Density functional theory study on the first hyperpolarizabilities of organoimido derivatives of hexamolybdates

The first hyperpolarizabilities and origin of nonlinear optical (NLO) properties of arylimido molybdate derivatives have been investigated by density functional theory (DFT). The molecular orbital character analysis reveals that organoimido-to-polyanion charge transfer may be responsible for the NLO properties of this kind of molybdate derivatives. The NLO study shows intra-ion charge transfer is helpful to increase the first hyperpolarizability of arylimido molybdate derivatives. The lengthening of organoimido pi-conjugation enhances the betavec value. System 4 has the largest betavec value at the static electronic field, 1.238 x 10(-27)esu. Orbital analysis shows that the degree of charge transfer between polyanion cluster and organic segment was increased when the second organoimido polyanion was introduced. The present investigation provides important insight into NLO origin and properties of polyanion arylimido molybdate derivatives.     

Energy decomposition analysis based on a block-localized wavefunction and multistate density functional theory

An interaction energy decomposition analysis method based on the block-localized wavefunction (BLW-ED) approach is described. The first main feature of the BLW-ED method is that it combines concepts of valence bond and molecular orbital theories such that the intermediate and physically intuitive electron-localized states are variationally optimized by self-consistent field calculations. Furthermore, the block-localization scheme can be used both in wave function theory and in density functional theory, providing a useful tool to gain insights on intermolecular interactions that would otherwise be difficult to obtain using the delocalized Kohn-Sham DFT. These features allow broad applications of the BLW method to energy decomposition (BLW-ED) analysis for intermolecular interactions. In this perspective, we outline theoretical aspects of the BLW-ED method, and illustrate its applications in hydrogen-bonding and π-cation intermolecular interactions as well as metal-carbonyl complexes. Future prospects on the development of a multistate density functional theory (MSDFT) are presented, making use of block-localized electronic states as the basis configurations.     

Applicability of hybrid density functional theory methods to calculation of molecular hyperpolarizability

The donor/acceptor (D/A) substituted pi-conjugated organic molecules possess extremely fast nonlinear optical (NLO) response time that is purely electronic in origin. This makes them promising candidates for optoelectronic applications. In the present study, we utilized four hybrid density functionals (B3LYP, B97-2, PBE0, BMK), Hartree-Fock, and second order Moller-Plesset correlation energy correction, truncated at second-order (MP2) methods with different basis sets to estimate molecular first hyperpolarizability (beta) of D/A-substituted benzenes and stilbenes (D=OMe, OH, NMe(2), NH(2); A=NO(2), CN). The results of density functional theory (DFT) calculations are compared to those of MP2 method and to the experimental data. We addressed the following questions: (1) the accurate techniques to compare calculated results to each other and to experiment, (2) the choice of the basis set, (3) the effect of molecular planarity, and (4) the choice of the method. Comparison of the absolute values of hyperpolarizabilities obtained computationally and experimentally is complicated by the ambiguities in conventions and reference values used by different experimental groups. A much more tangible way is to compare the ratios of beta's for two (or more) given molecules of interest that were calculated at the same level of theory and measured at the same laboratory using the same conventions and reference values. Coincidentally, it is the relative hyperpolarizabilities rather than absolute ones that are of importance in the rational molecular design of effective NLO materials. This design includes prediction of the most promising candidates from particular homologous series, which are to be synthesized and used for further investigation. In order to accomplish this goal, semiquantitative level of accuracy is usually sufficient. Augmentation of the basis set with polarization and diffuse functions changes beta by 20%; however, further extension of the basis set does not have significant effect. Thus, we recommend 6-31+G(*) basis set. We also show that the use of planar geometry constraints for the molecules, which can somewhat deviate from planarity in the gas phase, leads to sufficient accuracy (with an error less than 10%) of predicted values. For all the molecules studied, MP2 values are in better agreement with experiment, while DFT hybrid methods overestimate beta values. BMK functional gives the best agreement with experiment, with systematic overestimation close to the factor of 1.4. We propose to use the scaled BMK results for prediction of molecular hyperpolarizability at semiquantitative level of accuracy.     

Synthesis and properties of conjugated oligoyne-centered π-extended tetrathiafulvalene analogues and related macromolecular systems

Alkynyl-substituted phenyldithiafulvenes have been found to act as versatile building blocks for the construction of π-conjugated molecular rods, shape-persistent macrocycles (SPMs), and conducting polymers. Through Cu(I)-catalyzed alkynyl homocoupling, a series of linear-shaped π-extended tetrathiafulvalene analogues (exTTFs) carrying conjugated oligoynes (ranging from diyne to hexayne) as the central π-bridge were readily prepared. The solid-state properties and reactivities of diyne- and tetrayne-centered exTTFs were characterized by X-ray crystallography and differential scanning calorimetry (DSC), while the electronic properties of the oligoyne-exTTFs were elucidated by UV-vis absorption spectroscopy and density functional theory (DFT) calculations. Cyclic voltammetric analysis showed that the terminal phenyldithiafulvene groups of the oligyne-exTTFs could undergo oxidative coupling to form tetrathiafulvalene vinylogue (TTFV)-linked polymer wires. Through a different synthetic route involving oxidative dimerization and Pd/Cu-catalyzed alkynyl homocoupling, the acetylenic phenyldithiafulvene precursors led to shape-persistent macrocycles where the formation of trimeric macrocycles was particularly favored due to the small ring strain incurred. Finally, spectroelectrochemical studies on these oligoyne and TTF hybrid materials disclosed electrochromic and molecular redox-controlled switching properties applicable to molecular electronic and optoelectronic devices.     

Electronic,optical, and charge transport properties of A-π-A electron acceptors for organic solar cells: Impact of anti-aromatic π structures

Anti-aromatization and isomerization are found to be an effective way to tune the optoelectronic properties of A-π-A electron acceptors for organic photovoltaics.     

Exact-exchange density functional theory for hyperpolarizabilities

Time-dependent density functional theory (TDDFT) employing the exact-exchange functional (TDDFTx) has been formulated using the optimized effective potential method for the beta static hyperpolarizabilities, where it reduces to coupled-perturbed Kohn-Sham theory. A diagrammatic technique is used to take the functional derivatives for the derivation of the adiabatic second kernel, which is required for the analytical calculation of the beta static hyperpolarizabilities with DFT. The derived formulas have been implemented using Gaussian basis sets. The structure of the adiabatic exact-exchange second kernel is described and numerical examples are presented. It is shown that no current DFT functional satisfies the correct properties of the second kernel. Not surprisingly, TDDFTx, which corrects the self-interaction error in standard DFT methods and has the correct long-range behavior, provides results close to those of time-dependent Hartree-Fock in the static limit.     

Theoretical investigations of the equol molecule: semi-empirical and density functional theory calculations

The structural and electronic properties of the equol molecule, an estrogenic isoflavone, have been investigated theoretically by performing semi-empirical self-consistent field molecular orbital and density functional theory calculations. The geometry of the system has been optimized at the level of AM1 method and the electronic properties have been calculated at the level of B3LYP functional.     

Inverse sodium hydride: density functional theory study of the large nonlinear optical properties

"Inverse sodium hydride" (AdzH(+)Na-) is an alkalide compound synthesized in recent experiments containing the unusual charge distribution H+ and Na- (inverse charge state). The new class of compounds interests scientists to investigate their especial structures and properties. In this paper, the structures of three alkalides compounds, (Me)3NH(+)Na-, AdzH(+)Na-, and AdzLi(+)Na-, have been obtained in theory. Especially, the structure of AdzLi(+)Na- is still researched by experimental scientists. We investigated the NLO properties of the alkalides complexes for the first time and found that inverse sodium hydride AdzH(+)Na- has a considerably large NLO response beta0 = 5.7675 x 10(4) au by density functional theory (DFT). To understand the essential features of the large NLO properties, four related systems have been also calculated. Their first hyperpolarizabilities are beta0 = 7.357 x 10(3) au for (Me)3NH(+)Na-, beta0 = 3.9 au for (Me)3NH+, beta0 = 1.10 x 10(2) au for (Me)3NH(+)Cl-, and beta0 = 6.20681 x 10(5) au for AdzLi(+)Na-, respectively. By comparing, we found that, first, the Na- anion plays a crucial role in the considerably large first hyperpolarizability of inverse sodium hydride and, second, the first hyperpolarizability of inverse sodium hydride increases with the charge value of the sodium anion. The above results are useful for designing potential NLO materials.     

Tunable third-order NLO properties of acene derivatives with molecular structural modification

The substitution of heteroatoms and the expansion of π-conjugated units have significant effects on the photoelectric properties of polycyclic aromatic hydrocarbons (PAHs). In this study, based on the experimental molecule PBC, 10 acene derivatives containing the pyrrole group were designed by three strategies: (1) changing the connection position of the pyrrole group, (2) exchanging the position of the N atom, and (3) increasing the length of the π-linker. Density functional theory (DFT) was used to optimize the molecular geometric structure. Time-dependent density functional theory (TD-DFT) was used to calculate the relevant parameters of the excited states. The results show that both of the pyrrole group and the N atom in the para-position, and the addition of the π-linker can reduce the energy gap, cause redshift of the linear absorption peak, and increase the two photon absorption (TPA) cross-section. The analyses of the charge density difference (CDD) and the charge-transfer matrix (CTM) proved that the electron transfer is mainly concentrated in the π-linker. Moreover, the participation of the multi-ring skeleton on both sides decreases gradually with the increase of the length of the π-linker. The length of the π-linker changes the dominant transition channel and intramolecular charge-transfer (ICT) characteristics of TPA, thus affecting the transition dipole moments and nonlinear absorption properties. The second hyperpolarizability of the designed molecule PBI5-p5 is also significantly superior to that of similar materials reported. It is expected that the above molecular design strategies and comprehensive analysis of nonlinear optical (NLO) properties could provide theoretical support for the research on acene derivatives.     

Characterization of the temporary anion states on perfluoroalkanes via stabilized Koopmans' theorem in long-range corrected density functional theory

The stabilized Koopmans' theorem (SKT) in long-range corrected density functional theory is used to characterize the temporary anion states of perfluoro-n-alkanes (n-PFAs) from C(2) to C(5), and perfluorocycloalkanes (c-PFAs) from C(3) to C(4). In this approach, stabilization is accomplished by varying the exponents of appropriate diffuse functions. The energies of temporary anion states are then identified by investigating the relationship between the resultant eigenvalues and scale parameter. The characteristics of resonance orbitals are also examined. For the lowest unfilled orbitals of perfluoroalkanes, results indicate that they are mainly from the π-bonding interactions between all neighboring C atoms. In addition, their energies decrease as the sizes of the perfluoroalkanes increase. Moreover, the energies of the c-C(3)F(6)/c-C(4)F(8) are lower than those of the corresponding n-C(3)F(8)/n-C(4)F(10). When compared with experimental data, our SKT calculations can yield conformable results. Thus, this SKT approach can provide more information on the resonance states of perfluoroalkanes.     

Application of the stabilization method to temporary anion states of CH3CN, CH3NC, CH3SCN, and CH3NCS in density functional theory with asymptotically corrected potentials

In this paper, density functional theory (DFT) with asymptotically corrected potentials is used to investigate CH(3)CN, CH(3)NC, CH(3)SCN, and CH(3)NCS molecules. For the energies of σ* and π* temporary anion states, the stabilized Koopmans' theorem (S-KT) using long-range correction functional and stabilized Koopmans-based (S-KB) approximation using local functional, are adopted. The stabilization procedure is accomplished by varying the exponents of appropriate diffuse functions. Results indicate that the calculations based on asymptotically corrected density functionals can yield better energy results of temporary anion states over conventional DFT methods.     

Lithium adsorption on graphite from density functional theory calculations

The structural, energetic, and electronic properties of the Li/graphite system are studied through density functional theory (DFT) calculations using both the local spin density approximation (LSDA), and the gradient-corrected Perdew-Burke-Ernzerhof (PBE) approximation to the exchange-correlation energy. The calculations were performed using plane waves basis, and the electron-core interactions are described using pseudopotentials. We consider a disperse phase of the adsorbate comprising one Li atom for each 16 graphite surface cells, in a slab geometry. The close contact between the Li nucleus and the graphene plane results in a relatively large binding energy (larger than 1.1 eV). A detailed analysis of the electronic charge distribution, density difference distribution, and band structures indicates that one valence electron is entirely transferred from the atom to the surface, which gives rise to a strong interaction between the resulting lithium ion and the cloud of pi electrons in the substrate. We show that it is possible to explain the differences in the binding of Li, Na, and K adatoms on graphite considering the properties of the corresponding cation/aromatic complexes.     

Vibrational spectroscopic and density functional theory studies of chloranil-imidazole interaction

The present work reports vibrational spectra and density functional theory calculations for chloranil, imidazole and their complexes. The experimentally observed infrared and Raman bands have been assigned with the help of calculated vibrational frequencies and potential energy distribution analysis. Some bands of chloranil and imidazole have been found to shift on the complex formation due to partial electronic charge transfer from imidazole to chloranil. The charge transfer between these molecules is also corroborated by the electronic absorption spectroscopy and calculations. The theoretical values of the interaction energy of various possible chloranil-imidazole interactions suggest that the two molecules interact preferably via N and H atoms of imidazole and CO group of chloranil with their molecular planes almost perpendicular to each other.     

PyCDFT: A Python package for constrained density functional theory

We present PyCDFT, a Python package to compute diabatic states using constrained density functional theory (CDFT). PyCDFT provides an object-oriented, customizable implementation of CDFT, and allows for both single-point self-consistent-field calculations and geometry optimizations. PyCDFT is designed to interface with existing density functional theory (DFT) codes to perform CDFT calculations where constraint potentials are added to the Kohn–Sham Hamiltonian. Here, we demonstrate the use of PyCDFT by performing calculations with a massively parallel first-principles molecular dynamics code, Qbox, and we benchmark its accuracy by computing the electronic coupling between diabatic states for a set of organic molecules. We show that PyCDFT yields results in agreement with existing implementations and is a robust and flexible package for performing CDFT calculations. The program is available at https://dx.doi.org/10.5281/zenodo.3821097 .     

Calculation of origin-independent optical rotation tensor components in approximate time-dependent density functional theory

We outline an implementation of the origin-independent optical rotation tensor, which includes electric dipole-magnetic dipole and electric dipole-electric quadrupole polarizability. The method is based on approximate time-dependent density functional theory. We utilize time-periodic magnetic-field-dependent basis functions as well as a modified velocity-gauge formulation of dynamic polarizability tensors in order to obtain a gauge-origin independence. To ensure gauge-origin independence of the results within a given numerical accuracy, density fit coefficient derivatives are employed. A damping constant has been introduced into the linear response equations to treat both resonance and nonresonance regions of optical activity. We present calculations for trans-2,3-dimethyloxirane and derivatives thereof as well as calculations for androst-4,17-dien-3-one. In the Appendix, we derive the equivalence between the common-gauge origin and gauge-including atomic orbitals formulations for the optical rotation tensor in time-dependent DFT.     

二芳基氨(硼)-π-碳硼烷三元化合物的二阶非线性光学性质的理论研究

采用密度泛函理论(DFT)方法对二芳基氨(硼)-π-十二顶点碳硼烷三元化合物的结构及二阶非线性光学(NLO)性质进行计算.结果表明,化合物共轭桥长度及二芳基氨(硼)对化合物偶极矩的影响较小.随着分子共轭桥的增长,分子的电子空间范围R2增大,从而使极化率和第一超极化率增大.通过分析化合物的电子光谱和对应的分子轨道组成可知,分子中电荷转移主要发生在二芳基氨(硼)和π-桥之间,碳硼烷的贡献较少.二芳基氨和二芳基硼的供电子能力差异可以调节分子的二阶NLO响应.     

Red shifting of absorption maxima of phenothiazine based dyes by incorporating electron-deficient thiadiazole derivatives as π-spacer

This study was carried out to design phenothiazine based dyes by incorporating electron-deficient thiadiazole derivatives as π-spacer. Density functional theory and time-dependent density functional theory calculations of the geometries, electronic structures and absorption spectra of the dyes before and after binding to titanium oxide were carried out. Effects of the electron-deficient units on the spectra and electrochemical properties have been investigated. Compared with the reference compound CS1A, Dyes 1–4 display remarkably enhanced spectral responses in the red portion of the solar spectrum. The newly designed dyes demonstrate desirable energetic and spectroscopic parameters, and may lead to efficient metal-free organic dye sensitizers for DSSCs.     

Time-dependent density functional theory gradients in the Amsterdam density functional package: geometry optimizations of spin-flip excitations

An implementation of time-dependent density functional theory (TDDFT) energy gradients into the Amsterdam density functional theory program package (ADF) is described. The special challenges presented by Slater-type orbitals in quantum chemical calculation are outlined with particular emphasis on details that are important for TDDFT gradients. Equations for the gradients of spin-flip TDDFT excitation energies are derived. Example calculations utilizing the new implementation are presented. The results of standard calculations agree well with previous results. It is shown that starting from a triplet reference, spin-flip TDDFT can successfully optimize the geometry of the four lowest singlet states of CH₂ and three other isovalent species. Spin-flip TDDFT is used to calculate the potential energy curve of the breaking of the C?CC bond of ethane. The curve obtained is superior to that from a restricted density functional theory calculation, while at the same time the problems with spin contamination exhibited by unrestricted density functional theory calculations are avoided.     

General excitations in time-dependent density functional theory

A general framework within time-dependent density functional theory is presented for the calculation of excitations to states of arbitrary multiplicity in molecular systems with a non-singlet ground state. The proposed approach combines generalized orbital excitation operators designed to generate excited states which have well-defined multiplicities and the noncollinear formulation of density functional theory and it can be straightforwardly implemented in currently existing density functional programs.     

A density functional theory approach to noncovalent interactions via interacting monomer densities

A recently proposed "DFT + dispersion" treatment (Rajchel et al., Phys. Rev. Lett., 2010, 104, 163001) is described in detail and illustrated by more examples. The formalism derives the dispersion-free density functional theory (DFT) interaction energy and combines it with the dispersion energy from separate DFT calculations. It consists of the self-consistent polarization of DFT monomers restrained by the exclusion principle via the Pauli blockade technique. Within the monomers a complete exchange-correlation potential should be used, but between them only the exact exchange operates. The application to a wide range of molecular complexes from rare-gas dimers to hydrogen-bonds to π-electron interactions shows good agreement with benchmark values.