that respect energetic and steric requirements including at least two hydrogen bonds and 11 ± 0.5Å distance between the 9‐CH₃ of purine and 5‐CH₃ of pyrimidine. The calculated free energy of formation ΔΔG at the DFT B3LYP/6‐31G*‐PCM/BEM level pointed out the CG and AT pairs as the most favored, followed closely by G_enolT, in good agreement with Michaelis–Menten first order kinetics (CG ≈ AT > G_enolT). Unusual DNA base pairs complexes such as AG (BEM) and CT (PCM) resulted to be stable, but it is very difficult to assume that they are likely to be included in the double strand DNA. The calculated enthalpy and dipole moments of isolated DNA bases agree well with experiment. The free energy of hydration, ΔG_hyd, was found to depend on the electrostatic term, while cavitation‐dispersion components are almost constant. The stability of DNA complexes in water resulted from PCM calculations is markedly influenced by the free energy of hydration. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Computational NMR coupling constants: Shifting and scaling factors for evaluating 1JCH

Optimized shifting and/or scaling factors for calculating one‐bond carbon–hydrogen spin–spin coupling constants have been determined for 35 combinations of representative functionals (PBE, B3LYP, B3P86, B97‐2 and M06‐L) and basis sets (TZVP, HIII‐su3, EPR‐III, aug‐cc‐pVTZ‐J, ccJ‐pVDZ, ccJ‐pVTZ, ccJ‐pVQZ, pcJ‐2 and pcJ‐3) using 68 organic molecular systems with 88 ¹J_CH couplings including different types of hybridized carbon atoms. Density functional theory assessment for the determination of ¹J_CH coupling constants is examined, comparing the computed and experimental values. The use of shifting constants for obtaining the calculated coupling improves substantially the results, and most models become qualitatively similar. Thus, for the whole set of couplings and for all approaches excluding those using the M06 functional, the root‐mean‐square deviations lie between 4.7 and 16.4 Hz and are reduced to 4–6.5 Hz when shifting constants are considered. Alternatively, when a specific rovibrational contribution of 5 Hz is subtracted from the experimental values, good results are obtained with PBE, B3P86 and B97‐2 functionals in combination with HIII‐su3, aug‐cc‐pVTZ‐J and pcJ‐2 basis sets. Copyright © 2013 John Wiley & Sons, Ltd.     

A challenge for density functional theory: the XONO and XNO2 (X=F, Cl, and Br) molecules

The equilibrium geometries, harmonic frequencies, dipole moments, infrared intensities, and relative energies of the cis-XONO, trans-XONO, and XNO₂ (X=F, Cl, and Br) have been investigated using four functionals in common use in Kohn-Sham density functional theory (DFT) calculations. Two of the functionals include non-local or gradient correction terms, while the other two also incorporate some exact Hartree-Fock exchange and are labeled hybrid functionals. The quality of the results obtained from the functionals is determined by comparison to previously published high-level coupled-cluster calculations. The hybrid functionals perform better for prediction of the equilibrium geometries, where the two gradient corrected functionals yield qualitatively incorrect molecular structures for cis-FONO and cis-ClONO. None of the functionals perform well in predicting all six harmonic frequencies, showing that the correlation between equilibrium geometries and harmonic frequencies is not as strong for these DFT methods as it is for conventional wavefunction ab initio methods, such as coupled-cluster theory. Results from the various functionals generally come into better agreement with each other and also with the coupled-cluster results moving down the periodic table. Received: 12 February 1997 / Accepted: 25 March 1997     

Structure and Stability of C20H3 Radical

Density functional theory B3LYP with 6-31G* basis set has been used to investigate the geometries, rotational constants, dipole moments, energy gaps and vibrational frequencies of nine series of isomers of C20H3 radical. The result shows that the bowl-like structure with C1 symmetry is the most stable structure, in which the three hydrogen atoms locate on the edge carbon atoms, and the two hydrogen atoms are neighbouring and the other one has a two- carbon atom interval to the neighbouring hydrogen. In addition, the relationship between the energy and the position of one hydrogen atom from end to middle on the linear structures of C20H3 radical with two hydrogens atoms located on two ends was obtained, which shows the energy increase monotonously. Furthermore, hydrogenation can relax the strain and make the isomer of C20 more stable.     

Benchmark calculations of 29Si–1H spin–spin coupling constants across double bond

Benchmark calculations of geminal and vicinal ²⁹Si–¹H spin–spin coupling constants across double bond in three reference alkenylsilanes have been carried out at both DFT and SOPPA levels in comparison with experiment. At the former, four density functionals, B3LYP, B3PW91, PBE0 and KT3, were tested in combination with five representative basis sets. At the latter, three main SOPPA‐based methods, SOPPA, SOPPA(CC2) and SOPPA(CCSD), were examined in combination with the same series of basis sets. On the whole, the wavefunction methods showed much better results as compared to DFT, with the most efficient combination of SOPPA/cc‐pVTZ‐su2 characterized by a mean absolute error of only 0.4 Hz calculated for a set of nine coupling constants in three compounds with a sample span of around 40 Hz. Copyright © 2012 John Wiley & Sons, Ltd.     

Comparison of large basis set DFT and MP2 calculations in the study of the barrier for internal rotation of 2,3,5,6‐tetrafluoroanisole

The barrier for internal rotation around the ? OCH₃ bond in 2,3,5,6‐tetrafluoroanisole was calculated using the density functional theory (DFT) and second‐order Møller–Plesset (MP2) methods with Pople's basis sets up to 6‐311++G(3df,2p) and Jensen basis sets up to pc‐3. The results are converged only if fairly large basis sets are used (at least 6‐311++G(3df,2pd) or pc‐2). Both the DFT and MP2 potential energy curves show internal structure. Two minima and three maxima are observed on the curves, arising from the interplay between lone‐pair delocalization and changes in the hybridization around the oxygen atom, together with the attraction between the positively polarized hydrogens in the methyl group and the negatively polarized fluorine atom at the ortho position. These critical points are somehow ironed out by the addition of zero‐point and thermal corrections to the energy curves. At this level, the MP2 method can describe reasonably well the previously determined single‐well experimental rotational barrier, 2.7 ± 2.0 kcal/mol at 298 K, while all DFT methods yield a much smaller result. As observed experimentally, the ? OCH₃ group is perpendicular to the aryl ring in the equilibrium structure, although two very close minima with an intermediate hump at 90° are still observable. The theoretical free energy barrier of rotation at the MP2(full)/pc‐2 level is 2.0 ± 1.0 kcal/mol, in reasonable agreement with the experimental determination. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

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.     

Microwave spectrum,structure, dipole moment and internal rotation of trans-ethylmethylether

Microwave spectra of ethylmethylether and its eleven isotopically substituted species were measured. The r_s structure of the trans isomer was determined from the observed moments of inertia. Structural parameters of this isomer were roughly equal to those of the reported r_s structure for dimethylether and diethylether. The CH₂-O bond length was definitely shorter by about 0.01 Å than the CH₃-O bond length and the C-C bond length was nearly equal to those of ethylchloride and bromide. The OCH₃ group tilted by about 2° 13' towards lone pair electrons of the oxygen atom while no significant tilt angle was found for the CH₃C group.Dipole moments of the trans isomer for the normal and two deuterated species were determined by Stark-effect measurements. For the normal species, the dipole moment was μ_a = 0.146 ± 0.022 D,μ_b = 1.165 ± 0.020 D and μ_total=1.174 ± 0.022 D making an angle of 7° 5' ± 32' with the b inertial axis. Direction of the dipole moment in the molecule was discussed.From splittings of the observed spectra, barriers to internal rotations of two CH₃ groups were obtained in the one-top approximation. They were 2702 ± 7 and 3300 ± 25 cal mol^?1 for the OCH₃ and CH₃C groups, respectively, from the analysis of splittings in the first excited CH₃ torsional states. The coupling effects among two tops and the skeletal torsion were briefly discussed.