Comparative study of unscreened and screened molecular static linear polarizability in the Hartree–Fock,hybrid‐density functional,and density functional models

The sum‐over‐states (SOS) polarizabilities are calculated within approximate mean‐field electron theories such as the Hartree–Fock approximation and density functional models using the eigenvalues and orbitals obtained from the self‐consistent solution of the single‐particle equations. The SOS polarizabilities are then compared with those calculated using the finite‐field (FF) method. Three widely used mean‐field models are as follows: (1) the Hartree–Fock (HF) method, (2) the three parameter hybrid generalized gradient approximation (GGA) (B3LYP), and (3) the parameter‐free generalized gradient approximation due to Perdew–Burke–Ernzerhof (PBE). The comparison is carried out for polarizabilities of 142 molecules calculated using the 6‐311++G(d,p) basis set at the geometries optimized at the B3LYP/6‐311G** level. The results show that the SOS method almost always overestimates the FF polarizabilities in the PBE and B3LYP models. This trend is reversed in the HF method. A few exceptions to these trends are found. The mean absolute errors (MAE) in the screened (FF) and unscreened (SOS) polarizability are 0.78, 1.87, and 3.44 ų for the HF, B3LYP, and PBE‐GGA methods, respectively. Finally, a simple scheme is devised to obtain FF quality polarizability from the SOS polarizability. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

First hyperpolarizability of polymethineimine with long-range corrected functionals

Using the long-range corrected (LC) density functional theory (DFT) scheme introduced by Iikura et al. [J. Chem. Phys. 115, 3540 (2001)] and the Coulomb-attenuating model (CAM-B3LYP) of Yanai et al. [Chem. Phys. Lett. 393, 51 (2004)], we have calculated the longitudinal dipole moments and static electronic first hyperpolarizabilities of increasingly long polymehtineimine oligomers. For comparison purposes Hartree-Fock (HF), Moller-Plesset perturbation theory (MP2), and conventional pure and hybrid functionals have been considered as well. HF, generalized gradient approximation (GGA), and conventional hybrids provide too large dipole moments for long oligomers, while LC-DFT allows to reduce the discrepancy with respect to MP2 by a factor of 3. For the first hyperpolarizability, the incorrect evolution with the chain length predicted by HF is strongly worsened by BLYP, Perdew-Burke-Ernzerhof (PBE), and also by B3LYP and PBE0. On the reverse, LC-BLYP and LC-PBE hyperpolarizabilities are correctly predicted to be positive (but for the two smallest chains). Indeed, for medium and long oligomers LC hyperpolarizabilities are slightly smaller than MP2 hyperpolarizabilities, as it should be. CAM-B3LYP also strongly improves the B3LYP results, though a bit less impressively for small chain lengths. The present study demonstrates the efficiency of long-range DFT, even in very pathological cases.     

一些密度泛函方法预测电子亲和势

选取了杂化泛函B3LYP, B3PW91, O3LYP, PBE0, 以及与之相对应的GGA泛函BLYP, BPW91, OLYP和PBE, 还选取了能更好地兼顾强相互作用和弱相互作用的X3LYP泛函和在预测NMR的化学位移有较好表现的OPBE泛函, 以及两种meta-GGA泛函VSXC和TPSS, 共12种泛函, 详细地考察了这些泛函在预测EA方面的准确性.     

Comparison of aromatic NH···π, OH···π, and CH···π interactions of alanine using MP2, CCSD, and DFT methods

A comparison of the performance of various density functional methods including long‐range corrected and dispersion corrected methods [MPW1PW91, B3LYP, B3PW91, B97‐D, B1B95, MPWB1K, M06‐2X, SVWN5, ωB97XD, long‐range correction (LC)‐ωPBE, and CAM‐B3LYP using 6‐31+G(d,p) basis set] in the study of CH···π, OH···π, and NH···π interactions were done using weak complexes of neutral (A) and cationic (A⁺) forms of alanine with benzene by taking the Møller–Plesset (MP2)/6‐31+G(d,p) results as the reference. Further, the binding energies of the neutral alanine–benzene complexes were assessed at coupled cluster (CCSD)/6‐31G(d,p) method. Analysis of the molecular geometries and interaction energies at density functional theory (DFT), MP2, CCSD methods and CCSD(T) single point level reveal that MP2 is the best overall performer for noncovalent interactions giving accuracy close to CCSD method. MPWB1K fared better in interaction energy calculations than other DFT methods. In the case of M06‐2X, SVWN5, and the dispersion corrected B97‐D, the interaction energies are significantly overrated for neutral systems compared to other methods. However, for cationic systems, B97‐D yields structures and interaction energies similar to MP2 and MPWB1K methods. Among the long‐range corrected methods, LC‐ωPBE and CAM‐B3LYP methods show close agreement with MP2 values while ωB97XD energies are notably higher than MP2 values. © 2010 Wiley Periodicals, Inc. J Comput Chem 2010     

脯氨酸的构象及性质

用X3LYP法在6-311++G(d, p)和6-311++G(3df, 3pd)基组水平上对脯氨酸15种构象的几何结构、相对能量、电子结构、红外光谱、偶极矩、极化率等性质进行了研究, 并与PBE1PBE/6-311++G(d, p)的结果和文献相比较, 从而得到: (1) 的脯氨酸的15种构象中能量最低的有4种, 不同构象中存在着强弱不同的5种氢键, 其中以N…H—O氢键最强, 并存在特殊的C—H…O=C氢键. 两种方法计算的几何结构数据相近, 均与实验值吻合; (2) 在构象相对能差计算方面, X3LYP具有明显的优势, 用中等基组就可以得到与高水平从头算法和大基组相同的结果, 而PBE1PBE法计算的相对能值则相差较大; (3) 脯氨酸不同构象中偶极矩最大和极化率最小的是最稳定的构象1和2, 两种方法计算的结果一致.     

Geometry, dipole moment, polarizability and first hyperpolarizability of polymethineimine: an assessment of electron correlation contributions

We have investigated the geometries as well as the longitudinal dipole moment (micro), polarizability (alpha), and first hyperpolarizability (beta) of polymethineimine oligomers using different approaches [Hartree-Fock (HF), second-order M?ller-Plesset (MP2), and hybrid density functional theory (DFT) methods (B3LYP and PBE0)] for evaluating the geometries and the nonlinear optical properties. It turns out that (i) HF and the selected DFT methods provide the incorrect sign for beta of short and medium size oligomers. (ii) The B3LYP and PBE0 electron correlation correction are too small for micro, too large for alpha, and for some oligomer lengths, they are in the wrong direction for beta. (iii) On the contrary to polyacetylene, the hybrid-DFT geometries are in poor agreement with MP2 geometries; the former showing much smaller bond length alternations.     

Performance of six functionals (LDA, PBE, PBESOL, B3LYP, PBE0, and WC1LYP) in the simulation of vibrational and dielectric properties of crystalline compounds. The case of forsterite Mg2SiO4

The performance of six different density functionals (LDA, PBE, PBESOL, B3LYP, PBE0, and WC1LYP) in describing the infrared spectrum of forsterite, a crystalline periodic system with orthorhombic unit cell (28 atoms in the primitive cell, Pbmn space group), is investigated by using the periodic ab initio CRYSTAL09 code and an all‐electron Gaussian‐type basis set. The transverse optical (TO) branches of the 35 IR active modes are evaluated at the equilibrium geometry together with the oscillator strengths and the high‐frequency dielectric tensor ?_∞. These quantities are essential to compute the dielectric function ?(ν), and then the reflectance spectrum R(ν), which is compared with experiment. It turns out that hybrid functionals perform better than LDA and GGA, in general; that B3LYP overperforms WC1LYP and, in turn, PBE0; that PBESOL is better than PBE; that LDA is the worst performing functional among the six under study. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

A DFT conformational analysis and VCD study on methyl tetrahydrofuran-2-carboxylate

DFT calculations were performed on (S)-methyl tetrahydrofuran-2-carboxylate to facilitate the interpretation of IR and VCD spectra. The potential energy surface could not be described unambiguously using the 6-31G* basis set in combination with different density functionals including B1LYP, B3LYP, B3P86, B3PW91, B98, BHandH, BHandHLYP, MPW1PW91 and PBE1PBE. In contrast, a uniform conformational picture could be found using the cc-pVTZ basis set. Using this large basis set and the collection of nine functionals from above, the dipole and rotational strengths were calculated, and compared to experimental values which were extracted from the experimental IR and VCD spectra for (+)-(S)-methyl tetrahydrofuran-2-carboxylate. A detailed analysis on the agreement between experiment and simulated spectra was performed by assigning the experimental bands based on the harmonic fundamentals obtained for all functionals except BHandH, which performs badly over the whole line. Assessing the dipole strengths, all tested functionals perform equally well. For the rotational strengths, differences can be observed: B3LYP, B1LYP and B98 give the highest correlation with experiment, while PBE1PBE gives the lowest correlation. Comparable conclusions are obtained using a neighborhood similarity measure.     

Evaluation of DFT methods for computing the interaction energies of homomolecular and heteromolecular dimers of monosubstituted benzene

We present density functional theory (DFT) interaction energies for the sandwich and T‐shaped conformers of substituted benzene dimers. The DFT functionals studied include TPSS, HCTH407, B3LYP, and X3LYP. We also include Hartree–Fock (HF) and second‐order Møller–Plesset perturbation theory calculations (MP2), as well as calculations using a new functional, P3LYP, which includes PBE and HF exchange and LYP correlation. Although DFT methods do not explicitly account for the dispersion interactions important in the benzene–dimer interactions, we find that our new method, P3LYP, as well as HCTH407 and TPSS, match MP2 and CCSD(T) calculations much better than the hybrid methods B3LYP and X3LYP methods do. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Structures and stability of medium-sized silicon clusters. III. Reexamination of motif transition in growth pattern from Si15 to Si20

It has been established from experiments that stable medium-sized ionic clusters Si15-Si20 are prolate in shape. Density-functional theories (DFTs) also predict that nearly all low-lying neutral clusters in this size range are prolate in shape. Moreover, most of them are built onto two generic structural motifs, either the tricapped-trigonal-prism (TTP) Si9 motif or the six/six Si6Si6 (sixfold-puckered hexagonal ring Si6 plus six-atom tetragonal bipyramid Si6) motif. However, it appears that the exact location of the TTP-to-six/six motif transition is dependent on the functional (e.g., PBE or BLYP) used in the DFT calculations. Here, we present total-energy calculations for two series of clusters (one series containing six/six motif and the other containing the TTP motif) in the size range of Si16-Si20. The calculations were based on all-electron DFT methods with a medium [6-311G (2d)] and a large (cc-pVTZ) basis sets, as well as coupled-cluster single and double substitutions (including triple excitations) [CCSD(T)] method with a modest (cc-pVDZ) basis set. In the DFT calculations, two popular hybrid density functionals, the B3LYP and PBE1PBE, were selected. It is found that the B3LYP total-energy calculations slightly favor the six/six motif, whereas the PBE1PBE calculations slightly favor the TTP motif. The CCSD(T) total-energy calculations, however, show that isomers based on the six/six motif are energetically slightly favorable in the size range of Si16-Si20. Hence, the TTP-to-six/six motif transition is more likely to occur at Si16.     

Theoretical calculation of bond dissociation energies and heats of formation for nitromethane and polynitromethanes with density functional theory

The C? NO₂ bond dissociation energies (BDEs) and the heats of formation (HOFs) of nitromethane and polynitromethanes (dinitromethane, trinitromethane, and tetranitromethane) system in gas phase at 298.15 K were calculated theoretically. Density functional theory (DFT) B3LYP, B3P86, B3PW91, and PBE0 methods in combination with different basis sets were employed. It was found that the C? NO₂ bond BDEs can be improved from B3LYP to B3PW91 to B3P86 or PBE0 functional. Levels of theory employing B3P86 and PBE0 functionals were found to be sufficiently reliable without the presence of diffusion functions. As the number of NO₂ groups on the same C atom increases, the PBE0 functional performs better than the B3P86 functional. Regarding the calculated HOFs, all four functionals can yield satisfactory results with deviations of <2 kcal mol^?1 from experimental ones for CH₂(NO₂)₂ and CH(NO₂)₃, when the diffusion functions are not augmented. For the C(NO₂)₄ molecule, the large basis sets augmented with polarization functions and diffusion functions are required to yield a good result. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Performance of density functional theory in computing nonresonant vibrational (hyper)polarizabilities

A set of exchange‐correlation functionals, including BLYP, PBE0, B3LYP, BHandHLYP, CAM‐B3LYP, LC‐BLYP, and HSE, has been used to determine static and dynamic nonresonant (nuclear relaxation) vibrational (hyper)polarizabilities for a series of all‐trans polymethineimine (PMI) oligomers containing up to eight monomer units. These functionals are assessed against reference values obtained using the Møller–Plesset second‐order perturbation theory (MP2) and CCSD methods. For the smallest oligomer, CCSD(T) calculations confirm the choice of MP2 and CCSD as appropriate for assessing the density functionals. By and large, CAM‐B3LYP is the most successful, because it is best for the nuclear relaxation contribution to the static linear polarizability, intensity‐dependent refractive index second hyperpolarizability, static second hyperpolarizability, and is close to the best for the electro‐optical Pockels effect first hyperpolarizability. However, none of the functionals perform satisfactorily for all the vibrational (hyper)polarizabilities studied. In fact, in the case of electric field‐induced second harmonic generation all of them, as well as the Hartree–Fock approximation, yield the wrong sign. We have also found that the Pople 6–31+G(d) basis set is unreliable for computing nuclear relaxation (hyper)polarizabilities of PMI oligomers due to the spurious prediction of a nonplanar equilibrium geometry. © 2013 Wiley Periodicals, Inc.     

Relative energy of the high-(5T2g) and low-(1A1g) spin states of [Fe(H2O)6]2+, [Fe(NH3)6]2+, and [Fe(bpy)3]2+: CASPT2 versus density functional theory

High-level ab initio calculations using the CASPT2 method and extensive basis sets were performed on the energy differences of the high-[(5)T(2g):t(2g) (4)e(g) (2)] and low-[(1)A(1g):t(2g) (6)] spin states of the pseudo-octahedral Fe(II) complexes [Fe(H(2)O)(6)](2+), [Fe(NH(3))(6)](2+), and [Fe(bpy)(3)](2+). The results are compared to the results obtained from density functional theory calculations with the generalized gradient approximation functional BP86 and two hybrid functionals B3LYP and PBE0, and serve as a calibration for the latter methods. We find that large basis set CASPT2 calculations may provide results for the high-spin/low-spin splitting DeltaE(HL) that are accurate to within 1000 cm(-1), provided they are based on an adequately large CAS[10,12] reference wave function. The latter condition was found to be much more stringent for [Fe(bpy)(3)](2+) than for the other two complexes. Our "best" results for DeltaE(HL) (including a zero-point energy correction) are -17 690 cm(-1) for [Fe(H(2)O)(6)](2+), -8389 cm(-1) for [Fe(NH(3))(6)](2+), and 3820 cm(-1) for [Fe(bpy)(3)](2+).     

Relative energy of the high-(5T2g) and low-(1A1g) spin states of the ferrous complexes [Fe(L)(NHS4)]: CASPT2 versus density functional theory

High-level ab initio calculations using multiconfigurational perturbation theory [complete active space with second-order perturbation theory (CASPT2)] were performed on the transition energy between the lowest high-spin (corresponding to (5T2g) in Oh) and low-spin (corresponding to 1A1g in Oh) states in the series of six-coordinated Fe(II) molecules [Fe(L)(NHS4)], where NHS4 is 2,2'-bis(2-mercaptophenylthio)diethylamine dianion and L=NH3, N2H4, PMe3, CO, and NO+. The results are compared to (previous and presently obtained) results from density functional theory (DFT) calculations with four functionals, which were already shown previously by Casida and co-workers [Fouqueau et al., J. Chem. Phys. 120, 9473 (2004); Ganzenmuller et al., ibid. 122, 234321 (2005); Fouqueau et al., ibid. 122, 044110 (2005); Lawson Daku et al., ChemPhysChem 6, 1393 (2005)] to perform well for the spin-pairing problem in these and other Fe(II) complexes, i.e., OLYP, PBE0, B3LYP, and B3LYP*. Very extended basis sets were used both for the DFT and CASPT2 calculations and were shown to be necessary to obtain quantitative results with both types of method. This work presents a sequel to a previous DFT/CASPT2 study of the same property in the complexes [Fe(H2O)6]2+, [Fe(NH3)6]2+, and [Fe(bpy)3]2+ [Pierloot et al., J. Chem. Phys. 125, 124303 (2006)]. The latter work was extended with new results obtained with larger basis sets and including the OLYP functional. For all considered complexes, the CASPT2 method predicts the correct ground state spin multiplicity. Since experimental data for the actual quintet-singlet (free) energy differences are not available, the performance of the different DFT functionals was judged based on the comparison between the DFT and CASPT2 results. From this, it was concluded that the generalized gradient OLYP functional performs remarkably well for the present series of ferrous compounds, whereas the success of the three hybrid functionals varies from case to case.     

Comparison of some dispersion-corrected and traditional functionals as applied to peptides and conformations of cyclohexane derivatives

We compare the energetic and structural properties of fully optimized α-helical and antiparallel β-sheet polyalanines and the energetic differences between axial and equatorial conformations of three cyclohexane derivatives (methyl, fluoro, and chloro) as calculated using several functionals designed to treat dispersion (B97-D, ωB97x-D, M06, M06L, and M06-2X) with other traditional functionals not specifically parametrized to treat dispersion (B3LYP, X3LYP, and PBE1PBE) and with experimental results. Those functionals developed to treat dispersion significantly overestimate interaction enthalpies of folding for the α-helix and predict unreasonable structures that contain Ramachandran φ and ψ and C = O[ellipsis (horizontal)]N H-bonding angles that are out of the bounds of databases compiled the β-sheets. These structures are consistent with overestimation of the interaction energies. For the cyclohexanes, these functionals overestimate the stabilities of the axial conformation, especially when used with smaller basis sets. Their performance improves when the basis set is improved from D95?? to aug-cc-pVTZ (which would not be possible with systems as large as the peptides).     

Coupled cluster and density functional theory calculations of atomic hydrogen chemisorption on pyrene and coronene as model systems for graphene hydrogenation

Ab initio coupled cluster and density functional theory studies of atomic hydrogen addition to the central region of pyrene and coronene as molecular models for graphene hydrogenation were performed. Fully relaxed potential energy curves (PECs) were computed at the spin-unrestricted B3LYP/cc-pVDZ level of theory for the atomic hydrogen attack of a center carbon atom (site A), the midpoint of a neighboring carbon bond (site B), and the center of a central hexagon (site C). Using the B3LYP/cc-pVDZ PEC geometries, we evaluated energies at the PBE density functional, as well as ab initio restricted open-shell ROMP2, ROCCSD, and ROCCSD(T) levels of theory, employing cc-pVDZ and cc-pVTZ basis sets, and performed a G2MS extrapolation to the ROCCSD(T)/cc-pVTZ level of theory. In agreement with earlier studies, we find that only site A attack leads to chemisorption. The G2MS entrance channel barrier heights, binding energies, and PEC profiles are found to agree well with a recent ab initio multireference wave function theory study (Bonfanti et al. J. Chem. Phys.2011, 135, 164701), indicating that single-reference open-shell methods including B3LYP are sufficient for the theoretical treatment of the interaction of graphene with a single hydrogen atom.     

Computational study of static first hyperpolarizability of donor-acceptor substituted (E)-benzaldehyde phenylhydrazone

Various hybrid functionals (B3LYP, B97-2, PBE0, BMK, BH&HLYP, CAM-B3LYP, and LC-ωPBE) implemented in density functional theory were applied to give estimate of static first hyperpolarizabilty (β(0)) of (E)-benzaldehyde phenylhydrazone designated as (E)-BPH. Against those of MP2 computations as a function of the underlying density functional, good agreement was obtained with the BH&HLYP and CAM-B3LYP functionals. The LC-ωPBE functional and the B3LYP, PBE0, B97-2, and BMK functionals underestimated and overestimated β(0), respectively. The basis set effect on the calculated β(0) was also investigated. It turned out that the 6-311+G(2d,p) basis set provided excellent converged value of β(0). On the basis of the calculated results, we investigated the substituent effect on β(0) of donor-acceptor (D-A) substituted (E)-BPH systematically by using the BH&HLYP and CAM-B3LYP computations with the 6-311+G(2d,p) basis set. We proposed a Zwitterion structure to explain the calculated trend in the substituent effect and the enhanced hyperpolarizability of type II compounds (A-(E)-BPH-D) than type I compounds (D-(E)-BPH-A). Natural bonding orbital analysis carried out at BH&HLYP/6-311+G(2d,p)//B3LYP/6-31G(2df,p) level of theory substantiated the claim.     

A mixed experimental and theoretical study on chelidamate copper(II) complex with 4-methylpyrimidine

A new chelidamate complex, [Cu(chel)(H₂O)₂(mpd)] (chel = chelidamate; mpd = 4-methylpyrimidine), has been synthesized and characterized through a combination of single crystal X-ray analysis, electron paramagnetic resonance (EPR), ultraviolet-visible (UV-vis), and fourier transform infrared spectroscopy (FT-IR). The complex has six-coordinate distorted octahedral geometry around Cu(II). The theoretical vibrational frequencies and optimized geometric parameters (bond lengths and angles) have been calculated using Density Functional Theory (DFT)/B3LYP and Hartree Fock quantum chemical methods with 6-31G(d, p) basis set by Gaussian 09W software. The EPR spectrum of the compound showed that the paramagnetic center has rhombic symmetry. The EPR studies were carried out using the following unrestricted hybrid density functionals: B3LYP, CAM-B3LYP, HSEH1PBE, WB97XD, MPW1PW91, and BPV86. The UV–vis absorption spectra have been examined in different media and compared with the calculated one using TD-DFT method by applying the polarizable continuum model. Natural bond orbital property of complex has been performed by DFT/B3LYP with 6-31G (d, p) basis set.     

DFT study of the electronic and charge transfer properties of perfluoroarene–thiophene oligomers

The ground state structures of 5,5″-diperfluorophenyl-2,2′:5′,2″:5″,2‴-quaterthiophene (1), 5,5′-bis{1-[4-(thien-2-yl)perfluorophenyl]}-2,2′-dithiophene (2), 4,4′-bis[5-(2,2′-dithiophenyl)]-perfluorobiphenyl (3), 5,5″-diperfluorophenyl-2,2′:5′,2″-tertthiophene (4), 5,5′-diperfluorophenyl-2,2′-dihiophene (5), and 5,5-diperfluorophenylthiophene (6) have been optimized at the B3LYP/6-31G(d), B3LYP/6-31G(d,p), PBE0/6-31G(d), and PBE0/6-31G(d,p) level of theories. The B3LYP/6-31+G(d) and PBE0/6-31+G(d) level of theories have been applied to investigate the absorption spectra. The PBE0 functional is good to predict the C–S bond lengths while the C–F bond lengths are good envisaged with B3LYP functional. The increment of thiophene rings between two perfluoroarene rings leads to red shift in absorption spectra. The electron affinities are energetically destabilized while energetic stabilization of the radical-cation increases by decreasing the thiophene rings from four to one. The perfluoroarene rings leads to enhance the electron injection.