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     

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.     

Complete basis set prediction of methanol isotropic nuclear magnetic shieldings and indirect nuclear spin–spin coupling constants (SSCC) using polarization‐consistent and XZP basis sets and B3LYP and BHandH density functionals

Efficient B3LYP and BHandH density functionals were used to estimate methanol's nuclear magnetic isotropic shieldings and spin–spin coupling constants in the basis set limit. Polarization‐consistent pcS‐n and pcJ‐n (n = 0, 1, 2, 3 and 4), and segmented contracted XZP, where X = D, T, Q and 5, basis sets were used and the results fitted with simple mathematical formulas. The performance of the methods was assessed from comparison with experiment and higher level calculations. ¹J(CH) and ³J(HH) values were determined from very diluted solutions in deuterochloroform and compared with theoretical predictions. The agreement between complete basis set (CBS) density functional theory (DFT) predicted isotropic shieldings and spin–spin values and experiment was good. The BHandH/pcS‐n methanol shieldings obtained using structures optimized at the same level of theory are approaching the accuracy of the advanced coupled‐cluster‐singles‐doubles‐approximate triples (CCSD(T)) calculations. Copyright © 2009 John Wiley & Sons, Ltd.     

An ab initio calculation of 14n quadrupole coupling constants

Ab initio SCF-MO calculations of ¹⁴N quadrupole coupling constants are reported for HCN, HNC, CH₃CN, CH₃NC, NH₃, NH₂NH₂, FCN, N₂O, (CN)₂, BrCN, pyridine and pyrazine. There is excellent correlation between calculation and experiment yielding Q = 1.503 ± 0.159 × 10^?26 cm² for the ¹⁴N nuclear quadrupole moment. Dunning sp basis sets are more than adequate for such calculations, STO/4G basis sets yielding almost identical results for pyridine and pyrazine. Unsuccessful attempts were made to correlate coupling constants with electronic population analysis indices.     

Dynamics and structural changes of small water clusters on ionization

Despite utmost importance in understanding water ionization process, reliable theoretical results of structural changes and molecular dynamics (MD) of water clusters on ionization have hardly been reported yet. Here, we investigate the water cations [(H₂O)_{n = 2–6}⁺] with density functional theory (DFT), Möller–Plesset second‐order perturbation theory (MP2), and coupled cluster theory with single, double, and perturbative triple excitations [CCSD(T)]. The complete basis set limits of interaction energies at the CCSD(T) level are reported, and the geometrical structures, electronic properties, and infrared spectra are investigated. The characteristics of structures and spectra of the water cluster cations reflect the formation of the hydronium cation moiety (H₃O⁺) and the hydroxyl radical. Although most density functionals fail to predict reasonable energetics of the water cations, some functionals are found to be reliable, in reasonable agreement with high‐level ab initio results. To understand the ionization process of water clusters, DFT‐ and MP2‐based Born‐Oppenheimer MD (BOMD) simulations are performed on ionization. On ionization, the water clusters tend to have an Eigen‐like form with the hydronium cation instead of a Zundel‐like form, based on reliable BOMD simulations. For the vertically ionized water hexamer, the relatively stable (H₂O)₅⁺ (5sL4A) cluster tends to form with a detached water molecule (H₂O). © 2013 Wiley Periodicals, Inc.     

Theoretical insight into structural and electronic properties of cationic Scn+ (n=2-13): A benchmark study

Geometric, thermodynamic and electronic properties of cationic scandium clusters are studied. Geometric optimizations and stable spin states of Sc₂⁺ are assessed on high level ab-initio coupled cluster method CCSD(T) with different dunning correlation consistent basis sets (aug-cc-pVDZ, aug-cc-pVTZ and aug-cc-pVQZ). Then, 23 DFT functionals belonging to different classes are evaluated at 6-31G (d), LANL2MB, LANL2DZ and Def2-SVP basis sets, and the results are compared with the benchmarked coupled cluster calculations. Due to excellent correlation, PBEPBE/LANL2DZ was chosen to perform calculation of higher scandium cationic clusters Sc_n⁺ (n = 3-13). In addition, we explored relative stability, binding energies, second order energy differences, vertical ionization energies, vertical electron affinities and HOMO-LUMO gaps. Moreover, these results are also compared with the neutral scandium clusters.     

Estimation of isotropic nuclear magnetic shieldings in the CCSD(T) and MP2 complete basis set limit using affordable correlation calculations

A linear correlation between isotropic nuclear magnetic shielding constants for seven model molecules (CH₂O, H₂O, HF, F₂, HCN, SiH₄ and H₂S) calculated with 37 methods (34 density functionals, RHF, MP2 and CCSD(T)), with affordable pcS‐2 basis set and corresponding complete basis set results, estimated from calculations with the family of polarization‐consistent pcS‐n basis sets is reported. This dependence was also supported by inspection of profiles of deviation between CBS estimated nuclear shieldings and shieldings obtained with the significantly smaller basis sets pcS‐2 and aug‐cc‐pVTZ‐J for the selected set of 37 calculation methods. It was possible to formulate a practical approach of estimating the values of isotropic nuclear magnetic shielding constants at the CCSD(T)/CBS and MP2/CBS levels from affordable CCSD(T)/pcS‐2, MP2/pcS‐2 and DFT/CBS calculations with pcS‐n basis sets. The proposed method leads to a fairly accurate estimation of nuclear magnetic shieldings and considerable saving of computational efforts. Copyright © 2013 John Wiley & Sons, Ltd.     

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.     

Difluorobenzenes revisited: an experimental and theoretical study of spin–spin coupling constants for 1,2‐, 1,3‐, and 1,4‐difluorobenzene

The experimental spin–spin coupling constants (SSCCs) for 1,3‐ and 1,4‐difluorobenzene have been determined anew, and found to be consistent with previously determined values. SSCCs for 1,2‐, 1,3‐, and 1,4‐difluorobenzene have been analyzed by comparing them with the coupling constants computed using the second‐order polarization propagator approximation (SOPPA) and the equation‐of‐motion coupled cluster singles and doubles method (EOM‐CCSD). Eighty experimental values have been analyzed using SOPPA calculations, and a subset of 40 values using both SOPPA and EOM‐CCSD approaches. One‐bond coupling constants ¹J(C? C) and ¹J(C? F) are better described by EOM‐CCSD, whereas one‐bond ¹J(C? H) values are better described by SOPPA. An empirical equation is presented which allows for the prediction of unknown coupling constants from computed SOPPA values. A similar approach may prove useful for predicting coupling constants in larger systems. Copyright © 2009 John Wiley & Sons, Ltd.     

CH2CO＋CH2的多通道反应的理论研究

利用密度泛函(DFT)和自然键轨道理论(NBO)及高级电子耦合簇[CCSD(T)]和电子密度拓扑(AIM)方法, 对单重态和三重态CH₂与CH₂CO反应的微观机理进行了研究. 在B3LYP/6-311＋G(d,p)水平上优化了反应通道各驻点的几何构型. 在CCSD(T)/6-311＋G(d,p)水平上计算了各物种的单点能量, 并对总能量进行了校正. 计算表明, 单重态CH₂与CH₂CO的C—H键可发生插入反应, 与C＝C、C＝O可发生加成反应, 存在三条反应通道, 产物为CO和C₂H₄, 从能量变化和反应速控步骤能垒两方面考虑, 反应II更容易发生. 对反应通道中的关键点进行了自然键轨道及电子密度拓扑分析. 三重态CH₂与CH₂CO的反应存在三条反应通道, 一条是与C-H键的插入反应, 另一条是三重态CH₂与C＝C发生加成反应, 产物为CO和三重态C₂H₄, 通道II势垒较低, 更容易发生. 最后一条涉及双自由基的反应活化能最大, 最难发生.     

Reassessment of the Mechanisms of Thermal C−H Bond Activation of Methane by Cationic Magnesium Oxides: A Critical Evaluation of the Suitability of Different Density Functionals

The mechanisms of the thermal reactions of the two iconic magnesium oxide cations MgO^.+ and Mg₂O₂^.+ with methane have been re-evaluated at the CCSD(T)/CBS//CCSD/def2-TZVP level of theory. For the reaction of MgO^.+ with CH₄, only the classical hydrogen-atom transfer (HAT) was found; in contrast, for the Mg₂O₂^.+/CH₄ couple, both HAT and proton-coupled electron-transfer (PCET) exist as mechanistic variants. In order to evaluate the suitability of density functional theory (DFT) methods, the reactions were computed by using 27 density functionals. The results obtained demonstrate that the various DFT methods often deliver rather different results for both geometric and energetic features. As to the prediction of the apparent barriers, pure functionals give the largest mean absolute errors. BMK, ωB97XD, and the double-hybrid functional mPW2PLYP were confirmed to come closest to the results provided by CCSD(T)/CBS. Thus, mechanistic conclusions based on a single DFT method should be viewed with great caution. In summary, this study may assist in the selection of a suitable quantum chemical method to unravel the mechanistic details of C−H bond activation by charged metal oxides.     

Three-dimensional Potential Energy Surface and Bound States of the Ar2-Ne Complex

The first three-dimensional interaction potential energy surface (PES) of the Ar₂-Ne complex is developed using the single and double excitation coupled cluster theory with noniterative treatment of triple excitations CCSD(T). The aug-cc-pVQZ basis sets are employed for all atoms, including an additional (3s3p2d2f1g) set of midpoint bond functions. The calculated single point energies are fitted to an analytic two-dimensional potential model at each of seven fixed r_Ar2 values. The seven model potentials are then used to construct the three-dimensional PES by interpolating along (r—r_e) using a sixth-order polynomial. The PES is used in the following rovibrational energy levels calculations. The comparisons of theoretical transition frequencies and spectroscopic constants with the experimental results are given.     

Water trimer cation

By using density functional theory (DFT) and high-level ab initio theory, we have investigated the structure, interaction energy, electronic property, and IR spectra of the water trimer cation [(H₂O) ₃ ⁺ ]. Two structures of the water trimer cation [the H₃O⁺ containing linear (3Lp) structure versus the ring (3OO) structure] are compared. For the complete basis set (CBS) limit of coupled cluster theory with single, double, and perturbative triple excitations [CCSD(T)], the 3Lp structure is 11.9?kcal/mol more stable than the 3OO structure. This indicates that the ionization of water clusters produce the hydronium cation moiety (H₃O⁺) and the hydroxyl radical. It is interesting to note that the calculation results of the water trimer cation vary seriously depending on the calculation level. At the level of M?ller?CPlesset second-order perturbation (MP2) theory, the stability of 3OO is underestimated due to the underestimated O??O hemibonding energy. This stability is also underestimated even for the CCSD(T) single point calculations on the MP2-optimized geometry. For the 3OO structure, the MP2 and CCSD(T) calculations give closed-ring structures with a hemi-bond between two O atoms, while the DFT calculations show open-ring structures due to the overestimated O??O hemibonding energy. Thus, in order to obtain reliable stabilities and frequencies of the water trimer cation, the CCSD(T) geometry optimizations and frequency calculations are necessary. In this regard, the DFT functionals need to be improved to take into account the proper O??O hemibonding energy.     

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

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

A theoretical analysis of substituted aromatic compounds

The substituents ? CH₃, ? F, ? NO₂, ? OCH₃, and ? CH₂?CH₂ were placed at the ortho, meta, and para positions on the aromatic molecules aniline, benzaldehdye, nitrobenzene, and phenol. MMFF94, AM1, B3LYP, M06, M06‐2X, ωB97X, ωB97X‐d, and RI‐MP2 using cc‐pVDZ and cc‐pVTZ and CCSD(T) with cc‐pVDZ basis sets were used to calculate the geometries and energies of all regiomers of the molecules. Relative energies of the ortho and meta regiomers relative to the para regiomers were calculated and compared to the CCSD(T) values. A good basis set correlation between cc‐pVDZ and cc‐pVTZ was observed in RI‐MP2. Overall, RI‐MP2 gave the best correlation with the CCSD(T) results. All of the hybrid functionals showed similar accuracy and could effectively describe the intramolecular hydrogen‐bonding interactions of these compounds. The methoxy group at the para position in methoxyaniline, methoxyphenol, methoxynitrobenzene, and methoxybenzaldehyde was rotated around the phenyl‐O bond. HF, along with the cc‐pVDZ basis with the other methods, generated inaccurate energy profiles for p‐methoxyphenol. For the density functional theory methods, it was necessary to use improved grids to get smooth curves. © 2013 Wiley Periodicals, Inc.     

Electronic structure and thermochemistry for monocarbides MC,MC+ and MC− (M=Zn,Cd, Hg): CCSD(T) and DFT works

In this work, the ab-initio coupled cluster CCSD(T) method and the B3LYP, BP91W and CAM-B3LYP functional of DFT method in conjunction with the aug-cc-pVTZ-PP basis have been applied to study the group 12 monocarbides MC, MC⁺ and MC^?. The potential energy curves (PECs) for the three electronic states ³Σ^?, ⁵Σ^? and ¹Δ of the MC and the two states ²∑^- and ⁴∑^- for the MC⁺ cations and MC^? anions have been investigated. In addition, Bond distance Re, transition energy Te, vibrational frequency ω_e, ionization energy IE, electron affinity EA, dipole moment μ, dissociation energy D₀ and heat formation ΔH°f₀/ΔH°f₂₉₈, were determined for each species. The analysis of the dissociation energy for ZnC, CdC and HgC shows the decrease in the stability of the monocarbides from Zn to Hg. For ΔH°f₀/ΔH°f₂₉₈ values of MC, which are not known experimentally or theoretically, we recommend the following CCSD(T) predictions of ZnC, CdC and HgC: 181.3/178.54, 180.65/178.4 and 175.35/174.71 kcal/mol respectively. Comparing the three functionals with the CCSD(T) results, the CAM-B3LYP functional shows excellent predictive agreement for the various properties of the group 12 monocarbides.     

A Theoretical Study of the Kinetics of the Hydrogen Atom Abstraction Reactions from Cyclopropane by H,O (3P), and Cl (2P3/2) Atoms and OH Radicals

The rate constants of the H‐abstraction reactions from cyclopropane by H, O (³P), Cl (²P_3/2), and OH radicals have been calculated over the temperature range of 250?2500 K using two different levels of theory. Calculations of optimized geometrical parameters and vibrational frequencies are performed using the MP2 method combined with the cc‐pVTZ basis set and the 6–311++G(d,p) basis set. Single‐point energy calculations have been carried out with the highly correlated ab initio coupled cluster method in the space of single, double, and triple (perturbatively) electron excitations CCSD(T) using either the cc‐pVTZ, aug‐cc‐pVTZ, and aug‐cc‐pVQZ basis sets or the 6–311++G(3df,3pd) basis set. The CCSD(T) calculated potential energies have been extrapolated to the complete basis limit (CBS) limit. The Full Configuration Interaction (FCI) energies have been also estimated using the continued‐fraction approximation as proposed by Goodson (J. Chem. Phys., 2002, 116, 6948–6956). Canonical transition‐state theory combined with an Eckart tunneling correction has been used to predict the rate constants as a function of temperature using two kinetic models (direct abstraction or complex mechanism) at two levels of theory (CCSD(T)‐cf/CBS//MP2/cc‐pVTZ and CCSD(T)‐cf/6–311++G(3df,3pd)//MP2/6–311++G(d,p)). The calculated kinetic parameters are in reasonable agreement with their literature counterparts for all reactions. In the light of these trends, the use of the Pople‐style basis sets for studying the reactivity of other systems such as larger cycloalkanes or halogenated cycloalkanes is recommended because the 6–311++G(3df,3pd) basis set is less time consuming than the aug‐cc‐pVQZ basis set. Based on our calculations performed at the CCSD(T)‐cf/CBS//MP2/cc‐pVTZ level of theory, the standard enthalpy of formation at 298 K for the cyclopropyl radical has been reassessed and its value is (290.5 ± 1.6) kJ mol^?1.     

Ab initio Study of Anharmonic Force Field and Spectroscopic Constants for Germanium Dichloride

Ab initio study of the equilibrium structure, spectroscopy constants, and anharmonic force field for several isotopomers of germanium dichloride (⁷⁰GeCl₂, ⁷²GeCl₂, and ⁷⁶GeCl₂) have been carried out at the MP2 and CCSD(T) levels of theory using cc-pVTZ basis set. The calculated geometries, rotational constants, vibration-rotation interaction constants, harmonic frequencies, anharmonic constants, quartic and sextic centrifugal distortion constants, cubic and quartic force constants are compared with experimental data. For small mass differences of the Ge isotopes, the isotopic effects for germanium dichloride are much weaker. The agreements are satisfactory for these two methods, but the deviations of CCSD(T) results are slightly larger than that of MP2, because of CCSD(T)'s inadequate treatment of electron correlation in hypervalent Cl atom.     

2D Ligand ENDOR and TRIPLE resonance studies of Cu(II)-doped DTGS single crystals

The deuteron hyperfine and quadrupole coupling tensors in the bis(glycinato)-Cu(II) ((ND₂CH₂COO)₂Cu) complex in ferroelectric triglycine sulfate (DTGS) single crystals were measured by ENDOR spectroscopy. These data indicate that the molecular symmetry of the Cu complex is C₁. From TRIPLE resonance experiments the signs of the isotropic coupling constants were determined. Structural information was obtained from the principal values of the quadrupole coupling tensors of the deuterium atoms and their direction cosines. Using the relationship between the deuterium quadrupole constant and ND bond lengths, the positions of the deuterons in bis(glycinato)-Cu(II) were estimated. The negative signs of the isotropic hyperfine coupling constants were explained by spin polarization of the deuteron 1s orbitals. The values of the anisotropic hyperfine coupling constants are discussed in the framework of conventional molecular-orbital theory and can be understood quite satisfactorily.     

DFT calculations of <Superscript>14</Superscript>N, <Superscript>17</Superscript>O,and <Superscript>2</Superscript>H NQR parameters: Investigation of hydrogen bond interactions in sulfapyridine crystalline structure

DFT calculations of electric field gradient (EFG) tensors at the sites of ¹⁴N, ¹⁷O, and ²H nuclei are carried out to characterize the hydrogen bond (HB) interactions in the sulfapyridine crystal structure. One-molecule (monomer) and hydrogen-bonded hexameric cluster models of sulfapyridine are constructed according to available X-ray coordinates where the proton positions are optimized. Then, EFG tensors are calculated for both monomer and target molecule in the hexameric cluster of sulfapyridine to show the effect of HB interactions on the tensors. The calculated EFG tensors are converted to the experimentally measurable nuclear quadrupole resonance (NQR) parameters: quadrupole coupling constant (C _Q ) and asymmetry parameter (η _Q ). The results reveal different contribution of various nuclei to N-H⋯N and N-H⋯O HB interactions in the cluster where the N2 and O1 have major contributions. The computations are performed with B3LYP and B3PW91 functionals DFT method and 6-311+G* and 6-311++G** standard basis sets using the Gaussian 98 package.