On the performance of long‐range‐corrected density functional theory and reduced‐size polarized LPol‐n basis sets in computations of electric dipole (hyper)polarizabilities of π‐conjugated molecules

Static longitudinal electric dipole (hyper)polarizabilities are calculated for six medium‐sized π‐conjugated organic molecules using recently developed LPol‐n basis set family to assess their performance. Dunning's correlation‐consistent basis sets of triple‐ζ quality combined with MP2 method and supported by CCSD(T)/aug‐cc‐pVDZ results are used to obtain the reference values of analyzed properties. The same reference is used to analyze (hyper)polarizabilities predicted by selected exchange‐correlation functionals, particularly those asymptotically corrected. © 2012 Wiley Periodicals, Inc.     

Revisiting the relationship between the bond length alternation and the first hyperpolarizability with range-separated hybrid functionals

We monitor the influence of the bond length alternation (BLA) modification on the static electronic polarizability and first hyperpolarizability of two polymethineimine oligomers. Four theoretical approaches are compared: HF, PBE0, LC-omegaPBE, and MP2. For the dodecamer, both HF and PBE0 are unable to foresee even the qualitative evolution of the first hyperpolarizability when varying the BLA. On the contrary, LC-omegaPBE provides (non)linear optics properties in agreement with MP2 results, especially for the longer chains. This confirms the interest of range-separated hybrids for the computation of the (hyper)polarizabilities of extended pi-conjugated compounds.     

A comparative study of DFT and traditional ab initio methodologies on the OsO4 molecule

The performance of different conventional ab initio methodologies and density functional procedures is compared through its application to the theoretical calculation of the bond distance and harmonic vibrational frequencies of the OsO₄ molecule. The problem of the basis set is first considered, with up to nine different basis sets being tested in calculations using the hybrid Becke3LYP density functional, and the most appropriate basis set is used in the comparison of Hartree–Fock, post‐Hartree–Fock, and density functional methods. The post‐Hartree–Fock methods analyzed are MP2, CISD, and CCSD(T), and the density functionals tested are SVWN, BLYP, BPW91, and Becke3LYP. The results show that for this particular system density functional methods perform better than do HF‐based methods with the exception of CCSD(T), which gives the best overall results. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 544–551, 2000     

On the vibrational linear and nonlinear optical properties of compounds involving noble gas atoms: HXeOXeH,HXeOXeF, and FXeOXeF

The vibrational (hyper)polarizabilities of some selected Xe derivatives are studied in the context of Bishop–Kirtman perturbation theory (BKPT) and numerical finite field methodology. It was found that for this set of rare gas compounds, the static vibrational properties are quite large, in comparison to the corresponding electronic ones, especially those of the second hyperpolarizability. This also holds for the dc‐Pockels β(?ω;ω,0), Kerr γ(?ω;ω,0,0) and electric field second harmonic generation γ (?2ω;ω,ω,0) effects, although the computed nuclear relaxation (nr) vibrational contributions are smaller in magnitude than the static ones. HXeOXeH was used to study the effects of electron correlation, basis set, and geometry. Geometry effects were found to lead to noticeable changes of the vibrational and electronic second hyperpolarizability. A limited study of the effect of Xe insertion to the nr vibrational properties is also reported. Assessment of the results revealed that Xe insertion has a remarkable effect on the nr (hyper)polarizabilities. In terms of the BKPT, this is associated with a remarkable increase of the electrical and mechanical anharmonicity terms. The latter is consistent with the anharmonic character of several vibrational modes reported for rare gas compounds. © 2013 Wiley Periodicals, Inc.     

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.     

Theoretical investigation of the (hyper)polarizabilities of pyrrole homologues C4H4XH (X = N, P, As, Sb, Bi). A coupled-cluster and density functional theory study

Geometries, inversion barriers, static and dynamic electronic and vibrational dipole polarizability (alpha), and first (beta) and second (gamma) hyperpolarizability of the pyrrole homologues C(4)H(4)XH (X = N, P, As, Sb, Bi) have been calculated by Hartree-Fock, M?ller-Plesset second-order perturbation theory, coupled-cluster theory accounting for singles, doubles, and noniterative triple excitations methods, as well as density functional theory using B3LYP and PBE1PBE functionals and Sadlej's Pol and 6-311G basis sets. Relativistic effects on the heavier homologues stibole and bismole have been taken into account within effective core potential approximation. The results show that the electronic (hyper)polarizabilities monotonically increase with the atomic number of the heteroatom, consistent with the decrease in the molecular hardness. Ring planarization reduces the carbon-carbon bond length alternation of the cis-butadienic unit, enhancing the electronic polarizability values (alpha(e)) by 4-12% and the (hyper)polarizability values (and gamma(e)) by 30-90%. Pure vibrational and zero-point vibrational average contributions to the (hyper)polarizabilities have been determined within the clamped nucleus approach. In the static limit, the pure vibrational hyperpolarizabilities have a major contribution. Anharmonic corrections dominate the pure vibrational hyperpolarizabilities of pyrrole, while they are less important for the heavier homologues. Static and dynamic electronic response properties of the pyrrole homologues are comparable to or larger than the corresponding properties of the furan and cyclopentadiene homologue series.     

Electronic and vibrational contributions to first hyperpolarizability of donor-acceptor-substituted azobenzene

In this study we report on the electronic and vibrational (hyper)polarizabilities of donor-acceptor-substituted azobenzene. It is observed that both electronic and vibrational contributions to the electric dipole first hyperpolarizability of investigated photoactive molecule substantially depend on the conformation. The contributions to the nuclear relaxation first hyperpolarizability are found to be quite important in the case of two considered isomers (cis and trans). Although the double-harmonic term is found to be the largest in terms of magnitude, it is shown that the total value of the nuclear relaxation contribution to vibrational first hyperpolarizability is a result of subtle interplay of higher-order contributions. As a part of the study, we also assess the performance of long-range-corrected density functional theory in determining vibrational contributions to electric dipole (hyper)polarizabilities. In most cases, the applied long-range-corrected exchange-correlation potentials amend the drawbacks of their conventional counterparts.     

Donor–acceptor diethynylsilane oligomers: A second‐order nonlinear optical material

The interest in the study of oligomers has been motivated mainly because of their solubility in common solvents and also their capacity to be crystallized, which allowed for chemical processing leading to important applications in the area of material sciences. In this work, we carried out an investigation of polydiethynylsilane (PDES) decamers substituted with electron donor (D) and acceptor (A) groups, which is certainly of relevance, once PDES itself is known to display large third‐order optical susceptibility. Therefore, density functional theory calculations of static first hyperpolarizability (β) were performed using various functionals with the 6‐31G(d) basis set along with correlated MP2 calculation used as reference for comparison. The influence of A and D substituents on the magnitude of β was investigated by matching the acceptor (dicyanovinyl, nitrobenzene) and donor (propyl, propoxy, and phenylamine) groups attached at both ends of the oligomer. The largest β value was predicted for the derivative having the phenylamine and dicyanovinyl groups, which is around 30 times the relative value for the nonsubstituted decamer, what is a very impressive enhancement reported for the first time in the literature, strongly suggesting that disubstituted diethynylsilane decamers are potential building blocks for molecular‐based materials with second‐order nonlinear responses. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 49: 1410–1419, 2011     

Anharmonic vibrational spectroscopy calculations with electronic structure potentials: comparison of MP2 and DFT for organic molecules

Density functional theory (DFT) technique is the most commonly used approach when it comes to computation of vibrational spectra of molecular species. In this study, we compare anharmonic spectra of several organic molecules such as allene, propyne, glycine, and imidazole, computed from ab initio MP2 potentials and DFT potentials based on commonly used BLYP and B3LYP functionals. Anharmonic spectra are obtained using the direct vibrational self-consistent field (VSCF) method and its correlation-corrected extension (CC-VSCF). The results of computations are compared with available experimental data. It is shown that the most accurate vibrational frequencies are obtained with the MP2 method, followed by the DFT/B3LYP method, while DFT/BLYP results are often unsatisfactory. Contribution to the Mark S. Gordon 65th Birthday Festschrift Issue.     

Electron correlation effects on the first hyperpolarizability of push-pull π-conjugated systems

The first hyperpolarizability (β) of representative push-pull π-conjugated compounds has been calculated at several levels of approximation to assess the effects of electron correlation. First, the 6-31+G(d) basis set has been shown to give the best balance between accuracy and computational resources for a polyene linker whereas for polyyne linker, the 6-31G(d) basis set is already an optimal choice. As a result of cancellations between higher order contributions, the MP2 method turns out to be the method of choice to predict β of push-pull π-conjugated systems since it closely reproduces the values obtained with the reference CCSD(T) scheme. Moreover, the SDQ-MP4 and CCSD approaches provide rarely improved estimates over MP2 while the MP4 method does not represent an improvement over MP4-SDQ or the SCS-MP2 method, over MP2. Among density functional theory exchange-correlation functionals, LC-BLYP is reliable when characterizing the changes of first hyperpolarizability upon enlarging the π-conjugated linker or upon changing the polyyne linker into a polyene segment. Nevertheless, its reliability is very similar to what can be achieved with the Hartree-Fock method and the MP2 scheme is by far more accurate. On the other hand, the BLYP, B3LYP, and BHandHLYP functionals perform quantitatively better in a number of cases but the trends are poorly described. This is also the case of the B2-PLYP and mPW2-PLYP functionals, which are often the most accurate, though they underestimate the increase of β when going from polyyne to polyene linkers and overestimate the enhancement of β with chain length.     

CAS–SCF and density functional calculations of second hyperpolarizabilities for a nitronyl nitroxide radical

In this study, we investigated a multireference‐based nondynamical electron correlation dependence of the second hyperpolarizability, γ. We performed complete active space self‐consistent‐field (CAS–SCF) calculations including the effect of π electrons. Although the sign of γ obtained by CAS–SCF calculation was found to be negative, the magnitude of γ was found to be much larger than that at the CCSD(T) level. We also applied density functional (DF) methods with different exchange–correlation functionals (BLYP and B3LYP) to the calculation of γ. Although the B3LYP method is found to provide negative γ, its magnitude is much smaller than that at the CCSD(T) level. This feature is discussed in detail by using γ density plots. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 329–336, 1999     

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     

Calculation of the Vibrationally Resolved,Circularly Polarized Luminescence of d‐Camphorquinone and (S,S)‐trans‐β‐Hydrindanone

Circularly polarized luminescence (CPL), the differential emission of left‐ and right‐handed circularly polarized light from a molecule, is modeled by using time‐dependent density functional theory. Calculations of the CPL spectra for the first electronic excited states of d‐camphorquinone and (S,S)‐trans‐β‐hydrindanone under the Franck–Condon approximation and using various functionals are presented, as well as calculations of absorption, emission, and circular dichroism spectra. The functionals B3LYP, BHLYP, and CAM‐B3LYP are employed, along with the TZVP and aug‐cc‐pVDZ Gaussian‐type basis sets. For the lowest‐energy transitions, all functionals and basis sets perform comparably, with the long‐range‐corrected CAM‐B3LYP better reproducing the excitation energy of camphorquinone but leading to a blue shift with respect to experiment for hydrindanone. The vibrationally resolved spectra of camphorquinone are very well reproduced in terms of peak location, widths, shapes, and intensities. The spectra of hydrindanone are well reproduced in terms of overall envelope shape and width, as well as the lack of prominent vibrational structure in the emission and CPL spectra. Overall the simulated spectra compare well with experiment, and reproduce the band shapes, emission red shifts, and presence or absence of visible vibrational fine structure.     

Assessment of the OLYP and O3LYP density functionals for first-row transition metals

We have investigated the performance of the OLYP and O3LYP density functionals for predicting atomic excitation energies and ionization potentials, and bond dissociation energies, geometries, and vibrational frequencies for selected first-row transition metal compounds, including hydrides (MH) and singly charged methylene and methyl cations. The OLYP and O3LYP functionals are similar to the well-known BLYP and B3LYP functionals, respectively, but use a new optimized exchange functional (OPTX) developed by Handy and Cohen (Mol Phys 2001, 99, 403) in place of the standard B88 exchange. A previous study by us on organic reactions (J Chem Phys 2002, 117, 1331) indicated that both OLYP and O3LYP gave results for heats of reaction and barrier heights that were overall superior to those using the popular B3LYP functional. For transition metals, however, although OLYP is overall superior to BLYP for molecular calculations, it is inferior to B3LYP. O3LYP provides results for molecules of about the same quality as B3LYP. For atomic excitation and 4s ionization energies, unless relativistic effects are included, OLYP and O3LYP are clearly worse than both BLYP and B3LYP. There is thus no real incentive to use either OLYP or O3LYP in place of B3LYP for calculations involving first-row transition metals.     

Analytical nuclear excited‐state gradients for the Tamm–Dancoff approximation using uncoupled frozen‐density embedding

We report the derivation and implementation of analytical nuclear gradients for excited states using time‐dependent density functional theory using the Tamm–Dancoff approximation combined with uncoupled frozen‐density embedding using density fitting. Explicit equations are presented and discussed. The implementation is able to treat singlet as well as triplet states and functionals using the local density approximation, the generalized gradient approximation, combinations with Hartree–Fock exchange (hybrids), and range‐separated functionals such as CAM‐B3LYP. The new method is benchmarked against supermolecule calculations in two case studies: The solvatochromic shift of the (vertical) fluorescence energy of 4‐aminophthalimide on solvation, and the first local excitation of the benzonitrile dimer. Whereas for the 4‐aminophthalimide–water complex deviations of about 0.2 eV are obtained to supermolecular calculations, for the benzonitrile dimer the maximum error for adiabatic excitation energies is below 0.01 eV due to a weak coupling of the subsystems. © 2017 Wiley Periodicals, Inc.     

Electronic and vibrational linear and nonlinear polarizabilities of Li@C60 and [Li@C60]+

Electronic and vibrational nuclear relaxation (NR) contributions to the dipole (hyper)polarizabilities of the endohedral fullerene Li@C(60) and its monovalent cation [Li@C(60)](+) are calculated at the (U)B3LYP level. Many results are new, while others differ significantly from those reported previously using more approximate methods. The properties are compared with those of the corresponding hypothetical noninteracting systems with a valence electron transferred from Li to the cage. Whereas the NR contribution to the static linear polarizabilities is small in comparison with the corresponding electronic property, the opposite is true for the static hyperpolarizabilities. A relatively small, but non-negligible, NR contribution to the dc-Pockels effect is obtained in the infinite frequency approximation.     

Electronic structures of 3d-metal mononitrides

Bond distances, vibrational frequencies, electron affinities, ionization potentials, and dissociation energies of the title molecules in neutral, positively, and negatively charged ions were studied by use of density functional methods B3LYP, BLYP, BHLYP, BPW91, and B3PW91. The calculated results are compared with experiments and previous theoretical studies. It was found that the calculated properties are highly dependent on the functionals employed, in particular for the dissociation energy and vibrational frequency. For neutral species, pure density functional methods BLYP and BPW91 have relatively good performance in reproducing the experimental bond distance and vibrational frequency. For cations, hybrid exchange functional methods B3LYP and B3PW91 are good in predicting the dissociation energy. For both neutral and charged species, BHLYP tends to give smaller dissociation energy.