Assessment of the efficiency of long-range corrected functionals for some properties of large compounds

Using the long-range correction (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 a series of properties that are known to be poorly reproduced by standard functionals: Bond length alternation of pi-conjugated polymers, polarizabilities of delocalized chains, and electronic spectra of extended dyes. For each of these properties, we present cases in which traditional hybrid functionals do provide accurate results and cases in which they fail to reproduce the correct trends. The quality of the results is assessed with regard to experimental values and/or data arising from electron-correlated wave function approaches. It turns out that (i) both LC-DFT and CAM-B3LYP provide an accurate bond length alternation for polyacetylene and polymethineimine, although for the latter they decrease slightly too rapidly with chain length. (ii) The LC generalized gradient approximation and MP2 polarizabilities of long polyphosphazene and polymethineimine oligomers agree almost perfectly. In the same way, CAM-B3LYP corrects the major part of the B3LYP faults. (iii) LC and CAM techniques do not help in correcting the nonrealistic evolution with chain length of the absorption wavelengths of cyanine derivatives. In addition, though both schemes significantly overestimate the ground to excited state transition energy of substituted anthraquinone dyes, they provide a more consistent picture once a statistical treatment is performed than do traditional hybrid functionals.     

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.     

Metameric influences on conformational selectivity for zwitterionic pyridinium cyclopentadienide and its aza analogues. Quantum mechanical studies on linear and nonlinear optoelectronic properties

This contribution reports the structure–property correlations for few already synthesized bi-aryl types of zwitterionic molecules. Quantum mechanical methodologies like, HF, MP2, B3LYP, CAM-B3LYP, LC-ωPBE, M06-2X, and ωB97xD were used to investigate the optoelectronic properties of some interesting metameric pairs, where the molecules were bonded either through Reichardt's or Brooker's modes. Different bonding modes and inter-ring attractive forces are assigned to investigate three distinct cases (i) metameric enforcements & preferential resonance stabilizations, (ii) inter-ring hydrogen bonded stabilizations through hetero-atoms in the ring, and (iii) an amalgamation of these two forces. Computations indicate unusual structural preferences (planar vs. twisted) by the metameric pairs, and thus direct reflections of these behaviors on some of the important tensorial properties like, dipole moments, polarizabilities, hyperpolarizabilities, and so forth were observed. The metameric manipulation on structure–property correlations shown by these molecules can be utilized as useful strategies for efficient chromophore design, not only in the field of nonlinear optics, but also in other areas of research connecting to advanced functional materials for technological applications.     

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     

A theoretical study of P4O10: vibrational analysis, infrared and Raman spectra

The normal mode frequencies and the corresponding vibrational assignments of tetraphosphorus decaoxide (P4O10) in tetrahedral (Td) symmetry are examined theoretically and experimentally. The Gaussian 98 set of quantum chemistry codes at the HF/6-311G*, MP2/6-311G*, and DFT/B3LYP/6-311G* levels of theory are used. By comparison to experimental normal mode frequencies deduced by Gilliam et al. [J. Phys. Chem. B 107 (2003) 2892], Chapman [Spectrochim. Acta A, 24 (1968) 1687], Beattie et al. [J. Chem. Soc. A (1970) 449], Konings et al. [J. Mol. Spectrosc. 152 (1992) 29] and the present work, correction factors for predominant vibrational motions are determined and compared. Normal modes were decomposed into five non-redundant motions (P-O stretch, P=O stretch, P-O-P bend, P-O-P wag, and P=O wag). Standard deviations found for the HF, MP2, and DFT corrected frequencies compared to experiment are 9, 5, and 4 cm(-1), respectively. Electron distribution for selected molecular orbitals is considered.     

Anharmonic vibrational frequency shifts upon interaction of phenol+ with the open shell ligand O2. The performance of DFT methods versus MP2

Anharmonic vibrational frequency shifts of the phenol(+) O-H stretching mode upon complex formation with the open-shell ligand O(2) were computed at several DFT and MP2 levels of theory, with various basis sets, up to 6-311++G(2df,2pd). It was found that all DFT levels of theory significantly outperform the MP2 method with this respect. The best agreement with the experimental frequency shift for the hydrogen-bonded minimum on the potential energy surfaces was obtained with the HCTH/407 functional (-93.7 cm(-1) theoretical vs -86 cm(-1) experimental), which is a significant improvement over other, more standard DFT functionals (such as, e.g., B3LYP, PBE1PBE), which predict too large downshifts (-139.9 and -147.7 cm(-1), respectively). Good agreement with the experiment was also obtained with the mPW1B95 functional proposed by Truhlar et al. (-109.2 cm(-1)). We have attributed this trend due to the corrected long-range behavior of the HCTH/407 and mPW1B95 functionals, despite the fact that they have been designed primarily for other purposes. MP2 method, even with the largest basis set used, manages to reproduce only less than 50% of the experimentally detected frequency downshift for the hydrogen-bonded dimer. This was attributed to the much more significant spin contamination of the reference HF wave function (compared to DFT Kohn-Sham wave functions), which was found to be strongly dependent on the O-H stretching vibrational coordinate. All DFT levels of theory outperform MP2 in the case of computed anharmonic OH stretching frequency shifts upon ionization of the neutral phenol molecule as well. Besides the hydrogen-bonded minimum, DFT levels of theory also predict existence of two other minima, corresponding to stacked arrangement of the phenol(+) and O(2) subunits. mPW1B95 and PBE1PBE functionals predict a very slight blue shift of the phenol(+) O-H stretching mode in the case of stacked dimer with the nearly perpendicular orientation of oxygen molecule with respect to the phenolic ring, which is entirely of electrostatic origin, in agreement with the experimental observations of an additional band in the IR photodissociation spectra of phenol(+)-O(2) dimer [Patzer, A.; Knorke, H.; Langer, J.; Dopfer, O. Chem. Phys. Lett. 2008, 457, 298]. The structural features of the minima on the studied PESs were discussed in details as well, on the basis of NBO and AIM analyses.     

Nonlinear optical property calculations by the long-range-corrected coupled-perturbed Kohn-Sham method

The long-range correction (LC) scheme for the exchange functional of density-functional theory (DFT) was combined with the coupled-perturbed Kohn-Sham (CPKS) method to calculate nonlinear optical response properties. By using this LC-CPKS method, we calculated the hyperpolarizabilities of typical molecules and the dipole moments, polarizabilities, and hyperpolarizabilities of push-pull pi-conjugated systems: p-nitroaniline, 4-amino-4'-nitrostilbene, and alpha,omega-nitroaminopolyenes. It was found that the LC scheme clearly improved the calculation of these optical properties for all of these systems, which have been significantly overestimated by conventional DFTs. We therefore concluded that the long-range exchange interaction played an important role in calculating the optical properties using the DFT formalism.     

Theoretical study of the vibrational frequencies of carbon disulfide

A benchmark comparison for different computational methods and basis sets has been presented. In this study, five computational methods (Hartree–Fock (HF), MP2, B3LYP, MPW1MP91, and PBE1PBE) along with 18 basis sets have been applied to optimize the geometry of carbon disulfide (CS₂), and further calculate the vibrational frequencies of the optimized geometries. The differences between the calculated frequencies and corresponding experimental data are used to evaluate the efficiency of each combination of computational method and basis set. The comparison of frequency difference indicates that B3LYP generally gives the best prediction of frequencies for CS₂, whereas the other two density functional theory (DFT) methods, i.e., MPW1PW91 and PBE1PBE, often give parallel results. Although MP2 predicts the frequencies with accuracy almost as good as those from DFT methods, in a particular case, HF calculation outperforms MP2 as well as MPW1PW91 and PBE1PBE for prediction of the frequency of asymmetrical stretching for CS₂. © 2013 Wiley Periodicals, Inc.     

TDDFT-SOS Studies on the Polarizabilities and Second-order Hyperpolarizabilities of Zn_3O_3 II-VI Semiconductor Clusters

1 INTRODUCTION II-VI semiconductor materials with ZnO as the representative possess wide forbidden gaps and high exciton binding energy, which have paved the way for the study of exciton characters and short wave photo-conducting devices. They present wide appli- cations, such as ultraviolet laser transmitting device, piezoelectric device, optical waveguild and high efficient quantum dot luminous apparatus[1～8]. Re- cently, II-VI semiconductor cluster materials with nano-structure ha…     

TDDFT-SOS Studies on the Polarizabilities and Second-order Hyperpolarizabilities of Zn3O3 Ⅱ-Ⅵ Semiconductor Clusters

The geometrical structure of semiconductor clusters including Zn3O3 was optimized by the DFT B3LYP method. With the same basis sets, dipole moments, polarizabilities and second- order hyperpolarizabilities have been calculated and compared with the results obtained by TDDFT B3LYP method combined with sum-over-state (SOS) formula. The calculation results indicate that the dipole moments of the ground state depend on the atom radius and electronegative differences between elements and are their balance point as well. The polarizabilities of the clusters accord with the rule of the corresponding energy transformation from ground to excited state. The results predict an increase of second-order hyperpolarizabilities with increasing the distances between atoms in the clusters as well as a decrease of the polarizabilities and second-order hyperpolarizabilities in the same serial of semiconductor clusters with increasing the dipole moments of the ground states. The changes of dipole moments in ground states are inconsistent with transition moments. Spatial structure, charge transfer and other factors play an important role in composing the transition moments.     

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     

Enhanced optoelectronic properties with aromatic bridges: A computational study on N-methyl pyridinium and phenolate types of push-pull zwitterions

A series of zwitterions with varying bridges, connecting N-methyl pyridinium acceptor, with phenolate donor, are investigated using various methodologies like, HF, B3LYP, CAM-B3LYP and ωB97xD. In this systematic study effects of various mono aromatic rings as bridges, on the response properties like, the dipole moments (μ), polarizabilities (α), hyperpolarizabilities (β) and adiabatic absorptions were analyzed using CPHF and TDDFT (or TDHF) theories. Compared to many traditional bridges, as well as without a bridge, enhanced nonlinear optical (2ND order NLO) responses were observed for these aromatically bridged zwitterions (with benzene ring as bridge ~5.3 times and ~7.9 times enhanced hyperpolarizabilities were observed compared to either the ethylene bridge or without any bridge cases, respectively). Also, many significant differences and large enhancements in response properties were observed compared to our earlier works on non-zwitterionic system (~4.3 times enhanced hyperpolarizability—benzene as bridge case). For some bridge cases, 10- to 15-fold enhanced hyperpolarizabilities were observed compared to without any bridge case. This work reports a class of non-TICT chromophores, promoting bridge aromaticity control on structure–property correlation, as a suitable and efficient chromophore design strategy to create a wide range of function molecular chromophores. Also, unidirectional natures of response properties and large dipole moments can make these zwitterions suitable 1D-molecular materials for various contemporary technological applications, as poled polymer-based materials.     

Dynamic polarizabilities of polyaromatic hydrocarbons using coupled-cluster linear response theory

Coupled-cluster theory with single and double excitations is applied to the calculation of optical properties of large polyaromatic hydrocarbons. Dipole polarizabilities are reported for benzene, pyrene, and the oligoacenes sequence n=2-6. Dynamic polarizabilities were calculated on polyacences as large as pentacene for a single frequency and for benzene and pyrene at many frequencies. The basis set effect was studied for benzene using a variety of basis sets in the Pople [Theor. Chim. Acta 28, 213 (1973)] and Dunning [J. Chem. Phys. 90, 1007 (1989)] families up to aug-cc-pVQZ and the Sadlej pVTZ basis [Collect. Czech. Chem. Commun. 53, 1995 (1998)], which was used exclusively for the largest molecules. Geometries were optimized using HF, B3LYP, PBE0, and MP2 and compared to experiment to measure method dependence and the possible role of bond-length alternation. Finally, the polarizability results were compared to four common density functionals (B3LYP, BLYP, PBE0, PBE).     

Comparison of the Hartree-Fock,Møller-Plesset,and Hartree-Fock-Slater method with respect to electrostatic properties of small molecules

Summary The results of various quantum chemical calculations, the Hartree-Fock (HF) method, the Møller-Plesset perturbation theory (MP2), and the Hartree-Fock-Slater (HFS) method are compared. Atomic charges, dipole moments, topological properties of the electron density distribution and polarizabilities, and first hyperpolarizabilities are calculated. Atomic charges obtained with the HFS method are found to be very close to those calculated with the MP2 method, from which we conclude that the HFS method describes to some extent electron correlation effects. Performing an MP2 calculation after an HF calculation improves the molecular dipole moments considerably, yielding values close to the experimental ones. HFS calculations are computationally less demanding than MP2 and yield comparable results for the electron density distributions, dipole moments and polarizabilities.     

Quantum Monte Carlo calculations of the dissociation energy of the water dimer

We report diffusion quantum Monte Carlo (DMC) calculations of the equilibrium dissociation energy D(e) of the water dimer. The dissociation energy measured experimentally, D(0), can be estimated from D(e) by adding a correction for vibrational effects. Using the measured dissociation energy and the modern value of the vibrational energy Mas et al., [J. Chem. Phys. 113, 6687 (2000)] leads to D(e)=5.00+/-0.7 kcal mol(-1), although the result Curtiss et al., [J. Chem. Phys. 71, 2703 (1979)] D(e)=5.44+/-0.7 kcal mol(-1), which uses an earlier estimate of the vibrational energy, has been widely quoted. High-level coupled cluster calculations Klopper et al., [Phys. Chem. Chem. Phys. 2, 2227 (2000)] have yielded D(e)=5.02+/-0.05 kcal mol(-1). In an attempt to shed new light on this old problem, we have performed all-electron DMC calculations on the water monomer and dimer using Slater-Jastrow wave functions with both Hartree-Fock approximation (HF) and B3LYP density functional theory single-particle orbitals. We obtain equilibrium dissociation energies for the dimer of 5.02+/-0.18 kcal mol(-1) (HF orbitals) and 5.21+/-0.18 kcal mol(-1) (B3LYP orbitals), in good agreement with the coupled cluster results.     

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.     

Ab initio procedure for aqueous-phase pKa calculation: the acidity of nitrous acid

We present an ab initio procedure for accurately calculating aqueous-phase pKa values and apply it to study the acidity of nitrous acid (HNO2, or HONO). The aqueous-phase pK(a) of nitrous acid was obtained from calculated gas-phase acidities and solvation free energies via a thermodynamic cycle and the solvation model chemistry of Barone et al. (J. Chem. Phys. 1997, 107, 3210). Solvation free energies were calculated at the HF/6-31G(d) level using the dielectric-polarizable continuum and the integral equation formalism-polarizable continuum solvent models (D-PCM and IEF-PCM, respectively), with the D-PCM model yielding the most accurate pKa values. For HF free energies of solvation, significant improvements in accuracy could be made by moving to the larger 6-311++G(3df,3pd) and aug-cc-pVQZ basis sets. Solvation free energies were also calculated using the density functional theory (DFT) methods B3LYP, TPSS, PBE0, B1B95, VSXC, B98 and O3LYP, with the most accurate methods being TPSS and VSXC, which provided average errors of less than 0.11 pKa units. Solvation free energies calculated with the different DFT methods were relatively insensitive to the basis set used. Our theoretical calculations are compared with experimental results obtained using stopped flow spectrophotometry. The pKa of nitrous acid was measured as 3.16 at 25 degrees C, and the enthalpy and entropy of nitrous acid dissociation were calculated from measurements as 6.7 kJ mol(-1) and -38.4 J mol(-1) K(-1), respectively, between 25 and 45 degrees C. The UV/visible absorption spectra of the nitrite ion and nitrous acid were also examined, and molar extinction coefficients were obtained for each.     

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.