Quadratic response functions in the time-dependent four-component Hartree-Fock approximation

The second-order response function has been implemented in the time-dependent four-component Hartree-Fock approximation. The implementation is atomic orbital direct and formulated in terms of Fock-type matrices. It employs a quaternion symmetry scheme that provides maximum computational efficiency with consideration made to time-reversal and spatial symmetries. Calculations are presented for the electric dipole first-order hyperpolarizabilities of CsAg and CsAu in the second-harmonic generation optical process beta(-2omega;omega,omega). It is shown that relativistic corrections to property values are substantial in these cases--the orientationally averaged hyperpolarizabilities in the static limit beta(0;0,0) are overestimated in nonrelativistic calculations by 18% and 66% for CsAg and CsAu, respectively. The dispersion displays anomalies in the band gap region due to one- and two-photon resonances with nonrelativistically spin-forbidden states. Although weakly absorbing these states inflict divergences in the quadratic response function, since the response theoretical approach which is used adopts the infinite excited-state lifetime approximation. This fact calls for caution in applications where knowledge of the exact positioning of all excited states in the spectrum is unknown.     

Real-time time-dependent density functional theory approach for frequency-dependent nonlinear optical response in photonic molecules

We present ab initio calculations of frequency-dependent linear and nonlinear optical responses based on real-time time-dependent density functional theory for arbitrary photonic molecules. This approach is based on an extension of an approach previously implemented for a linear response using the electronic structure program SIESTA. Instead of calculating excited quantum states, which can be a bottleneck in frequency-space calculations, the response of large molecular systems to time-varying electric fields is calculated in real time. This method is based on the finite field approach generalized to the dynamic case. To speed the nonlinear calculations, our approach uses Gaussian enveloped quasimonochromatic external fields. We thereby obtain the frequency-dependent second harmonic generation beta(-2omega;omega,omega), the dc nonlinear rectification beta(0;-omega,omega), and the electro-optic effect beta(-omega;omega,0). The method is applied to nanoscale photonic nonlinear optical molecules, including p-nitroaniline and the FTC chromophore, i.e., 2-[3-Cyano-4-(2-{5-[2-(4-diethylamino-phenyl)-vinyl]-thiophen-2-yl}-vinyl)-5,5-dimethyl-5H-furan-2-ylidene]-malononitrile, and yields results in good agreement with experiment.     

Structures, stabilities, and electronic and optical properties of C52 fullerene, ions, and metallofullerenes

The 437 classical isomers of fullerene C52 have been studied by PM3, HCTH/3-21G, and B3LYP6-31G(d). C(2):029 with the least number of adjacent pentagons is predicted to be the most stable isomer. The investigations show that both the number of adjacent pentagons and the degree of aromaticity play important roles in the relative stabilities of fullerene isomers. To clarify the relative stabilities of the C52 isomers in a wide range of temperatures, the entropy contributions are taken into account on the basis of the Gibbs energy at the B3LYP6-31G(d) level. C(2):029 prevails in a wide temperature range. In addition, the electronic spectra and second-order hyperpolarizabilities are determined by means of ZINDO and sum-over-states model. The static second-order hyperpolarizability of C(2):029 is 51% larger than that of C60. Furthermore, intensity-dependent refractive index gamma (-omega;omega,omega,-omega) (omega=1.1653 eV) of C(2):029 is 13 times larger than that of C60. The encapsulation of Ca atom in C52 fullerene is exothermic and the metallofullerene Ca-C52 is described as Ca2+-C52(2-).     

Structures, stabilities, and electronic and optical properties of C62 fullerene isomers

The 2385 classical isomers and four nonclassical isomers of fullerene C62 have been studied by PM3, HCTH/3-21G//SVWN/STO-3G, B3LYP/6-31G(d)//HCTH/3-21G, and B3LYP/6-31G(d)//B3LYP/6-31G(d). The Cs:7mbr isomer, with a chain of four adjacent pentagons surrounding a heptagon, is predicted to be the most stable isomer, followed by C2v:4mbr which is 3.15 kcal/mol higher in energy. C2:0032 with three pairs of adjacent pentagons is the most stable isomer in the classical framework. To clarify the relative stabilities of C62 isomers at high temperatures, the entropy contributions are taken into account on the basis of the Gibbs energy at the B3LYP/6-31G(d) level. Analyses reveal that Cs:7mbr prevails in a wide temperature range. The vibrational frequencies of the five most stable C62 fullerene isomers are also predicted at the B3LYP/6-31G(d) level, and the simulated IR spectra show important differences in positions and intensities of the vibrational modes for different isomers. The nucleus-independent chemical shift and the density of states of the three most stable isomers show that the square in C2v:4mbr and the adjacent pentagons in Cs:7mbr and C2:0032 possess high chemical reactivity. In addition, the electronic spectra and second-order hyperpolarizabilities are determined by means of ZINDO and the sum-over-states mode. The intensity-dependent refractive index gamma(-omega; omega, omega, -omega) at omega = 2.3305 eV of Cs:7mbr is very large because of resonance with the external field. The second-order hyperpolarizabilities of the five most stable isomers of C62 are predicted to be larger than those of C60.     

Theory of molecular optoelectronics. IX. Calculation of χ(2) from theoretical hyperpolarizabilities for DAN

Components of the crystal quadratic susceptibility tensor χ⁽²⁾ for second-harmonic generation are calculated for the title compound, 4-(N, N-dimethylamino)-2-acetamido-nitrobenzene. Input data are the crystal structure and refractive indices and CNDO hyperpolarizabilities; two different sets of refractive indices give similar results. The calculations yield effective polarizabilities as well as both rigorous and anisotropic Lorentz local electric fields. Susceptibility components are close to 10 pm V^?1, rather smaller than those deduced experimentally and showing a weaker dependence on direction; Kleinman symmetry is mostly observed within 10%. Screened dipoledipole interactions using CNDO dipole moments amount to ?80 kJ mol^?1, implying permanent fields of 2 GV m^?1.     

Theoretical investigation of the large nonlinear optical properties of (HCN)n clusters with Li atom

Two new classes of (HCN)(n)...Li and Li...(HCN)(n) (n = 1, 2, 3) clusters with the electride characteristic are formed in theory by the metal Li atom attaching to the (HCN)(n) (n = 1, 2, 3) clusters. Because of the interaction between the Li atom and the (HCN)(n) part, the 2s valence electron of the Li atom becomes a loosely bound excess electron. Our high-level ab initio calculations show that these new clusters with the excess electron have large first hyperpolarizabilities, for example, beta(0) = -15,258 au for (HCN)...Li and beta(0) = -3401 au for Li...(HCN) at the QCISD/6-311++G(3df,3pd) level (only beta(0) = -2.8 au for HCN monomer(26)). Obviously, the excess electron from the Li atom plays a crucial role in the large first hyperpolarizabilities of these clusters. The beta(0) value of (HCN)(n)...Li (beta(0) > 10(4) au, from sigma --> pi* transition) is larger than that of Li...(HCN)(n) (beta(0) > 10(3) au, from sigma --> sigma* transition) for n = 1, 2, or 3. In addition, two interesting rules have been observed. They are that |beta(0)| decreases with lengthening of the HCN chain for (HCN)(n)...Li clusters and that |beta(0)| increases as n increases for Li...(HCN)(n) clusters. In this paper, we discuss two classes of clusters that are highly similar to the electride structure model, of which the structural characteristics are that alkali metal atoms ionize to form cations and trapped electrons under the action of other polar molecules. Thus, the investigation on the large first hyperpolarizabilities of (HCN)(n)...Li and Li...(HCN)(n) (n = 1, 2, 3) may prompt one to study the unusual nonlinear optical responses of some electrides.     

The nitrogen edge-doped effect on the static first hyperpolarizability of the supershort single-walled carbon nanotube

The nitrogen edge-doped effect on the structure, dipole moment, and first hyperpolarizability of the supershort single-walled carbon nanotube (5, 0) has been studied systematically. For the nitrogen edge-doped effect on the structure, the mean diameter on the nitrogen-doped side (D(u)) decreases as the number of doped-nitrogen (n) increases (4.044 (1) > 3.991 (2) > 3.941 (3) > 3.891 (4) > 3.844 A (5)). Significantly, the nitrogen edge-doped effects on the dipole moment and first hyperpolarizability are revealed for the first time and these new effects are dramatic for the supershort single-walled carbon nanotube (5, 0). Among the beta(0) values of these seven nitrogen-doped structures, the largest beta(0) (3155 au) is larger by almost 450 times than the very small beta(0) (7 au) of undoped structure (D(5h)). For nitrogen-doped structures, the order of the beta(0) values is 3155 (1) > 2677 (2A) approximately 2817 (2B) > 1465 (3A) approximately 1458 (3B) > 670 (4) > 254 au (5), which shows two interesting relationships between the beta(0) value and nitrogen-doped number: (1) the smaller the nitrogen-doped number, the larger the beta(0) value. (2) The structures with the same number of doped-nitrogen have almost the same beta(0) values (1465 for 3A and 1458 au for 3B). As for the frequency-dependent beta (-omega; omega, 0) and beta (-2omega; omega, omega), the dependence on the nitrogen-doped number (n) is similar to the case of static beta(0). For beta (-2omega; omega, omega) values at omega = 0.005 au are 3220 (1) > 2720 (2A) approximately = 2862 (2B) > 1480 (3A) approximately = 1477 (3B) > 676 (4) > 256 au (5). In addition, the important monotonic dependences of the beta value on the D(u) and electronic spatial extent are also observed. The new knowledge of influence the beta value will be beneficial to design high-performance nonlinear optical (NLO) materials.     

1 Pi<--X1 Sigma+ band systems of jet-cooled ScCo and YCo

Rotationally resolved resonant two-photon ionization (R2PI) spectra of ScCo and YCo are reported. The measured spectra reveal that these molecules possess ground electronic states of (1)Sigma(+) symmetry, as previously found in the isoelectronic Cr(2) and CrMo molecules. The ground state rotational constants for ScCo and YCo are B(0)(")=0.201 31(22) cm(-1) and B(0) (")=0.120 96(10) cm(-1), corresponding to ground state bond lengths of r(0) (")=1.812 1(10) A and r(0) (")=1.983 0(8) A, respectively. A single electronic band system, assigned as a (1)Pi<--X (1)Sigma(+) transition, has been identified in both molecules. In ScCo, the (1)Pi state is characterized by T(0)=15,428.8, omega(e)(')=246.7, and omega(e)(')x(e)(')=0.73 cm(-1). In YCo, the (1)Pi state has T(0)=13 951.3, omega(e)(')=231.3, and omega(e)(')x(e) (')=2.27 cm(-1). For YCo, hot bands originating from levels up to v(")=3 are observed, allowing the ground state vibrational constants omega(e)(")=369.8, omega(e)(")x(e)(")=1.47, and Delta G(12)(")=365.7 cm(-1) to be deduced. The bond energy of ScCo has been measured as 2.45 eV from the onset of predissociation in a congested vibronic spectrum. A comparison of the chemical bonding in these molecules to related molecules is presented.     

Ab initio molecular orbital investigation of the amine-alanes (CH(3))(n)H(3)(-)(n)AlNX(3) and phosphane-alanes (CH(3))(n)H(3)(-)(n)AlPX(3) (X = H, F, and Cl; n = 0-3) complexes

We report on ab initio calculations at the G2(MP2) level of the structures and Al-N(P) bond complexation energies of the (CH(3))(n)H(3)(-)(n)AlNX(3) and (CH(3))(n)H(3)(-)(n)()AlPX(3) (X = H, F, and Cl; n = 0-3) donor-acceptor complexes. For the (CH(3))(3)AlNX(3) and (CH(3))(3)AlPX(3) complexes, the C(3)(v) symmetry is found to be favored, and for the other complexes the C(s) symmetry is found to be favored. The G2(MP2) calculated complexation energies show for the amine ligands the trend NH(3) > NCl(3) > NF(3). A similar trend PH(3) approximately PCl(3) > PF(3) is predicted for the phosphane ligands. The NBO partitioning scheme shows that there is no correlation between the stability and the charge transfer.     

Ligand-controlled First Hyperpolarizabilities of a Series of Tetrahedral Iridium Clusters Ir4（CO）9L： a TDDFT Study

A series of tetrahedral iridium carbonyl clusters coordinated by systematically varied series of ligands have been studied by TDDFT method focusing on their electronic and non- linear optical properties. The clusters of Ir4（CO）12 （1）, Ir4（μ-CO）3（CO）9 （2）, Ir4（μ-L）（CO）10 （L = dppm 3, dppe 4, （Ph2P）2CHMe 5, Ph2P（CH2）3PPh2 6） and Ir4（CO）10（phen） （phen = 1,10-phen- anthroline） （7） exhibit the first static hyperpolarizabilities of medium magnitude （βtot-10×10^-30 esu）. The second order nonlinear optical response of the seven clusters increase from 0 to 23 ×10^-30 esu; the high symmetric cluster Ir4（CO）12 debases its symmetry and presents the second order nonlinear optical behavior as the coordination style of some carbonyls changes to bridge style, and then the response increases regularly with the systematical variation of the ligands. The origination of the first hyperpolarizability is discussed by the expanded orbital decomposition scheme. The results suggest the d-d electron transition from the apical iridium atom to the other three Ir atoms inside the metal skeleton, and d-πelectron transitions from metals to carbonyls are responsible for the first hyperpolarizabilities. Particularly, for cluster 7, the charge transfer from d orbitals of iridium to π＊ orbirals of phenanthroline originates the first hyperpolarizabilities.     

pi Molecular Orbital Crossing a(2)(chi)/b(1)(psi) in 1,10-Phenanthroline Derivatives. Ab Initio Calculations and EPR/ENDOR Studies of the 4,7-Diaza-1,10-phenanthroline Radical Anion and Its M(CO)(4) Complexes (M = Cr, Mo, W)

Ab initio, semiempirical, and HMO perturbation calculations were employed to assess the relative positioning of the closely situated low-lying unoccupied pi MOs a(2)(chi) and b(1)(psi) in 1,10-phenanthroline (phen) and its 3,4,7,8-tetramethyl (tmphen) and four symmetrical diaza derivatives (n,m-dap). Compared to a(2)(chi), the b(1)(psi) pi MO is distinguished by markedly higher MO coefficients at the chelating nitrogen pi centers in 1,10-positions; eventually, a higher Coulomb integral value at those positions will thus always favor the lowering of b(1) beyond a(2). Using the Coulomb integral parameter at the chelating 1,10-nitrogen pi centers as the HMO perturbation variable, the crossing of both energy levels in terms of decreasing preference for the a(2)(chi) over the b(1)(psi) orbital as the lowest unoccupied MO follows the sequence 5,6-dap > 2,9-dap > 4,7-dap > phen > 3,8-dap. The calculations reveal a(2)(chi) as the LUMO in 5,6-dap for all reasonable perturbation parameters, in agreement with previous observations for ruthenium(II) complexes which reveal a discrepancy between the lowest-lying "redox pi orbital" (a(2)) and the "optical pi MO" (b(1)) to which the most intense low-energy MLCT transition occurs. According to the HMO calculations, the situation is more ambiguous for the 4,7-dap analogue, yet EPR/ENDOR studies clearly show that the one-electron-reduced ligand and its tetracarbonylmetal(0) complexes (Cr, Mo, W) have the b(1)(psi) orbital singly occupied. Only ab initio calculations with double-zeta basis and inclusion of d polarization functions reproduced correctly the experimentally observed orbital ordering for tmphen (a(2) < b(1)) and for phen and 4,7-dap (b(1) < a(2)).     

Nonmonotonic composition dependence of vibrational phase relaxation rate in binary mixtures

We present here isothermal-isobaric N-P-T ensemble molecular dynamics simulations of vibrational phase relaxation in a model system to explore the unusual features arising due to concentration fluctuations which are absent in one component systems. The model studied consider strong attractive interaction between the dissimilar species to discourage phase separation. The model reproduces the experimentally observed nonmonotonic, nearly symmetric, composition dependence of the dephasing rate. In addition, several other experimentally observed features, such as the maximum of the frequency modulation correlation time tau(c) at mole fraction near 0.5 and the maximum rate enhancement by a factor of about 3 above the pure component value, are also reproduced. The product of mean square frequency modulation [] with tau(c) indicates that the present model is in the intermediate regime of inhomogeneous broadening. The nonmonotonic composition chi(A) dependence of the dephasing time tau(v) is found to be primarily due to the nonmonotonic chi dependence of tau(c), rather than due to a similar dependence in the amplitude of Delta omega(2)(0). The probability distribution of Delta omega shows a markedly non-Gaussian behavior at intermediate composition (chi(A) approximately =0.5). We have also calculated the composition dependence of the viscosity in order to explore the correlation between the composition dependence of viscosity eta(*) with that of tau(v) and tau(c). It is found that both the correlation time essentially follow the composition dependence of the viscosity. A mode coupling theory is presented to include the effects of composition fluctuations in binary mixture.     

Hyperpolarizabilities for the one-dimensional infinite single-electron periodic systems. II. Dipole-dipole versus current-current correlations

Based on Takayama-Lin-Liu-Maki model, analytical expressions for the third-harmonic generation, dc Kerr effect, dc-induced second-harmonic optical Kerr effect, optical Kerr effect or intensity-dependent index of refraction, and dc-electric-field-induced optical rectification are derived under the static current-current (J0J0) correlation for one-dimensional infinite chains. The results of hyperpolarizabilities under J0J0 correlation are then compared with those obtained using the dipole-dipole correlation. The comparison shows that the conventional J0J0 correlation, albeit quite successful for the linear case, is incorrect for studying the nonlinear optical properties of periodic systems.     

Reflection and polarization of light by semi-infinite turbid media: simple approximations

The paper is devoted to the investigation of the accuracy of the Rozenberg approximation for the reflection function of a semi-infinite absorbing random media. We found that this approximation can be used at y<0.5, where y= square root (1-omega (0))/(3(1-g)) . Here omega(0) is the single scattering albedo and g is the asymmetry parameter. We also propose the modified approximation, which can be used at least up to y=1-2, depending on the observation geometry.     

Rototranslational sum rules for electromagnetic hypershielding at the nuclei and related atomic Cartesian derivatives of the optical rotatory power

Two molecular properties, the nuclear electromagnetic hypershielding (psi(gamma,alphabeta) ('I)) and the gradient of the electric dipole-magnetic dipole polarizability (nabla(Igamma)G(alphabeta) (')), have been calculated using the time-dependent Hartree-Fock method. Provided the Hellmann-Feynman theorem is satisfied, these quantities are equivalent and are related through the nabla(Igamma)G(alphabeta) (')=eZ(I)psi(gamma,alphabeta) ('I) relation, where Z(I) is the atomic number of atom I and e the magnitude of the electron charge. In such a case, the determination of the nuclear electromagnetic hypershielding presents the computational advantage over the evaluation of the gradient of G(alphabeta) (') of requiring only the knowledge of nine mixed second-order derivatives of the density matrix with respect to both electric and magnetic fields (D(alpha,beta)(-omega,omega)) instead of the 3N (N is the number of atoms) derivatives of the density matrix with respect to the Cartesian coordinates (D(Igamma)). It is shown here for the H(2)O(2) molecule that very large basis sets such as the aug-cc-pVQZ or the R12 basis are required to satisfy the Hellmann-Feynman theorem. These basis set requirements have been substantiated by considering the corresponding rototranslational sum rules. The origin dependence of the rototranslational sum rules for the gradient of G(alphabeta) (') has then been theoretically described and verified for the H(2)O(2) molecule.     

On the determination of molecular hyperpolarizabilities by combining data from the Kerr effect and from electrically induced NMR line splitting

It is shown that in the calculation of the contribution to the Kerr effect in polar liquids by the hyperpolarizabilities, the effective field should be taken equal to the sum of the Lorentz field and the reaction field. Calculation of first hyperpolarizabilities on this basis by combining values of the Kerr constant with values of the alignment from electrically induced line splitting in NMR, yields for strongly polar molecules (μ ≈ 4 D) values that are smaller by an order of magnitude than those from previous calculations on the same effects, but that compare more favourably with other data.     

含碱金属分子簇体系的结构和NLO性质

采用MP2方法优化得到Li(HF)n(n=2~4)体系的三个环型结构. 使用高水平的从头算方法MP2/6-311++G(3df,3pd)计算了它们的偶极矩μ0、极化率α0和一阶超极化率β0. 得出了大的一阶超极化率的变化规律, 并揭示出额外电子是引起大一阶超极化率的主要原因.     

Conformation and intramolecular hydrogen bonding of 2-chloroacetamide as studied by microwave spectroscopy and quantum chemical calculations

The microwave spectrum of 2-chloroacetamide (ClCH2CONH2) has been investigated at room temperature in the 19-80 spectral range. Spectra of the 35ClCH2CONH2 and 37ClCH2CONH2 isotopomers of one conformer, which has a symmetry plane (Cs symmetry), were assigned. The amide group is planar, and an intramolecular hydrogen bond is formed between the chlorine atom and the nearest hydrogen atom of the amide group. The ground vibrational state, six vibrationally excited states of the torsional vibration about the CC bond, as well as the first excited state of the lowest bending mode were assigned for the 35ClCH2CONH2 isotopomer, whereas the ground vibrational state of 37ClCH2CONH2 was assigned. The CC torsional fundamental vibration has a frequency of 62(10) cm(-1), and the bending vibration has a frequency of 204(30) cm(-1). The rotational constants of the ground and of the six excited states of the CC torsion were fitted to the potential function Vz = 16.1( + 2.3) cm(-1), where z is a dimensionless parameter. This function indicates that the equilibrium conformation has Cs symmetry. Rough values of the chlorine nuclear quadrupole coupling constants were derived as chi(aa) = -47.62(52) and chi(bb) = 8.22(66) MHz for the 35Cl nucleus and chi(aa) = -34.6(10) and chi(bb) = 6.2(11) MHz for the 37Cl nucleus. Ab initio and density functional theory quantum chemical calculations have been performed at several levels of theory to evaluate the equilibrium geometry of this compound. The density functional theory calculations at the B3LYP/6-311++G(3df,2pd) and B3LYP/cc-pVTZ levels of theory as well as ab initio calculations at the MP2(F)/cc-pVTZ level predict correct lowest-energy conformation for the molecule, whereas the ab initio calculations at the QCISD(FC)/6-311G(d) and MP2(F)/6-311++G(d,p) levels predict an incorrect equilibrium conformation.     

60]Fullerene-containing polyurethane films with large ultrafast nonresonant third-order nonlinearity at telecommunication wavelengths

A significantly enhanced, ultrafast third-order optical nonlinearity at the wavelengths of 1150-1600 nm was demonstrated with cross-linked C60-containing polyurethane films using the Z-scan technique. Good-quality polymer films with a high loading of C60 derivative were obtained by cross-linking of the hydroxyl-containing C60 derivative and a triisocyanate. The positive Kerr coefficient with nonresonant nonlinear refractive index n2 falls in the range of (3.7 +/- 0.80) x 10-4 to (2.0 +/- 0.6) x 10-3 cm2/GW, and the calculated chi(3) and gamma values are up to 9.7 x 10-11 and 9.6 x 10-32 esu at 1550 nm, which are several orders of enhancement in third-order optical nonlinearity over pristine C60 in solution and 1-2 orders of enhancement over recently reported C60 derivatives and conjugated polymers.     

Correlations between bonding, size, and second hyperpolarizability (gamma) of small semiconductor clusters: ab initio study on Al(n)P(n) clusters with n=2, 3, 4, 6, and 9

A comprehensive investigation of the correlation between the second hyperpolarizability and the bonding and structural characteristics of stoichiometric aluminum phosphide clusters up to 18 atoms is presented. Several aluminum phosphide species displaying different types of configurations and bonding have been studied. The obtained ab initio and density functional finite field results suggest that the ionic AlP clusters are considerably less hyperpolarizable than the covalent bonded species. Other structural features such as symmetry, atoms' arrangement, and shape also play an important role on the hyperpolarizabilities of those species. However, they are only noticeable among clusters characterized by the same bonding patterns. Furthermore, the results of this study demonstrate that the bonding which is determined by the atoms' arrangement of a cluster has a more profound effect on the second hyperpolarizability than the cluster's composition or size. In addition, the mean second hyperpolarizability increases with the increasing number of atoms, assuming that the bonding characteristics among the clusters of increasing size are similar. On the other hand, the hyperpolarizability per atom rapidly decreases with the increase of atoms' number in the cluster and converges to values of approximately 900e(4)a(0)(4) and approximately 1300e(4)a(0)(4)E(h) (-3) at the HF/cc-pVDZ and MP2/cc-pVDZ levels of theory respectively. Lastly, this work provides the first systematic study on the hyperpolarizabilities of small aluminum phosphide clusters which, in their covalent forms, exhibit larger second order hyperpolarizabilities than the well studied small gallium arsenide clusters.