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.     

Charge-transfer excitations in uranyl tetrachloride ([UO2Cl4]2-): how reliable are electronic spectra from relativistic time-dependent density functional theory?

Four-component relativistic time-dependent density functional theory (TD-DFT) is used to study charge-transfer (CT) excitation energies of the uranyl molecule as well as the uranyl tetrachloride complex. Adiabatic excitation energies and vibrational frequencies of the excited states are calculated for the lower energy range of the spectrum. The results for TD-DFT with the CAM-B3LYP exchange-correlation functional for the [UO(2)Cl(4)](2-) system are in good agreement with the experimentally observed spectrum of this species and agree also rather well with other theoretical data. Use of the global hybrid B3LYP gives qualitatively correct results, while use of the BLYP functional yields results that are qualitatively wrong due to the too low CT states calculated with this functional. The applicability of the overlap diagnostic of Peach et al. (J. Chem. Phys.2008, 128, 044118) to identify such CT excitations is investigated for a wide range of vertical transitions using results obtained with three different approximate exchange-correlation functionals: BLYP, B3LYP, and CAM-B3LYP.     

Carbazole-Based Mono and Bis-styryl NLOphores: Structure Property Correlations

A detailed study of linear and nonlinear optical (NLO) properties obtained by spectroscopy and DFT computations of carbazole-based D-π-A (mono) and A-π-D-π-A (bis) extended styryl dyes is presented. Four different DFT functionals, B3LYP, MO6, BHandHLYP, and CAM-B3LYP are used for computations. The structure–property relationship is examined by correlating bond length alternation/bond order alternation with NLO properties of the dyes. The bis-carbazole styryl dyes possess a higher second-order hyperpolarizability (β) than the mono-carbazole styryl dyes. An increase in the polarity of the environment causes an increase in the first-order hyperpolarizability (β _CT or β ₀) and second-order hyperpolarizability (γ) of the mono- and bis-carbazole styryl compounds. The NLO properties calculated by the CAM-B3LYP and BHandHLYP functionals show good agreement with the spectroscopic results.     

Structural and electronic properties of polyacetylene and polyyne from hybrid and Coulomb-attenuated density functionals

The bond length alternation (BLA), the highest-occupied-lowest-unoccupied (HO-LU) orbital energy gap, and the corresponding excitation energy are determined for trans-polyacetylene (PA) and polyyne (PY) using density functional theory. Results from the Coulomb-attenuated CAM-B3LYP functional are compared with those from the conventional BHHLYP and B3LYP hybrid functionals. BLA values and HO-LU gaps are determined using both finite oligomer and infinite chain calculations, subject to periodic boundary conditions. TDDFT excitation energies are determined for the oligomers. The oligomer excitation energies and HO-LU gaps are then used, in conjunction with the infinite chain HO-LU gap, to estimate the infinite chain excitation energy. Overall, BHHLYP and CAM-B3LYP give BLA values and excitation energies that are larger and more accurate than those obtained using B3LYP. The results highlight the degree to which excitation energies can be approximated using the HO-LU gaps-at the infinite limit, this approximation works well for B3LYP, but not for the other functionals, where the HO-LU gap is significantly larger. The study provides further evidence for the high-quality theoretical predictions that can be obtained from the CAM-B3LYP functional.     

Activation enthalpies of pericyclic reactions: the performances of some recently proposed functionals

We have assessed the performances of three recently proposed functionals, RC (Ragot and Cortona in J Chem Phys 121:7671, 2004), TCA (Tognetti et al. in J Chem Phys 128:034101, 2008), and RevTCA (Tognetti et al. in Chem Phys Lett 460:536, 2008) by calculating the activation enthalpies for ten pericyclic reactions and eighteen 1,3-dipolar cycloadditions. We have found that the local functional (RC) gives results only marginally better than the local-density approximation ones, while the two GGA functionals, TCA and RevTCA, both strongly improve the results with respect to PBE. The performances of RevTCA, in particular, are not far different from those of a hybrid functional such as B3LYP.     

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).     

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.     

Calculation of electric dipole (hyper)polarizabilities by long-range-correction scheme in density functional theory: a systematic assessment for polydiacetylene and polybutatriene oligomers

The long-range correction (LC) for treating electron exchange in density functional theory, combined with the Becke-Lee-Yang-Parr (BLYP) exchange-correlation functional, was used to determine (hyper)polarizabilities of polydiacetylene/polybutatriene oligomers. In comparison with coupled-cluster calculations including single and double excitations as well as a perturbative treatment of triple excitations, our values indicate that the tendency of conventional functionals to result in a catastrophic overshoot for these properties is alleviated but not eliminated. No clear-cut preference for LC-BLYP over Hartree-Fock values is obtained. This analysis is consistent with the calculations of Sekino et al. [J. Chem. Phys. 126, 014107 (2007)] on polyacetylene and molecular hydrogen oligomers. Thus, the performance of LC-BLYP with regard to (hyper)polarizabilities of quasilinear conjugated systems is now well characterized.     

Diarylethene-dihydroazulene multimode photochrome: a theoretical spectroscopic investigation

Using Time-Dependent Density Functional Theory, we have assessed the structural, energetic and spectroscopic properties of a hybrid diarylethene-dihydroazulene multi-addressable switch synthesized by Mrozek et al. [Chem. Commun., 1999, 1487-1488]. All possible closed/open structures have been considered and the different activation barriers along each reaction path have been evaluated. The determination of the energetic profiles allowed us to pinpoint the thermally possible reactions. To simulate the electronic absorption spectra of this compact two-way four-state hybrid compound, we relied on a PCM-TD-DFT approach combined with a molecular orbital analysis. Key insights are reached and the experimental photochromic properties of this multi-component switch are rationalised. From a more methodological point of view, this work also shows that range-separated hybrid functionals (CAM-B3LYP and ωB97XD) allow to reproduce the measured spectroscopic features with a remarkable accuracy.     

High first-hyperpolarizabilities of thiobarbituric acid derivative-based donor-π-acceptor nonlinear optical-phores: Multiple theoretical investigations of substituents and conjugated bridges effect

A number of compounds including thiobarbituric acid derivative-based acceptor unit and diverse donor moieties along with two types of π-conjugated bridges have been constructed to aid in the design of the superior nonlinear optical (NLO) materials. The effect of varying the donor and bridge parts of this donor-bridge-acceptor system was analyzed in terms of structural and opto-electronic parameters such as bond length alternation and ultraviolet-visible absorption spectra. Various functionals with aug-cc-pVDZ basis set including B3LYP, PBE0, PBE38, BMK, CAM-B3LYP, and ωB97XD were employed to calculate the static and dynamic first-hyperpolarizabilities, and also the linear polarizabilities. Furthermore, the variation of the static first-hyperpolarizabilities has been explained satisfactorily in the light of the sum-over-states method and two-level model. The comprehensive study indicates that the coplanar compound D-5 with the low electronic absorption energy, strongest oscillator strength paired with the largest ground, and excited state dipole moment difference generates a dramatical increase in its static and dynamic first-hyperpolarizabilities, which would be the most worthwhile target for development as the NLO-phores.     

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.     

Communication: Bond length alternation of conjugated oligomers: Another step on the fifth rung of Perdew's ladder of functional

In this work, we present the application of the hybrid short-range density functional theory/long-range MP2 energy gradients to the bond length alternation in polymethineimine and polyacetylene conjugated oligomers. Compared to other density functional calculations, our results are quite superior, even to fourth rung functionals, usually better than MP2 and very close to the available CCSD(T) values.     

What is the best DFT functional for vibronic calculations? A comparison of the calculated vibronic structure of the S1-S0 transition of phenylacetylene with cavity ringdown band intensities

The sensitivity of vibronic calculations to electronic structure methods and basis sets is explored and compared to accurate relative intensities of the vibrational bands of phenylacetylene in the S(1)(A(1)B(2)) ← S(0)(X(1)A(1)) transition. To provide a better measure of vibrational band intensities, the spectrum was recorded by cavity ringdown absorption spectroscopy up to energies of 2000 cm(-1) above the band origin in a slit jet sample. The sample rotational temperature was estimated to be about 30 K, but the vibrational temperature was higher, permitting the assignment of many vibrational hot bands. The vibronic structure of the electronic transition was simulated using a combination of time-dependent density functional theory (TD-DFT) electronic structure codes, Franck-Condon integral calculations, and a second-order vibronic model developed previously [Johnson, P. M.; Xu, H. F.; Sears, T. J. J. Chem. Phys. 2006, 125, 164331]. The density functional theory (DFT) functionals B3LYP, CAM-B3LYP, and LC-BLYP were explored. The long-range-corrected functionals, CAM-B3LYP and LC-BLYP, produced better values for the equilibrium geometry transition moment, but overemphasized the vibronic coupling for some normal modes, while B3LYP provided better-balanced vibronic coupling but a poor equilibrium transition moment. Enlarging the basis set made very little difference. The cavity ringdown measurements show that earlier intensities derived from resonance-enhanced multiphoton ionization (REMPI) spectra have relative intensity errors.     

Effect of self-interaction error in the evaluation of the bond length alternation in trans-polyacetylene using density-functional theory

The calculation of the bond-length alternation (BLA) in trans-polyacetylene has been chosen as benchmark to emphasize the effect of the self-interaction error within density-functional theory (DFT). In particular, the BLA of increasingly long acetylene oligomers has been computed using the M?ller-Plesset wave-function method truncated at the second order and several DFT models. While local-density approximation (LDA) or generalized gradient corrected (GGA) functionals strongly underestimate the BLA, approaches including self-interaction corrections (SIC) provide significant improvements. Indeed, the simple averaged-density SIC scheme (ADSIC), recently proposed by Legrand et al. [J. Phys. B 35, 1115 (2002)], provides better results for the structure of large oligomers than the more complex approach of Krieger et al. [Phys. Rev. A 45, 101 (1992)]. The ADSIC method is particularly promising since both the exchange-correlation energy and potential are improved with respect to standard LDA/GGA using a physically appealing correction, through a different route than the more popular approach through the Hartree-Fock exchange inclusion within the hybrid functionals.     

Comparison of theoretical approaches for computing the bond length alternation of polymethineimine

Using electron-correlated wavefunction approaches and several pure and hybrid density functionals combined with three atomic basis sets, we have optimized the ground-state geometry of increasingly long polymethineimine oligomers presenting all-trans and gliding-plane symmetries. It turns out that MP2 bond length alternations (BLA) are in good agreement with higher-order electron-correlated wavefunction approaches, whereas, for both conformers, large qualitative and quantitative discrepancies between MP2 and DFT geometries have been found. Indeed, all the selected GGA, meta-GGA and hybrid functionals tend to overestimate bond length equalization in extended polymethineimine structures. On the other hand, self-interaction corrections included in the ADSIC framework provide, in this particular case, a more efficient approach to predict the BLA for medium-size oligomers.     

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.     

Validation of electronic structure methods for isomerization reactions of large organic molecules

In this work the ISOL24 database of isomerization energies of large organic molecules presented by Huenerbein et al. [Phys. Chem. Chem. Phys., 2010, 12, 6940] is updated, resulting in the new benchmark database called ISOL24/11, and this database is used to test 50 electronic model chemistries. To accomplish the update, the very expensive and highly accurate CCSD(T)-F12a/aug-cc-pVDZ method is first exploited to investigate a six-reaction subset of the 24 reactions, and by comparison of various methods with the benchmark, MCQCISD-MPW is confirmed to be of high accuracy. The final ISOL24/11 database is composed of six reaction energies calculated by CCSD(T)-F12a/aug-cc-pVDZ and 18 calculated by MCQCISD-MPW. We then tested 40 single-component density functionals (both local and hybrid), eight doubly hybrid functionals, and two other methods against ISOL24/11. It is found that the SCS-MP3/CBS method, which is used as benchmark for the original ISOL24, has an MUE of 1.68 kcal mol(-1), which is close to or larger than some of the best tested DFT methods. Using the new benchmark, we find ωB97X-D and MC3MPWB to be the best single-component and doubly hybrid functionals respectively, with PBE0-D3 and MC3MPW performing almost as well. The best single-component density functionals without molecular mechanics dispersion-like terms are M08-SO, M08-HX, M05-2X, and M06-2X. The best single-component density functionals without Hartree-Fock exchange are M06-L-D3 when MM terms are included and M06-L when they are not.