Theoretical Studies on the First Hyperpolarizabilities of One-dimensional Donor-bridge-acceptor Chromophores

The ground-state dipole moments and second-order nonlinear optical （NLO） properties of a series of one-dimensional （1D） chromophores with donor-bridge-acceptor （D-B-A） structures have been investigated by using the second-order MФller-Plesset （MP2） and density functional theory （DFT） methods with the basis set of 6-31＋G（d）. According to the calculated results, the relationship between the molecular static first hyperpolarizability （βμ） and the directions of electron transition has been summarized. In terms of the sign of βμ, these 1D organic chromophores were classified into two categories： type Ⅰ with negative βμ and type Ⅱ bearing positive βμ. The analyses show that the remarkable difference of the first hyperpolarizabilities between Ⅰ and Ⅱ chromophores is associated mainly with the electrostatic interaction between terminal groups and the transport electrons in excited states. Moreover, different from the popular viewpoint, the obtained results also show that most of this series of 1D D-B-A molecules are more charge-separated in the ground states than in the excited states. As a whole, this theoretical investigation, to some extent, can be considered as a useful reference in designing the NLO chromophores with large first hyperpolarizabilities.     

Density functional and chemical model study of the competition between methyl and hydrogen scission of propane and ��-scission of the propyl radical

In this work, we study the competence between the reactions of hydrogen and methyl scission during thermal cracking and combustion of propane, the emergence of the two isomers of the propyl radical, n-propyl and i-propyl, and their subsequent ??-scission reaction to ethene and methyl radical. The purpose of the study was to analyze the accuracy of density functional (DFT) methods as applied on this relatively well-known subset of the reactions implied in the production of propylene oxide from propane and propene. Conventional (B3LYP, B3PW91) and state-of-the-art (PBE0, M06, BMK) DFT methods were employed, and their accuracy checked against experimental data and calculations performed using model chemistries (complete basis set CBS-4M, QB3, and APNO, and G4 methods) and ab initio methods (MP2, CCSD(T) with a large 6-311 ++G(3df,2pd) basis set). The results obtained at the BMK level for the thermodynamics of the reactions are closer to experimental data than those afforded by any other DFT method and very similar actually to CBS or CCSD(T) results, even if a medium size basis set is used. Activation energies determined using two- and three-parameter Arrhenius equations are also very good, but the preexponential factors are incorrect. Tunneling and internal rotation corrections must be applied to obtain semiquantitative results.     

7,10,12顶点Fe(Ⅱ)碳硼烷夹心配合物NLO性质的DFT研究

采用密度泛函理论(DFT)CAM-B3LYP方法对系列7,10,12顶点Fe(Ⅱ)碳硼烷与1,2,4,5-Me4C6H2(dur1),1,2,3,4-Me4C5H(dur2)形成的夹心配合物的非线性光学(NLO)性质进行了计算分析.结果表明,Fe(Ⅱ)碳硼烷的顶点数和硝基的取代位置影响分子的几何构型,从而影响分子的NLO性质;Fe(Ⅱ)碳硼烷夹心配合物的偶极矩与极化率随碳硼烷的顶点数增加而增大;10顶点Fe(Ⅱ)碳硼烷分子的前线分子轨道能级差较小,其第一超极化率βtot值大于12及7顶点Fe(Ⅱ)碳硼烷分子;硝基与Fe(Ⅱ)处于对位时,其βtot值大于未取代分子;硝基与Fe(Ⅱ)处于邻位时,βtot值较未取代分子小;在此类Fe(Ⅱ)碳硼烷夹心配合物中,碳硼烷既可以作电子给体,也可以作电子受体.     

Linear optical transmission measurements and computational study of linear polarizabilities, first hyperpolarizabilities of a dinuclear iron(III) complex

The optical transmission spectral study of a dinuclear metal complex [FeL(MeOH)Cl]2 (L=N-(5-methylphenyl)-3-methoxysalicylaldimine) has been carried out. The linear optical characterization shows that this molecule has transparency in the visible range. To understand linear optical and microscopic second-order nonlinear optical (NLO) behavior of the compound, we have computed the electric dipole moment (mu) and dispersion-free first hyperpolarizabilities (beta) using Finite Field second-order M?ller-Plesset perturbation (FF MP2) procedure; and also dispersion-free linear polarizabilities (alpha), frequency-dependent linear polarizabilities within the linear optical spectrum and first hyperpolarizabilities at lambda=730-1050 and 1000-1400 nm wavelength areas using time-dependent Hartree-Fock (TDHF) method. The ab-initio calculation results reveal that the examined complex might have linear optical and microscopic NLO behavior with non-zero values.     

H3PAuR型单核Au(Ⅰ)配合物的结构和非线性光学系数的量子化学计算比较

采用量子化学ab initio和DFT中的不同方法和基组对H3PAuR型单核Au(Ⅰ)配合物结构和二阶NLO系数进行计算, 探讨不同计算方法和Au基组对计算结果产生的影响. 对计算结果分析表明, 不同计算方法对Au(Ⅰ)配合物结构和二阶NLO系数影响较大, 其中用考虑电子相关效应的DFT-B3LYP和MP2方法优化得到的Au—P配键长比用HF方法的短, 相应的二阶NLO系数比HF方法的大2倍左右; 同一计算方法下, Au基组中d轨道个数增加优化得到的Au—P配键键长减小; 随着Au基组的增大, 前线分子轨道能级差减小, 其中SDD和CEP-121G基组之间的变化更明显. 基组变化对分子二阶NLO系数的影响较小, 多数分子Au取不同基组计算的βμ值相差在10%以内.     

A comparison of quantum chemical models for calculating NMR shielding parameters in peptides: mixed basis set and ONIOM methods combined with a complete basis set extrapolation

This article compares several quantum mechanical approaches to the computation of chemical shielding tensors in peptide fragments. First, we describe the effects of basis set quality up to the complete basis set (CBS) limit and level of theory (HF, MP2, and DFT) for four different atoms in trans N-methylacetamide. For both isotropic shielding and shielding anisotropy, the MP2 results in the CBS limit show the best agreement with experiment. The HF values show quite a different tendency to MP2, and even in the CBS limit they are far from experiment for not only the isotropic shielding of carbonyl carbon but also most shielding anisotropies. In most cases, the DFT values differ systematically from MP2, and small basis-set (double- or triple-zeta) results are often fortuitously in better agreement with the experiment than the CBS ones. Second, we compare the mixed basis set and ONIOM methods, combined with CBS extrapolation, for chemical shielding calculations at a DFT level using various model peptides. From the results, it is shown that the mixed basis set method provides better results than ONIOM, compared to CBS calculations using the nonpartitioned full systems. The information studied here will be useful in guiding the selection of proper quantum chemical models, which are in a tradeoff between accuracy and cost, for shielding studies of peptides and proteins.     

Origin of near-infrared absorption and large second hyperpolarizability in oxyallyl diradicaloids: a three-state model approach

Bis(benzofuranonyl)methanolate (BM4i4i) dye and croconate dyes (derivatives of oxyallyl molecules) in general are known to have intense transitions in the near-infrared (NIR) region, indicating small transition energies and large transition dipole moments. These molecules have been reported in the literature to have very large resonant third-order nonlinear optical (NLO) susceptibilities and molecular hyperpolarizabilities (gamma). In this work we investigate using density functional theory (DFT)/ab initio/symmetry adapted cluster-configuration interaction (SAC-CI) techniques the oxyallyl substructure and attribute the NIR transition and the NLO activity to this substructure, which is common in all these molecules. Using valence bond (VB) theory, an analysis of a three-state model of this substructure is carried out. It is seen that the mixture of an intermediate diradical character and some zwitterionic character in the molecule and a large coupling between these two VB resonance forms is responsible for large gamma values. This can be used as a design principle for increasing NLO activity in oxyallyl derivatives.     

An assessment of theoretical procedures for predicting the thermochemistry and kinetics of hydrogen abstraction by methyl radical from benzene

The reaction enthalpy (298 K), barrier (0 K), and activation energy and preexponential factor (600-800 K) have been examined computationally for the abstraction of hydrogen from benzene by the methyl radical, to assess their sensitivity to the applied level of theory. The computational methods considered include high-level composite procedures, including W1, G3-RAD, G3(MP2)-RAD, and CBS-QB3, as well as conventional ab initio and density functional theory (DFT) methods, with the latter two classes employing the 6-31G(d), 6-31+G(d,p) and/or 6-311+G(3df,2p) basis sets, and including ZPVE/thermal corrections obtained from 6-31G(d) or 6-31+G(d,p) calculations. Virtually all the theoretical procedures except UMP2 are found to give geometries that are suitable for subsequent calculation of the reaction enthalpy and barrier. For the reaction enthalpy, W1, G3-RAD, and URCCSD(T) give best agreement with experiment, while the large-basis-set DFT procedures slightly underestimate the endothermicity. The reaction barrier is slightly more sensitive to the choice of basis set and/or correlation level, with URCCSD(T) and the low-cost BMK method providing values in close agreement with the benchmark G3-RAD value. Inspection of the theoretically calculated rate parameters reveals a minor dependence on the level of theory for the preexponential factor. There is more sensitivity for the activation energy, with a reasonable agreement with experiment being obtained for the G3 methods and the hybrid functionals BMK, BB1K, and MPW1K, especially in combination with the 6-311+G(3df,2p) basis set. Overall, the high-level G3-RAD composite procedure, URCCSD(T), and the cost-effective DFT methods BMK, BB1K, and MPW1K give the best results among the methods assessed for calculating the thermochemistry and kinetics of hydrogen abstraction by the methyl radical from benzene.     

Bond dissociation energies and radical stabilization energies: an assessment of contemporary theoretical procedures

Various contemporary theoretical procedures have been tested for their accuracy in predicting the bond dissociation energies (BDEs) and the radical stabilization energies (RSEs) for a test set of 22 monosubstituted methyl radicals. The procedures considered include the high-level W1, W1', CBS-QB3, ROCBS-QB3, G3(MP2)-RAD, and G3X(MP2)-RAD methods, unrestricted and restricted versions of the double-hybrid density functional theory (DFT) procedures B2-PLYP and MPW2-PLYP, and unrestricted and restricted versions of the hybrid DFT procedures BMK and MPWB1K, as well as the unrestricted DFT procedures UM05 and UM05-2X. The high-level composite procedures show very good agreement with experiment and are used to evaluate the performance of the comparatively less expensive DFT procedures. RMPWB1K and both RBMK and UBMK give very promising results for absolute BDEs, while additionally restricted and unrestricted X2-PLYP methods and UM05-2X give excellent RSE values. UM05, UB2-PLYP, UMPW2-PLYP, UM05-2X, and UMPWB1K are among the less well performing methods for BDEs, while UMPWB1K and UM05 perform less well for RSEs. The high-level theoretical results are used to recommend alternative experimental BDEs for propyne, acetaldehyde, and acetic acid.     

An evaluation of harmonic vibrational frequency scale factors

Scale factors for obtaining fundamental vibrational frequencies, low-frequency vibrational frequencies, zero-point vibrational energies (ZPVEs), and thermal contributions to enthalpy and entropy have been derived through a least-squares approach from harmonic frequencies determined at more than 100 levels of theory. Wave function procedures (HF, MP2, QCISD, QCISD(T), CCSD, and CCSD(T)) and a large and representative range of density functional theory (DFT) approaches (B3-LYP, BMK, EDF2, M05-2X, MPWB1K, O3-LYP, PBE, TPSS, etc.) have been examined in conjunction with basis sets such as 6-31G(d), 6-31+G(d,p), 6-31G(2df,p), 6-311+G(d,p), and 6-311+G(2df,p). The vibrational frequency scale factors were determined by a comparison of theoretical harmonic frequencies with the corresponding experimental fundamentals utilizing a standard set of 1066 individual vibrations. ZPVE scale factors were generally obtained from a comparison of the computed ZPVEs with experimental ZPVEs for a smaller standard set of 39 molecules, though the effect of expansion to a 48 molecule data set was also examined. In addition to evaluating the scale factors for a wide range of levels of theory, we have also probed the effect on scale factors of varying the percentage of incorporated exact exchange in hybrid DFT calculations using a modified B3-LYP functional. This has revealed a near-linear relationship between the magnitude of the scale factor and the proportion of exact exchange. Finally, we have investigated the effect of basis set size on HF, MP2, B3-LYP, and BMK scale factors by deriving values with basis sets ranging from 6-31G(d) up to 6-311++G(3df,3pd) as well as with basis sets in the cc-pVnZ and aug-cc-pVnZ series and with the TZV2P basis.     

A sum-over-state scheme of analysis of hyperpolarizabilities and its application to spiroconjugated molecular system

The static first and second hyperpolarizabilities of a number of spiromolecules with varying degree of polarity have been calculated at the HF and MP2 level using the 6-31+G* basis set and the B3LYP/6-31+G* optimized geometry. The variation of mean second hyperpolarizability in these molecular systems has been explained in terms of the ground state dipole moment, mean linear polarizability and second-order polarizability. A number of relationships among these quantities have been derived in the framework of the sum-over-state scheme and the generalized Thomas–Kuhn sum rule. The spiroconjugation results in the significant increase of the mean polarizability. The appreciable enhancement of first hyperpolarizability due to the spiroconjugation between two dipolar monomer units has been accounted for the rather significant increase of the mean polarizability tensor and the ground state dipole moment. The relatively larger value of the average second hyperpolarizability of the spiroconjugated molecules compared to that of the corresponding monomers arises from the rather significant increase of the nonaxial component γ _xxyy . The replacement of spirocarbon by spirosilicon results in the enhancement of the cubic polarizability manifold. The donor–acceptor substituted spirocompounds are predicted to be the superior third-order nonlinear optical (NLO) phores. The nature of π-conjugation in the monomer units around the spirocenter shows a strong modulation of the NLO properties of spirocompounds. The influence of electron correlation on the NLO properties at the MP2 level has been found to be rather significant.     

Systematic study of the structure-property relationship of a series of ferrocenyl nonlinear optical chromophores

A series of novel nonlinear optical (NLO) chromophores 1-4 incorporating the ferrocenyl (Fc) group as an electron donor and 2-dicyanomethylene-3-cyano-4-methyl-2,5-dihydrofuran (TCF) derivatives as electron acceptors are presented. The use of a constant Fc donor and varied acceptors and bridges makes it possible to systematically determine the contribution of the conjugated bridge and the acceptor strength to chromophore nonlinear optical activity. The X-ray crystal structures of all four chromophores allow for the systematic investigation of the structure-property relationship for this class of molecules. For example, the crystal structures reveal that both cyclopentadienyl groups in the ferrocenyl donor contribute to the electron donating ability. The first-order hyperpolarizabilities beta of these chromophores, measured by hyper-Rayleigh scattering (HRS) relative to p-nitroaniline are reported. These beta values are compared to those calculated by density functional theory (DFT). The excellent agreement between the theoretical and experimental beta values demonstrates that a linear relation exists between the hyperpolarizability and the bond length alternation. An electrooptic coefficient, r(33), of approximately 25 pm/V at 1300 nm, for compound 4, incorporated into a polymer matrix, is competitive with organic chromophores. Moreover, this r(33) is more than 30 times larger than the previously reported value for an organometallic chromophore in a poled polymer matrix. This work not only underscores the potential for Fc donor moieties, which have been underutilized, but also demonstrates that experimental characterization and theoretical simulations are now congruent, viable methods for assessing potential performance of NLO materials.     

Accurate calculation of the heats of formation for large main group compounds with spin-component scaled MP2 methods

Three MP2-type electron correlation treatments and standard density functional theory (DFT) approaches are used to predict the heats of formation for a wide variety of different molecules. The SCF and MP2 calculations are performed efficiently using the resolution-of-the-identity (RI) approximation such that large basis set (i.e., polarized valence quadruple-zeta quality) treatments become routinely possible for systems with 50-100 atoms. An atom equivalent scheme that corrects the calculated atomic energies is applied to extract the "real" accuracy of the methods for chemically relevant problems. It is found that the spin-component-scaled MP2 method (SCS-MP2, J. Chem. Phys, 2003, 118, 9095) performs best and provides chemical accuracy (MAD of 1.18 kcal/mol) for a G2/97 test set of molecules. The computationally more economical SOS-MP2 variant, which retains only the opposite-spin part of the correlation energy, is slightly less accurate (MAD of 1.36 kcal/mol) than SCS-MP2. Both spin-component-scaled MP2 treatments perform significantly better than standard MP2 (MAD of 1.77 kcal/mol) and DFT-B3LYP (MAD of 2.12 kcal/mol). These conclusions are supported by results obtained for a second test set of complex systems containing 70 molecules, including charged, strained, polyhalogenated, hypervalent, and large unsaturated species (e.g. C60). For this set, DFT-B3LYP performs badly (MAD of 8.6 kcal/mol) with many errors >10-20 kcal/mol while the spin-component-scaled MP2 methods are still very accurate (MAD of 2.8 and 3.7 kcal/mol, respectively). DFT-B3LYP shows an obvious tendency to underestimate molecular stability as the system size increases. Out of six density functionals tested, the hybrid functional PBE0 performs best. All in all, the SCS-MP2 method, together with large AO basis sets, clearly outperforms current DFT approaches and seems to be the most accurate quantum chemical model that routinely can predict the thermodynamic properties of large main group compounds.     

Development of calculation and analysis methods for the dynamic first hyperpolarizability based on the ab initio molecular orbital-quantum master equation method

We develop novel calculation and analysis methods for the dynamic first hyperpolarizabilities β [the second-order nonlinear optical (NLO) properties at the molecular level] in the second-harmonic generation based on the quantum master equation method combined with the ab initio molecular orbital (MO) configuration interaction method. As examples, we have evaluated off-resonant dynamic β values of donor (NH(2))- and/or acceptor (NO(2))-substituted benzenes using these methods, which are shown to reproduce those by the conventional summation-over-states method well. The spatial contributions of electrons to the dynamic β of these systems are also analyzed using the dynamic β density and its partition into the MO contributions. The present results demonstrate the advantage of these methods in unraveling the mechanism of dynamic NLO properties and in building the structure-dynamic NLO property relationships of real molecules.     

Trends in R-X bond dissociation energies (R = Me, Et, i-Pr, t-Bu; X = H, CH3, OCH3, OH, F): a surprising shortcoming of density functional theory

The performance of a variety of high-level composite procedures, as well as lower-cost density functional theory (DFT)- and second-order perturbation theory (MP2)-based methods, for the prediction of absolute and relative R-X bond dissociation energies (BDEs) was examined for R = Me, Et, i-Pr and t-Bu, and X = H, CH(3), OCH(3), OH and F. The methods considered include the high-level G3(MP2)-RAD and G3-RAD procedures, a variety of pure and hybrid DFT methods (B-LYP, B3-LYP, B3-P86, KMLYP, B1B95, MPW1PW91, MPW1B95, BB1K, MPW1K, MPWB1K and BMK), standard restricted (open-shell) MP2 (RMP2), and two recently introduced variants of MP2, namely spin-component-scaled MP2 (SCS-MP2) and scaled-opposite-spin MP2 (SOS-MP2). The high-level composite procedures show very good agreement with experiment and are used to evaluate the performance of the lower-level DFT- and MP2-based procedures. The best DFT methods (KMLYP and particularly BMK) provide very reasonable predictions for the absolute heats of formation and R-X BDEs for the systems studied. However, all of the DFT methods overestimate the stabilizing effect on BDEs in going from R = Me to R = t-Bu, leading in some cases to incorrect qualitative behavior. In contrast, the MP2-based methods generally show larger errors (than the best DFT methods) in the absolute heats of formation and BDEs, but better behavior for the relative BDEs, although they do tend to underestimate the stabilizing effect on BDEs in going from R = Me to R = t-Bu. The potentially less computationally expensive SOS-MP2 method offers particular promise as a reliable method that might be applicable to larger systems.     

Theoretical study of static electric properties of benzothiazole containing push–pull systems as potential candidates for NLO materials

The dipole moments μ, static polarizabilities , and first hyperpolarizabilities β _vec of benzothiazole based push–pull chromophores have been theoretically investigated by means of SCF-HF and DFT (B3LYP, B3PW91) methods with cc-pVDZ basis sets at geometries optimized with 3-21G basis sets. The main attention has been paid to hyperpolarizability β _vec as a microscopic quantity directly linked with the nonlinear optical (NLO) response of materials with the aim to choose the most suitable candidate(s) for NLO materials from the set of 24 molecules. The 4-dimethylamino-4′-nitrostilbene (DANS) has also been included as a reference compound. The influence of various structural modifications of benzothiazole containing chromophores on μ,, and β _vec has been studied. These modifications involve the variation in unsaturated chain length connecting the aromatic units, different positions of electron withdrawing NO₂ and CN group attached to four possible positions in benzothiazole fragment, addition of the second NO₂ group, and the replacement of benzene by five-membered heteroaromatic rings (pyrrole, furan, thiophene) at N(CH₃)₂ site. The structural parameters, frontier orbitals and relative stabilities of these systems are also reported. The DFT scheme exaggerates the magnitude as well as the chain length dependence of β _vec with respect to the HF results. Both B3LYP and B3PW91 functionals give very close results. The DFT optimized structures are characterized by larger delocalization, planarity, and polarization of substituents. The best candidates for NLO materials have been identified from the studied series based on the β _vec values.     

Comparison of some representative density functional theory and wave function theory methods for the studies of amino acids

Energies of different conformers of 22 amino acid molecules and their protonated and deprotonated species were calculated by some density functional theory (DFT; SVWN, B3LYP, B3PW91, MPWB1K, BHandHLYP) and wave function theory (WFT; HF, MP2) methods with the 6-311++G(d,p) basis set to obtain the relative conformer energies, vertical electron detachment energies, deprotonation energies, and proton affinities. Taking the CCSD/6-311++G(d,p) results as the references, the performances of the tested DFT and WFT methods for amino acids with various intramolecular hydrogen bonds were determined. The BHandHLYP method was the best overall performer among the tested DFT methods, and its accuracy was even better than that of the more expensive MP2 method. The computational dependencies of the five DFT methods and the HF and MP2 methods on the basis sets were further examined with the 6-31G(d,p), 6-311++G(d,p), aug-cc-pVDZ, 6-311++G(2df,p), and aug-cc-pVTZ basis sets. The differences between the small and large basis set results have decreased quickly for the hybrid generalized gradient approximation (GGA) methods. The basis set convergence of the MP2 results has been, however, very slow. Considering both the cost and the accuracy, the BHandHLYP functional with the 6-311++G(d,p) basis set is the best choice for the amino acid systems that are rich in hydrogen bonds.