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.     

Linear and non-linear optical properties of some donor–acceptor oxadiazoles by ab initio Hartree-Fock calculations

The molecular hyperpolarizability of some donor–acceptor oxadiazoles was investigated using ab initio methods. Ab initio optimizations were performed at the Hartree-Fock level using different basis sets, starting with the minimal basis set, and then split valence sets. The first hyperpolarizabilities were calculated at the Hartree-Fock level employing the corresponding basis sets using Gaussian 98W. In general, the first hyperpolarizability is dependent on the choice of method and basis set. In order to understand this phenomenon in the context of molecular orbital picture, we examined the molecular HOMOs and molecular LUMOs generated via HF/6-31G level. It has also been calculated the polarizability, anisotropy of polarizability and ground state dipole moment of all the molecules. Several of these oxadiazoles display significant second-order molecular nonlinearity, β(8.57–195.05 × 10⁻³⁰ esu) and provide the basis for future design of efficient nonlinear optical materials having the oxadiazole core.     

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.     

Borazine-based conjugated derivatives: Structural,electronic, and optical properties

The structural characteristics, electronic properties, and nonlinear optical properties of borazine-based conjugated derivatives have been explored at B3LYP/6-311G(d,p) level. The effects of various electron donor and acceptor substituents (H, F, Cl, Br, Me, CF₃, NH₂, OH, COOH, CHO, NO₂) on the structure, polarizability, frontier orbitals, the most intense electronic transition, and hyperpolarizabilities have studied. Calculations show that NO₂-substituted molecules have lowest hardness, the largest isotropic polarizability and anisotropy of polarizability, and first hyperpolarizability.     

Hartree-Fock-Roothaan calculations of dipolar polarizabilities for closed-shell atoms

Methods are suggested for optimization of Slater type atomic orbitals in polarizability calculations of closed-shell atoms using “bound” perturbation theory (algebraic version of the Hartree-Fock method). The size and composition of the basis set of atomic orbitals providing the Hartree-Fock limit for perturbation parameters are considered. Dipolar polarizabilities are calculated for He, Be, Ne, and Mg atoms and their isoelectronic series. Translated fromZhurnal Strukturnoi Khimii, Vol. 41, No. 3, pp. 439-448, May–June, 2000.     

Molecular (hyper)polarizabilities computed by pseudospectral methods

We have developed algorithms based on pseudospectral (PS) ab initio electronic structure methods for solving the first- and second-order Hartree-Fock/Kohn-Sham equations and evaluating molecular polarizabilities and first- and second-order hyperpolarizabilities in the spin-restricted and spin-unrestricted formalisms at the Hartree-Fock (HF) and density functional theory (DFT) levels. We carry out calculations on 50 small molecules to test the accuracy of the PS approach. Our results demonstrate that the molecular polarizability alpha computed by the PS method is essentially identical to the value obtained from conventional methods for both HF and DFT calculations, while the first-order hyperpolarizability beta and second-order hyperpolarizability gamma have mean unsigned percentage differences of 1.26% and 0.62% (HF) and 0.78% and 0.65% (DFT), respectively. We also present CPU timing comparisons between the PS and conventional methods at the 6-31 G(**) level for 14 molecules having 185 to 1185 basis functions. The timing results show that the PS method is 25 (PS-HF) and 13 (PS-DFT) times faster than the conventional method for a system with 500 basis functions. The PS methods are found scale as N(2.70) (PS-HF) and N(2.40) (PS-DFT), while the conventional methods scale as N(2.93) (PRISM-HF) and N(2.87) (PRISM-DFT), where N is the number of basis functions.     

One-pot synthesis,X-ray crystal structure,and identification of potential molecules against COVID-19 main protease through structure-guided modeling and simulation approach

Although antimicrobial resistance before the Covid-19 pandemic is a top priority for global public health, research is already ongoing on novel organic compounds with antimicrobial and antiviral properties in changing medical environments in connection with Covid 19. Thanks to the Biginelli reaction, which allows the synthesis of pyrimidine compounds, blockers of calcium channels, antibodies, antiviral, antimicrobial, anti-inflammatory, or antioxidant therapeutic compounds were investigated. In this paper, we aim to present Biginelli's synthesis, its therapeutic properties, and the structural–functional relationship in the test compounds that allows the synthesis of antimicrobial compounds. Both the DFT and TD-DFT computations of spectral data, molecular orbitals (HOMO, LUMO) analysis, and electrostatic potential (MEP) surfaces are carried out as an add-on to synthetic research. Hirshfeld surface analysis was also used to segregate the different intermolecular hydrogen bonds involved in the molecular packing strength. Natural Bond Orbital (NBO) investigation endorses the existence of intermolecular interactions mediated by lone pair, bonding, and anti-bonding orbitals. The dipole moment, linear polarizability, and first hyperpolarizabilities have been explored as molecular parameters. All findings based on DFT exhibit the best consistency with experimental findings, implying that synthesized molecules are highly stable. To better understand the binding mechanism of the SARS-CoV-2 M^pro, we performed molecular docking, molecular dynamics (MD) simulations, and binding free energy calculations.     

Computational Studies on the Sc<Subscript>n</Subscript>N<Subscript>m</Subscript> (n + m=10) Clusters: Structure,Electronic and Vibrational Properties

Besides the size and structure, compositions also dramatically affect the properties of clusters. In fact, the increased degree of freedom poses much more challenges to determine the global minimum structure of multi-component clusters. In this thesis, based on the CALYPSO structure searching method, the global minimum structures are obtained for Sc_nN_m (n + m=10) clusters at PW91/6-311+G(d) level. The growth behavior indicates that the cage unit tends to arrange into the compact configurations, and the occupied positions of N atoms shift from the surface towards the center of coordination site with the increasing number of Sc atoms. The relative stabilities have been discussed by analyzing the average binding energies and HOMO–LUMO gaps. In addition, the molecular orbitals, dipole moments, polarizability, hyperpolarizabilities, natural population, natural electron configuration, and Infared and Raman spectra calculations allow complete characterization of the electronic and vibrational properties for the global minimum structural clusters.     

五元杂环分子超极化率的电子相关效应

用有限场方法在HF和MP4水平上计算呋喃、吡咯和噻吩的极化率、一阶和二阶超极化率.结果表明,电子相关效应对各阶极化率,尤其是高阶极化率影响较大.MP2计算值较HF有显著改善,一阶超极化率的MP2,MP3和MP4计算值依次增大,二阶超极化率的MP2和MP4值相近,而MP3值小于MP2.呋喃、吡咯和噻吩的各阶极化率在各级微扰中均具有与HF水平上一致的相对大小顺序.     

Computational developments in generalized valence bond calculations

In this article a procedure for generating starting orbitals for generalized valence bond (GVB) calculations is presented. This is achieved by selecting orbitals which correspond to specific bonds or electron pairs. These orbitals can be identified from the localized molecular orbitals, for both occupied and virtual orbitals, which are obtained through a unitary transformation of the Hartree-Fock canonical molecular orbitals using the Boys's localization method. A scheme has also been implemented which achieves optimum convergence of the pairwise orbital optimization. An object-oriented GVB program is developed which automatically generates reliable initial GVB orbitals, leading to proper and fast convergence. © 1996 by John Wiley & Sons, Inc.     

Ionization energies of the diatomic halogens and interhalogens studied with relativistic hartree-fock-slater calculations

Vertical ionization energies from the outermost two π and two σ molecular orbitals in the diatomic halogen and interhalogen molecules have been calculated using a relativistic Hartree-Fock-Slater (HFS) method. The results obtained are in good agreement with the corresponding experimental ionization energies obtained from photoelectron spectroscopy. The spin-orbit splittings of the ²Π cationic states are rationalized in terms of the degree of localization of the partially filled π orbital in the cation on the header atom.     

A Homochiral Fulgide Organic Ferroelectric Crystal with Photoinduced Molecular Orbital Breaking

Thermally triggered spatial symmetry breaking in traditional ferroelectrics has been extensively studied for manipulation of the ferroelectricity. However, photoinduced molecular orbital breaking, which is promising for optical control of ferroelectric polarization, has been rarely explored. Herein, for the first time, we synthesized a homochiral fulgide organic ferroelectric crystal (E)-(R)-3-methyl-3-cyclohexylidene-4-(diphenylmethylene)dihydro-2,5-furandione ( 1 ), which exhibits both ferroelectricity and photoisomerization. Significantly, 1 shows a photoinduced reversible change in its molecular orbitals from the 3 π molecular orbitals in the open-ring isomer to 2 π and 1 σ molecular orbitals in the closed-ring isomer, which enables reversible ferroelectric domain switching by optical manipulation. To our knowledge, this is the first report revealing the manipulation of ferroelectric polarization in homochiral ferroelectric crystal by photoinduced breaking of molecular orbitals. This finding sheds light on the exploration of molecular orbital breaking in ferroelectrics for optical manipulation of ferroelectricity.     

Finite-field many-body perturbation theory IV. Basis set optimization in MBPT calculations of molecular properties. Molecular quadrupole moments

The choice of truncated basis sets and their optimization for MBPT calculations of molecular properties are discussed. It is pointed out that computing the correlation corrections to some kth order property by using the MBPT approach requires the knowledge of accurate perturbed orbitals through the kth order. Hence, it is argued that the basis set functions can be optimized with respect to the perturbed energies calculated within the coupled Hartree-Fock method. The proposed procedure is illustrated by MBPT calculations of quadrupole moments of H₂ and FH. Additionally, also some estimates of the quadrupole polarizability tensor components for these molecules are obtained.     

Momentum distribution of Hückel π electrons

The momentum distribution and related physical properties are examined for π molecular orbitals (MOs) of a conjugated hydrocarbon system obtained by the empirical Hückel method. Several general rules are derived and the momentum-space aspect of the Hückel π electron theory is clarified.     

Hybridization of a Flexible Cyclooctatetraene Core and Rigid Aceneimide Wings for Multiluminescent Flapping π Systems

The hybridization of flexible and rigid π‐conjugated frameworks is a potent concept for producing new functional materials. In this article, a series of multifluorescent flapping π systems that combine a flexible cyclooctatetraene (COT) core and rigid aceneimide wings with various π‐conjugation lengths has been designed and synthesized, and their structure/properties relationships have been investigated. Whereas these molecules have a V‐shaped bent conformation in the ground state, the bent structure changes to a planar conformation in the lowest excited singlet (S₁) state irrespective of the lengths of the aceneimide wings. However, the fluorescence behavior in solution is distinct between the naphthaleneimide system and the anthraceneimide system. The former has a nonemissive S₁ state owing to the significant contribution of the antiaromatic character of the planar COT frontier molecular orbitals, thereby resulting in complete fluorescence quenching in solution. In contrast, the latter anthraceneimide system shows an intense emission, which is ascribed to the planar but distorted S₁ state that shows the allowed transition between the π‐molecular orbitals delocalized over the COT core and the acene wings. The other characteristic of these π systems is the significantly redshifted fluorescence in the crystalline state relative to their monomer fluorescence. The relationship between the packing structures and the fluorescence properties was investigated by preparing a series of hybrid π systems with different sizes of substituents on the imide moieties, which revealed the effect of the twofold π‐stacked structure of the V‐shaped molecules on the large bathochromic shift in emission.     

Spectroscopic and theoretical optical properties of indoleninyl-substituted dibenzotetraaza[14]annulenes

Two new macrocyclic dibenzotetraaza[14]annulene (DBTAA) compounds with indolenine ( 5 ) and pyridoindolenine ( 6 ) moieties were synthesized and characterized by spectroscopy. Both DBTAAs exhibit strong UV-Vis absorption properties in the Soret band region. The theoretical second-order nonlinear optical property, electric dipole moment (μ), dispersion-free dipole polarizability (α) and first hyper-polarizability values were calculated by density functional theory and time dependent density functional theory. The ab-initio quantum mechanical calculation by time-dependent Hartree-Fock method was utilized to investigate the dynamic dipole polarizabilities, dynamic second-order, static, and dynamic third-order (γ) hyper-polarizabilities of the DBTAAs. The configuration interaction technique of all doubly occupied molecular orbitals possesses theoretically defined single-photon absorption (OPA) specifications for the examined structures. The computed maximum OPA wavelengths on both macrocyclic compounds coincide with the preceding measurement outcomes.     

The rotational barrier in ethane: a molecular orbital study

The energy change on each Occupied Molecular Orbital as a function of rotation about the C-C bond in ethane was studied using the B3LYP, mPWB95 functional and MP2 methods with different basis sets. Also, the effect of the ZPE on rotational barrier was analyzed. We have found that σ and π energies contribution stabilize a staggered conformation. The σ(s) molecular orbital stabilizes the staggered conformation while the stabilizes the eclipsed conformation and destabilize the staggered conformation. The π(z) and molecular orbitals stabilize both the eclipsed and staggered conformations, which are destabilized by the π(v) and molecular orbitals. The results show that the method of calculation has the effect of changing the behavior of the energy change in each Occupied Molecular Orbital energy as a function of the angle of rotation about the C-C bond in ethane. Finally, we found that if the molecular orbital energy contribution is deleted from the rotational energy, an inversion in conformational preference occurs.     

一类五核平面开口型过渡金属原子簇电子吸收光谱和二阶非线性光学性质的TDDFT研究

运用TDDFT B3LYP/LanL2DZ方法, 研究了一类具有非中心对称的五核平面开口构型过渡金属原子簇化合物[MoS₄Cu₄(py)₆X₂] (X＝Br, I)的电子吸收光谱和静态二阶非线性极化率, 估算了晶体的宏观二阶非线性光学系数. 电子吸收光谱的计算结果与实验测量结果比较符合; 碘系簇合物的静态二阶非线性极化率大于溴系. 详细讨论了该类金属簇合物电子吸收光谱的归属及其相关联的电子跃迁方式; 在微观水平上阐述了其二阶非线性光学性质的起源. 研究结果表明外围无机卤素配体4p/5p轨道到簇芯[MoS₄]杂化轨道的电子转移对静态二阶非线性极化率的贡献大于有机配体的贡献; 而过渡金属簇芯内的电子转移也有较大的贡献. 这对于理解过渡金属原子簇化合物内的电子转移对光学激发的作用以及用来设计新的无机-有机杂化二阶非线性光学材料有较大的帮助.     

Incorporation of solvent effects into density functional predictions of molecular polarizabilities and hyperpolarizabilities

A study of the effect of the field, the basis set, the functional, and the cavity size on molecular polarizabilities and hyperpolarizabilities of substituted benzenes in liquid or solution is reported. The calculations have been performed using the density functional theory (DFT) within the conductor‐like screening model (COSMO). The optimized computational parameters are adopted to calculate molecular polarizabilities and hyperpolarizabilities of substituted benzenes in liquid or solution. The results show good agreement with the experimental values. From comparison of the different theoretical results, it is found that at the same theoretical level, the selection of the different solvation models may play an important role in the calculations of molecular solvation polarizability, and using the same solvation model, the effects of the different theoretical methods are relatively small. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Density functional theory investigation of the polarizability and second hyperpolarizability of polydiacetylene and polybutatriene chains: treatment of exact exchange and role of correlation

The static polarizability and second hyperpolarizability of increasingly large polydiacetylene and polybutatriene (PBT) chains have been evaluated using the optimized effective potential for exact exchange (OEP-EXX) method developed by Yang and Wu [Phys. Rev. Lett. 89, 143002 (2002)], where the unknown part of the effective potential is expressed as a linear combination of Gaussian functions. Various conventional atomic orbital basis sets were employed for the exchange potential (X basis) as well as for the Kohn-Sham orbitals [molecular orbital (MO) basis]. Our results were compared to coupled-perturbed Hartree-Fock (CPHF) calculations and to ab initio correlated values obtained at various levels of approximation. It turns out that (a) small conventional basis sets are, in general, unsatisfactory for the X basis; (b) the performance of a given X basis depends on the MO basis and is generally improved when using a larger MO basis; (c) these effects are exaggerated for the second hyperpolarizability compared to the polarizability; (d) except for the second hyperpolarizability of PBT chains, using 6-311++G** for the X basis gives reasonable agreement with the CPHF results for all MO basis sets; (e) our results suggest that in the limit of a complete X basis the OEP-EXX values may approach the CPHF data; and (f) in general, the quality of a given conventional X basis degrades with the length of the oligomer, which correlates with the fact that the number of X basis functions becomes a smaller fraction of the number required to reproduce exactly the finite-basis-set Hartree-Fock energies. Linear and especially nonlinear electric field responses constitute a very stringent test for assessing the quality of functionals and potentials; appropriately tailored basis sets are needed to describe the latter. Finally, this study further highlights the importance of electron correlation effects on linear and nonlinear responses, for which correlated functionals with OEP are required.