Role played by the organometallic fragment on the first hyperpolarizability of iron–acetylide complexes: A TD-DFT study

The static first hyperpolarizabilities (β) for a series of both substituted thiophene-acetylide ligands and the corresponding η⁵–monocyclopentadienyliron(II) complexes were determined by density functional theory (DFT) calculations. The effect on the hyperpolarizabilities by various donor and acceptor substituents in the thiophene-acetylide ligands was studied. The nature and role of the electronic excitation contributions to the first hyperpolarizability, using time-dependent DFT (TD-DFT) calculations, are rationalized in terms of the two-level model. Our calculations show that the organometallic fragment can form a very effective push-pull system in combination with electron-withdrawing substituents in the thiophene-acetylide moiety, leading to enhanced static first hyperpolarizabilities. Also, an improvement of the magnitude of β is expected if solvation effects are taken into account.     

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.     

Dynamic (hyper)polarizabilities of the sulphur dioxide molecule: coupled cluster calculations including vibrational corrections

In this work we report results for dynamical (hyper)polarizabilities of the sulphur dioxide molecule with inclusion of vibrational corrections. The electronic contributions were computed analytically at the single and double coupled cluster level through response theories for the frequencies 0, 0.0239, 0.0428, 0.0656, 0.0720, and 0.0886 hartree. Contributions of the connected triple excitations to the dynamic electronic properties were also estimated through the multiplicative correction scheme. Vibrational corrections were calculated by means of the perturbation theoretical method. The results obtained show that the zero point vibrational correction is very small for all properties studied while the pure vibrational correction is relevant for the dc-Pockels effect, intensity dependent refractive index, and dc-Kerr effect. For these nonlinear optical processes, the pure vibrational corrections represent approximately 75%, 13%, and 6% of the corresponding electronic contributions for the higher frequencies quoted. The results presented for the polarizability are in good agreement with experimental values available in the literature. For the hyperpolarizabilities we have not obtained experimental results with precision sufficient for comparison.     

Density Functional Theory Investigation on the Second‐Order Nonlinear Optical Properties of Chlorobenzyl‐o‐Carborane Derivatives

The structures and second‐order nonlinear optical (NLO) properties of a series of chlorobenzyl‐o‐carboranes derivatives ( 1 – 12 ) containing different push‐pull groups have been studied by density functional theory (DFT) calculation. Our theoretical calculations show that the static first hyperpolarizability (β_tot) values gradually increase with increasing the π‐conjugation length and the strength of electron donor group. Especially, compound 12 exhibits the largest β_tot (62.404×10^?30 esu) by introducing tetrathiafulvalene (TTF), which is about 76 times larger than that of compound 1 containing aryl. This means that the appropriate structural modification can substantially increase the first hyperpolarizabilities of the studied compounds. For the sake of understanding the origin of these large NLO responses, the frontier molecular orbitals (FMOs), electron density difference maps (EDDMs), orbital energy and electronic transition energy of the studied compounds are analyzed. According to the two‐state model, the lower transition energy plays an important role in increasing the first hyperpolarizability values. This study may evoke possible ways to design preferable NLO materials.     

对苯二甲酸二苯酯类液晶化合物光谱和二阶非线性光学性质的理论研究

在密度泛函理论B3LYP/6-31G*水平上计算对苯二甲酸二苯酯类液晶化合物分子的几何结构、振动光谱、电子光谱和非线性光学性质, 分析讨论端接基对其光谱与非线性光学性质的影响. 结果表明, 端接基的引入对该类分子的几何结构影响不大. 烷氧基的链长对分子振动光谱的影响很小, 端基引入CN时, C＝O的伸缩振动频率蓝移9 cm^－1. TD-DFT计算表明, 最大吸收光谱源于分子中HOMO→LUMO的p→p*跃迁, 对应的最大吸收波长值在313～375 nm之间, 属于紫外区. 端接强供电子基团可以提高分子的二阶非线性光学性质.     

Spectroscopic constants and molecular properties of the X2Π and a4Σ− electronic states of the SiF radical

The potential energy curves (PECs) of the X²Π and a⁴Σ^? electronic states of the SiF radical have been studied by an ab initio quantum chemical method. The calculations have been made using the complete active space self‐consistent field (CASSCF) method, which is followed by the valence internally contracted multireference configuration interaction (MRCI) approach in combination with several correlation‐consistent basis sets. The effects on the PECs by the core‐valence correlation and relativistic corrections are included. The way to consider the relativistic correction is to use the third‐order Douglas–Kroll Hamiltonian approximation. The relativistic corrections are made at the level of cc‐pV5Z basis set. The core‐valence correlation corrections are performed using the cc‐pCV5Z basis set. To obtain more reliable results, the PECs determined by the MRCI calculations are also corrected for size‐extensivity errors by means of the Davidson modification (MRCI+Q). These PECs are extrapolated to the complete basis set limit by the total‐energy extrapolation scheme. Using these PECs, the spectroscopic parameters are determined and compared with those reported in the literature. With these PECs obtained by the MRCI+Q/CV+DK+56 calculations, the vibrational levels, inertial rotation, and centrifugal distortion constants of the first 20 vibrational state of each electronic state are calculated when the rotational quantum number J equals zero. Comparison with the Rydberg‐Klein‐Rees (RKR) data shows that the present results are reliable and accurate. The molecular constants of the X²Π and a⁴Σ^? electronic states determined by the MRCI+Q/CV+DK+56 calculations should be good prediction for future laboratory experiment. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Accurate Quantum‐Chemical Prediction of Enthalpies of Formation of Small Molecules in the Gas Phase

The coupled‐cluster approach, including single and double excitations and perturbative corrections for triple excitations, is capable of predicting molecular electronic energies and enthalpies of formation of small molecules in the gas phase with very high accuracy (specifically, with error bars less than 5 kJ mol^?1), provided that the electronic wavefunction is dominated by the Hartree–Fock configuration. This capability is illustrated by calculations on molecules containing O–H and O–F bonds, namely OH, FO, H₂O, HOF, and F₂O. To achieve this very high accuracy, it is imperative to account for electron‐correlation effects in a quantitative manner, either by using explicitly correlated two‐particle basis functions (R12 functions) or by extrapolating to the limit of a complete basis. Besides taking into account harmonic zero‐point vibrational energies, it is also necessary to account for anharmonic corrections to the zero‐point vibrational energies, to include the core orbitals into the coupled‐cluster calculations, and to account for spin–orbit corrections and scalar relativistic effects. These additional corrections constitute small but significant contributions in the range of 1–4 kJ mol^?1 to the enthalpies of formation of the aforementioned molecules. The highly accurate coupled‐cluster results, obtained by employing R12 functions and by including various corrections, are compared with standard Kohn–Sham density‐functional calculations as well as with the Gaussian‐2 and complete‐basis‐set model chemistries.     

Theoretical study of spectroscopic and molecular properties of several low‐lying electronic states of CO molecule

The potential energy curves (PECs) of eight low‐lying electronic states (X¹Σ⁺, a³Π, a′³Σ⁺, d³Δ, e³Σ^?, A¹Π, I¹Σ^?, and D¹Δ) of the carbon monoxide molecule have been studied by an ab initio quantum chemical method. The calculations have been performed using the complete active space self‐consistent field method, which is followed by the valence internally contracted multireference configuration interaction (MRCI) approach in combination with the correlation‐consistent aug‐cc‐pV5Z basis set. The effects on the PECs by the core‐valence correlation and relativistic corrections are included. The way to consider the relativistic corrections is to use the third‐order Douglas–Kroll Hamiltonian approximation at the level of a cc‐pV5Z basis set. Core‐valence correlation corrections are performed using the cc‐pCVQZ basis set. To obtain more reliable results, the PECs determined by the MRCI calculations are corrected for size‐extensivity errors by means of the Davidson modification (MRCI+Q). The spectroscopic parameters (D_e, T_e, R_e, ω_e, ω_ex_e, ω_ey_e, B_e, α_e, and γ_e) of these electronic states are calculated using these PECs. The spectroscopic parameters are compared with those reported in the literature. Using the Breit–Pauli operator, the spin–orbit coupling effect on the spectroscopic parameters is discussed for the a³Π electronic state. With the PECs obtained by the MRCI+Q/aug‐cc‐pV5Z+CV+DK calculations, the complete vibrational states of each electronic state have been determined. The vibrational manifolds have been calculated for each vibrational state of each electronic state. The vibrational level G(ν), inertial rotation constant B_ν, and centrifugal distortion constant D_ν of the first 20 vibrational states when the rotational quantum number J equals zero are reported and compared with the experimental data. Comparison with the measurements demonstrates that the present spectroscopic parameters and molecular constants determined by the MRCI+Q/aug‐cc‐pV5Z+CV+DK calculations are both reliable and accurate. © 2012 Wiley Periodicals, Inc.     

Raman Optical Activity of a Purely σ‐Bonded Helical Chromophore: (−)‐(M)‐σ‐[4]Helicene

The recent synthesis of enantiomerically pure (−)‐(M)‐σ‐[4]helicene has provided an archetype helical model system for vibrational optical activity, comparable to what π‐helicenes represent in the field of electronic optical activity. We present the first measurements and the first calculations of the Raman optical activity (ROA) of this interesting molecule. Observed and calculated ROA is large throughout the vibrational spectrum, in agreement with expectations, and spectacular effects, with Δ values close to 0.5%, occur in the 900‐cm⁻¹ region. Agreement between the experimental spectrum and the theoretical one, calculated with density‐functional theory for the vibrational part and Hartree‐Fock linear response theory for the molecular electronic tensors, is excellent, clearly the best that has been achieved to date in the field. This allows us to place confidence in the results of an analysis of Raman and ROA scattering generation in the molecule, obtained by a newly developed graphical procedure for extracting this kind of information from ab initio calculations. One finds that relative contributions made by carbon and hydrogen atoms can be comparable in size, but can also vary considerably, even between closely lying vibrations, and that, for most vibrations, the generation of ROA difference intensity is distributed rather differently than that of Raman intensity over the shape of the molecule. The sign of the ROA is, for the set of vibrations in the 900‐cm⁻¹ region, which we analyze in detail, determined by coupling terms between the two halves of the molecule, while Raman intensity is primarily generated within the two fragments, with coupling terms between them only adding to or substracting from it.     

A critical analysis of electronic density functionals for structural,energetic, dynamic,and magnetic properties of hydrogen fluoride clusters

We present extensive computational results on density functional calculations for hydrogen fluoride species (HF)_n (with 1≤n≤6) and compare them to results from other approaches and experiments, where available. Among the calculated properties we discuss equilibrium structural parameters, vibrational frequencies, electric dipole moments, IR intensities, dissociation energies, barriers for rearrangement by proton tunneling, NMR chemical shifts and spin couplings for ¹H and ¹⁹F, and magnetic susceptibilities. It is found that density functional (particularly BLYP) and even more so hybrid approaches (particularly B3LYP) provide useful results. However, we show that due to some characteristic deficiencies, these are in general not competitive with more quantitative results from large basis set MP2 calculations. The calculated magnetic properties do not indicate any “aromaticity” connected to a hypothetical electronic ring current. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 1695–1719, 1997     

A profound density functional theory study to unravel the spectroscopic and molecular properties of two Flavanols differing in α-pyrone ring position

A comprehensive theoretical model was designed for two new flavanols that have been reported from Glycosmis pentaphylla, differing in the placement of α-pyrone ring. The density functional theory (DFT) approach was utilized for computing different properties of these compounds to validate the experimental findings and stereochemical assignments. Electronic properties, geometric parameters, frontier molecular orbitals (FMOs), molecular electrostatic potential (MESP), and natural bond orbital analysis were performed for the first time at the PBE0-D3BJ/def2-TZVP level of theory for the compounds under study. The simulated vibrational frequencies for compounds 1 and 2 were computed and compared with the experimental results. nuclear magnetic resonance (NMR) (¹H and ¹³C) chemical shift values were computed at the PBE0-D3BJ/def2-TZVP/SMD_DMSO level of theory and showed a very good agreement with the experimental results for both the compounds. The electronic circular dichroism (ECD) and ultraviolet–visible (UV) spectra for both the compounds were obtained using time-dependent DFT in methanol, whose results exhibited excellent correlation with experimental data. The intermolecular interaction effect on geometric parameters, vibrational frequencies, and electronic properties were studied for the first time.     

Theoretical Study of the Substituent Effects on the Nonlinear Optical Properties of a Room‐Temperature‐Stable Organic Electride

Excess‐electron compounds can be considered as novel candidates for nonlinear optical (NLO) materials because of their large static first hyperpolarizabilities (β₀). A room‐temperature‐stable, excess‐electron compound, that is, the organic electride Na@(TriPip222), was successfully synthesized by the Dye group (J. Am. Chem. Soc. 2005 , 127, 12416). In this work, the β₀ of this electride was first evaluated to be 1.13×10⁶ au, which revealed its potential as a high‐performance NLO material. In particular, the substituent effects of different substituents on the structure, electride character, and NLO response of this electride were systemically studied for the first time by density functional theory calculations. The results revealed that the β₀ of Na@(TriPip222) could be further increased to 8.30×10⁶ au by introducing a fluoro substituent, whereas its NLO response completely disappeared if one nitryl group was introduced because the nitro‐group substitution deprived the material of its electride identity. Moreover, herein the dependence of the NLO properties on the number of substituents and their relative positions was also detected in multifluoro‐substituted Na@(TriPip222) compounds.     

Ab initio HF and DFT calculations on an organic non-linear optical material

The molecular geometric optimization, vibrational frequencies, and gauge-including atomic orbital (GIAO) ¹H and ¹³C chemical shift values of 3-[(1E)-N-ethylethanimidoyl]-4-hydroxy-6-methyl-2H-pyran-2-one have been investigated by using ab initio Hartree–Fock (HF) and density functional method (B3LYP: Becke-3-Lee–Yang–Parr) with 6–31G(d) and 6–31++G(d,p) basis sets. Also, the first hyperpolarizabilities have been calculated at the HF and B3LYP levels employing the corresponding basis sets. To understand this phenomenon in the context of molecular orbital picture, we examined the molecular HOMOs and molecular LUMOs generated via HF and B3LYP levels. The computed vibrational frequencies are used to determine the types of molecular motions associated with each of the experimental bands observed. Data of 3-[(1E)-N-ethylethanimidoyl]-4-hydroxy-6-methyl-2H-pyran-2-one display significant second-order molecular nonlinearity and provide the basis for design of efficient nonlinear optical materials.     

Molecular-beam-laser studies of the states X1Σ+ and A0+ of PbS

By using a molecular-beam apparatus, laser excitation spectra and microwave-optical double-resonance spectra were observed on the electronic states X¹Σ⁺ and A0⁺ of PbS. For the microwave spectra a resolution up to 10 kHz was achieved and microwave two-photon transitions could be detected. All information was combined into single fitting routine including data from other sources. Besides the usual Dunham parameters the fit model takes account of the breakdown of the Born-Oppenheimer approximation and the isotopic field shift. From the field shift of the electronic energy, the vibrational motion and the rotational motion the electron density as a function of the internuclear distance at the Pb nucleus is derived, which allows a more detailed discussion of the electronic structure of the molecule in combination with future quantum-chemical calculations. Additionally it is shown that the variation of the electron density along the vibrational motion at low vibrational levels can be as large as the variation for the electronic transition A0⁺ -X¹Σ⁺ in the case of PbS. The magnetic hyperfine structure of ²⁰⁷Pb is resolved in a molecule for the first time. The coupling parameter of PbS is compared with that of the isovalent molecule TlCl.     

Vibrational effects on the dynamic electric properties of hydrogen peroxide

In this work we present a method based on the perturbation theoretic approach of Bishop and co-workers [J. Chem. Phys. 95, 2646 (1991); 97, 5255 (1992); 108, 10013 (1998)] to calculate the effect of torsional motion on the polarizability and hyperpolarizabilities of hydrogen peroxide. The frequency dependence has been evaluated using the time-dependent Hartree-Fock method. The results obtained show that the zero-point vibrational averaging contributions are small compared to the corresponding electronic contributions. In the static limit the pure vibrational contributions are very large, specially for beta and gamma. These contributions are significant for the hyperpolarizabilities even in the visible region, except for the second harmonic generation and third harmonic generation processes.     

Synthesis,Crystal Structure and Density Functional Studies on 1N‐Phenyl‐3‐(2,4‐Dichlorophenyl)‐5‐(4‐Chlorophenyl)‐2‐Pyrazoline

1N‐Phenyl‐3‐(2,4‐dichlorophenyl)‐5‐(4‐chlorophenyl)‐2‐pyrazoline has been synthesized and characterized by elemental analysis, IR, UV‐Vis and X‐ray single crystal diffraction. Density functional calculations have been carried out for the title compound by using the B3LYP method with a 6‐311G** basis set. The calculated results show that the predicted geometry can reproduce well the structural parameters. The electronic absorption spectra calculated in the gas phase are better than those calculated in EtOH solvent to model the experimental electronic spectra. Natural Bond Orbital (NBO) analyses suggest that the above electronic transitions are mainly assigned to π → π* transitions. On the basis of vibrational analyses, the thermodynamic properties of the compound at different temperatures have been calculated, revealing the correlations between C⁰_{p, m}, S⁰_m, H⁰_m and temperature.     

A new hybrid DFT approach to electronic excitation and first hyperpolarizabilities of transition metal complexes

The electronic excitations and the static first hyperpolarizability of three typical transition metal (TM) aromatic carbonyl complexes, two tungsten pentacarbonyl derivatives (W(CO)₅L, L = Py and PyCHO) and one chromium tricarbonyl arene derivative (Cr(CO)₃Bz, Bz = benzene), have been theoretically studied by a variety of density functional methods. The assessments reveal that most of the conventional DFT methods including local density approximation, generalized gradient approximation (GGA), and the various kinds of hybrid exchange‐correlation (xc) methods present the first hyperpolarizabilities of these TM‐containing molecules with large deviations from the experiments. A one‐parameter hybrid xc functional is introduced by using the Perdew‐Wang 1991 gradient‐corrected correlation functional (PW91) and the Barone's‐modified PW91 exchange functional (mPW). The ratio between the exact and the density functional exchange is determined to be 0.40 by the adiabatic connection method. The application of the new hybrid functional to the three organometallic carbonyl molecules results in the satisfactory agreement between the calculated first hyperpolarizabilities and the experimental ones. The second‐order nonlinear optical properties of the three organometallic complexes are addressed to the metal‐to‐ligand charge transfers, and the extended π‐delocalization ligands benefit the enhancement of the first hyperpolarizability. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009     

Vibrational Circular Dichroism and Theoretical Study of the Conformational Equilibrium in (−)‐S‐Nicotine

We report an extensive study of the molecular and electronic structure of (?)‐S‐nicotine, to deduce the phenomenon that controls its conformational equilibrium and to solve its solution‐state conformer population. Density functional theory, ab initio, and molecular mechanics calculations were used together with vibrational circular dichroism (VCD) and Fourier transform infrared spectroscopies. Calculations and experiments in solution show that the structure and the conformational energy profile of (?)‐S‐nicotine are not strongly dependent on the medium, thus suggesting that the conformational equilibrium is dominated by hyperconjugative interactions rather than repulsive electronic effects. The analysis of the first recorded VCD spectra of (?)‐S‐nicotine confirmed the presence of two main conformers at room temperature. Our results provide further evidence of the hypersensitivity of vibrational optical activity spectroscopies to the three‐dimensional structure of chiral samples and prove their suitability for the elucidation of solution‐state conformer distribution.