Artykuły w czasopismach: „Gaussian-Type atomic orbitals”

1

Gomes, Andr� Severo Pereira, and Rog�rio Custodio. "Exact Gaussian expansions of Slater-type atomic orbitals." Journal of Computational Chemistry 23, no. 10 (2002): 1007–12. http://dx.doi.org/10.1002/jcc.10090.

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Desmarais, N., G. Dancausse, and S. Fliszár. "A simple quality test for self-consistent-field atomic orbitals." Canadian Journal of Chemistry 71, no. 2 (1993): 175–79. http://dx.doi.org/10.1139/v93-025.

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A quality test is proposed for SCF atomic orbitals, [Formula: see text] approximated as finite linear combinations of suitable basis functions [Formula: see text] The key is in a function, readily derived from the Hartree–Fock equation [Formula: see text] which is identically zero for true Hartree–Fock spin orbitals and not so for approximate orbitals. In this way, our test measures how closely approximate orbital descriptions approach the true Hartree–Fock limit and thus provides a quality ordering of orbital bases with respect to one another and with respect to that limit, in a scale uniquely defined by the latter. Moreover, this analysis also holds for atomic subspaces of our choice, e.g., the valence region. Examples are offered for representative collections of Slater- and Gaussian-type orbital expansions.

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3

Mohammed, Tawfik Mahmood. "Mathematical modeling of the electronic structure of Titanium dioxide $(TiO_2 )_6$ nanoparticles." University of Aden Journal of Natural and Applied Sciences 24, no. 2 (2022): 519–26. http://dx.doi.org/10.47372/uajnas.2020.n2.a19.

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The calculation of the number of atoms of the given dimensional nanoparticle, composed of different type atoms has been researched in this work. The calculations have been carried out for nanoparticles of titanium dioxide. Theoretical visual models have been configured, and quantum – mechanical calculations have been carried out for $(TiO_2 )_6$ nanoparticle. The calculations for titanium dioxide nanoparticle have been carried out on the basis of Gaussian atomic orbitals. Besides, Gaussian functions have been used as atomic orbitals. The numerical values of unknown coefficients of the linear combination of atomic orbitals of the atoms of the titanium nanoparticle have been found from the solution of Hartree–Fock–Roothaan (HFR) equations.The values of orbital energies, ionization potential, and the total electronic energy of titanium dioxide nanoparticles have been determined. The calculations show that ,titanium dioxide nanoparticle is tough, electrophile, and stable dielectric, material. The effective charge of atoms have been calculated, and the theoretical visual mode of titanium dioxide nanopartical have been constructed.

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Mitroy, J. "A Hartree - Fock Program for Atomic Structure Calculations." Australian Journal of Physics 52, no. 6 (1999): 973. http://dx.doi.org/10.1071/ph99042.

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The Hartree–Fock equations for a general open shell atom are described. The matrix equations that result when the single particle orbitals are written in terms of a linear combination of analytic basis functions are derived. Attention is paid to the complexities that occur when open shells are present. The specifics of a working FORTRAN program which is available for public use are described. The program has the flexibility to handle either Slater-type orbitals or Gaussian-type orbitals.

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Kuang, Jiyun, and C. D. Lin. "Molecular integrals over spherical Gaussian-type orbitals: I." Journal of Physics B: Atomic, Molecular and Optical Physics 30, no. 11 (1997): 2529–48. http://dx.doi.org/10.1088/0953-4075/30/11/007.

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Dacosta, Herbert F. M., Milan Trsic, and Alfredo M. Simas. "Hydrogen-type orbitals in terms of Gaussian functions." International Journal of Quantum Chemistry 65, no. 2 (1997): 143–50. http://dx.doi.org/10.1002/(sici)1097-461x(1997)65:2<143::aid-qua5>3.0.co;2-w.

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Berlu, Lilian, and Philip Hoggan. "Useful Integrals for Ab-Initio Molecular Quantum Similarity Measurements Using Slater Type Atomic Orbitals." Journal of Theoretical and Computational Chemistry 02, no. 02 (2003): 147–61. http://dx.doi.org/10.1142/s0219633603000513.

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Molecular quantum similarity measurements are based on a quantitative comparison of the one-electron densities of two molecules superposed and aligned to optimize a well-defined similarity function. In most previous work the densities have been related using a Dirac delta leading to the overlap-like quantum similarity function. The densities for the two molecules compared have generally been approximated often with a simple LCAO of s-gaussian functions. In this work, we present a one center two range expansion method for the evaluation of the overlap integrals involved in the overlap-like quantum similarity function over Slater type orbitals (STO). The single center and three types of two-center overlap integrals (involving four atomic orbitals; two in each molecule) have led to finite sums using a single center approach combined with selection rules obtained by analysis of orbital angular momentum (conservation). The three- and four-center integrals are also obtained analytically but involve infinite sums which require further study before leading to a complete set of integral codes for ab-initio quantum similarity.

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Tanaka, Kiyoaki. "X-ray molecular orbital analysis. I. Quantum mechanical and crystallographic framework." Acta Crystallographica Section A Foundations and Advances 74, no. 4 (2018): 345–56. http://dx.doi.org/10.1107/s2053273318005478.

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Molecular orbitals were obtained by X-ray molecular orbital analysis (XMO). The initial molecular orbitals (MOs) of the refinement were calculated by the ab initio self-consistent field (SCF) MO method. Well tempered basis functions were selected since they do not produce cusps at the atomic positions on the residual density maps. X-ray structure factors calculated from the MOs were fitted to observed structure factors by the least-squares method, keeping the orthonormal relationship between MOs. However, the MO coefficients correlate severely with each other, since basis functions are composed of similar Gaussian-type orbitals. Therefore, a method of selecting variables which do not correlate severely with each other in the least-squares refinement was devised. MOs were refined together with the other crystallographic parameters, although the refinement with the atomic positional parameters requires a lot of calculation time. The XMO method was applied to diformohydrazide, (NHCHO)2, without using polarization functions, and the electron-density distributions, including the maxima on the covalent bonds, were represented well. Therefore, from the viewpoint of X-ray diffraction, it is concluded that the MOs averaged by thermal vibrations of the atoms were obtained successfully by XMO analysis. The method of XMO analysis, combined with X-ray atomic orbital (AO) analysis, in principle enables one to obtain MOs or AOs without phase factors from X-ray diffraction experiments on most compounds from organic to rare earth compounds.

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Raynaud, Christophe, Laurent Maron, Jean-Pierre Daudey, and Franck Jolibois. "Reconsidering Car–Parrinello molecular dynamics using direct propagation of molecular orbitals developed upon Gaussian type atomic orbitals." Phys. Chem. Chem. Phys. 6, no. 17 (2004): 4226–32. http://dx.doi.org/10.1039/b402163k.

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Fernández Rico, J., R. López, I. Ema, and G. Ramírez. "Deformed atoms in molecules: analytical representation of atomic densities for Gaussian type orbitals." Journal of Molecular Structure: THEOCHEM 727, no. 1-3 (2005): 115–21. http://dx.doi.org/10.1016/j.theochem.2005.02.028.

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Njapba, S. Augustine, and Galadanci M. S. Garba. "Density functional theory study of the nuclear magnetic resonance properties and natural bond orbital analysis of germanium-phenyl nanocluster." Dutse Journal of Pure and Applied Sciences 10, no. 2c (2024): 162–75. http://dx.doi.org/10.4314/dujopas.v10i2c.16.

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In this study, the optimized molecular geometry and vibrational frequencies of novel germanium-phenyl nanostructure were calculated using the hybrid functional B3LYP/Lanl2dz as implemented in Gaussian 09 program. The obtained geometries from the calculations of density functional theory were used to carry out natural bond orbital analysis. The stabilization energy E2 that is related to the delocalization trend of electrons from donor to acceptor orbitals was also computed. The higher the stabilization energy E2, between a bonding orbital and an acceptor orbital the greater the interaction between them, signifying clear evidence of stabilization that is originating from the hyperconjugation of H- bonded interaction. Our results reveal strong stabilization energy E2, of orbital interaction between the bonding orbitals (Ge4-Ge6) and non-lone pair Ge8 with value of 81.36 Kcal/mol. The NMR isotropic chemical shift and magnetic shielding of [Ge9(C6H5)] nanostructure were calculated using Gauge-including atomic orbitals(GIAO) algorithm and results compared with experimental data. The theoretically calculated values of the coupling constant in the gas phase are 3 J (H − H) =10.99 Hz, 3 J (C − H) =10.99 Hz, and 3 J (C −C) =12.99Hz respectively and are observed to be bigger than the experimental value with a difference of about 3.29 Hz. The spin-spin coupling constant 3J was calculated by means of the generalized Karplus-type relationship.

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12

Pinchon, Didier, and Philip E. Hoggan. "Gaussian approximation of exponential type orbitals based on B functions." International Journal of Quantum Chemistry 109, no. 2 (2009): 135–44. http://dx.doi.org/10.1002/qua.21705.

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Wang, Jian, and Alexei A. Stuchebrukhov. "DFT calculation of electron tunneling currents: Real-space (grid) molecular orbitals vs. Gaussian-type molecular orbitals." International Journal of Quantum Chemistry 80, no. 4-5 (2000): 591–97. http://dx.doi.org/10.1002/1097-461x(2000)80:4/5<591::aid-qua8>3.0.co;2-j.

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Boettger, J. C., M. D. Jones, and R. C. Albers. "Structural properties of crystalline uranium from linear combination of Gaussian-type orbitals calculations." International Journal of Quantum Chemistry 75, no. 4-5 (1999): 911–15. http://dx.doi.org/10.1002/(sici)1097-461x(1999)75:4/5<911::aid-qua55>3.0.co;2-x.

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Kuang, Jiyun, and C. D. Lin. "Molecular integrals over spherical Gaussian-type orbitals: II. Modified with plane-wave phase factors." Journal of Physics B: Atomic, Molecular and Optical Physics 30, no. 11 (1997): 2549–67. http://dx.doi.org/10.1088/0953-4075/30/11/008.

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Platonenko, Alexander, Sergei Piskunov, Thomas C. K. Yang, et al. "Electronic Structure of Mg-, Si-, and Zn-Doped SnO2 Nanowires: Predictions from First Principles." Materials 17, no. 10 (2024): 2193. http://dx.doi.org/10.3390/ma17102193.

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We investigated the electronic structure of Mg-, Si-, and Zn-doped four-faceted [001]- and [110]-oriented SnO2 nanowires using first-principles calculations based on the linear combination of atomic orbitals (LCAO) method. This approach, employing atomic-centered Gaussian-type functions as a basis set, was combined with hybrid density functional theory (DFT). Our results show qualitative agreement in predicting the formation of stable point defects due to atom substitutions on the surface of the SnO2 nanowire. Doping induces substantial atomic relaxation in the nanowires, changes in the covalency of the dopant–oxygen bond, and additional charge redistribution between the dopant and nanowire. Furthermore, our calculations reveal a narrowing of the band gap resulting from the emergence of midgap states induced by the incorporated defects. This study provides insights into the altered electronic properties caused by Mg, Si, and Zn doping, contributing to the further design of SnO2 nanowires for advanced electronic, optoelectronic, photovoltaic, and photocatalytic applications.

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17

Boettger, Jonathan Carl. "Spin-polarized fully relativistic linear combinations of Gaussian-type orbitals calculations for fcc plutonium." International Journal of Quantum Chemistry 95, no. 4-5 (2003): 380–86. http://dx.doi.org/10.1002/qua.10588.

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Domnin, Anton V., Ilia E. Mikhailov, and Robert A. Evarestov. "DFT Study of WS2-Based Nanotubes Electronic Properties under Torsion Deformations." Nanomaterials 13, no. 19 (2023): 2699. http://dx.doi.org/10.3390/nano13192699.

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In this study, the influence of torsional deformations on the properties of chiral WS2-based nanotubes was investigated. All calculations presented in this study were performed using the density functional theory (DFT) and atomic gaussian type orbitals basis set. Nanotubes with chirality indices (8, 2), (12, 3), (24, 6) and (36, 9) corresponding to diameters of 10.68 Å, 14.90 Å, 28.26 Å and 41.90 Å, respectively, are examined. Our results reveal that for nanotubes with smaller diameters, the structure obtained through rolling from a slab is not optimal and undergoes spontaneous deformation. Furthermore, this study demonstrates that the nanotube torsion deformation leads to a reduction in the band gap. This observation suggests the potential for utilizing such torsional deformations to enhance the photocatalytic activity of the nanotubes.

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19

Palmer, Michael H. "The ab initio Calculation of Nuclear Quadrupole Coupling Constants with Special Reference to 33S." Zeitschrift für Naturforschung A 47, no. 1-2 (1992): 203–16. http://dx.doi.org/10.1515/zna-1992-1-235.

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AbstractThe ab initio calculation of 33S nuclear quadrupole coupling constants (NQCC) for a range of S-containing compounds with S2, S4 and S6 bonding types is described. All of the calculations used a triple zeta valence + polarisation basis set (TZVP) of gaussian type orbitals; all of the molecules were studied at the TZVP equilibrium geometry. The electric field gradients (EFG) calculated were correlated with the experimental NQCC obtained by either microwave spectroscopy (MW), nuclear quadrupole resonance (NQR) or NMR relaxation methods; although the experimental data cover a wide diversity of chemical types over a long period of time, the slope of the relationship between the EFG (qii) and the NQCC (χii) yields a value for the 33S atomic quadrupole moment of - 0.064 barn, very close to recent calculations with a large atomic basis set, and to experimental data. The relationship between the EFG tensor components and the internal molecular structure features is discussed for a diverse series of molecules.

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Ishida, Kazuhiro. "ACE algorithm for the rapid evaluation of the electron-repulsion integral over Gaussian-type orbitals." International Journal of Quantum Chemistry 59, no. 3 (1996): 209–18. http://dx.doi.org/10.1002/(sici)1097-461x(1996)59:3<209::aid-qua4>3.0.co;2-1.

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Cesco, J. C., C. C. Denner, G. O. Giubergia, et al. "Implementation of atomic basis set composed of 1s Gaussian and 1s Slater-type orbitals to carry out quantum mechanics molecular calculations." Journal of Computational Chemistry 20, no. 6 (1999): 604–9. http://dx.doi.org/10.1002/(sici)1096-987x(19990430)20:6<604::aid-jcc6>3.0.co;2-o.

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Kalinin, N. V., and V. A. Saleev. "Ab initio modeling of Raman and infrared spectra of calcite." Computer Optics 42, no. 2 (2018): 263–66. http://dx.doi.org/10.18287/2412-6179-2018-42-2-263-266.

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Calcite is the most thermodynamically stable polymorphic phase of the CaCO3 crystal. It is widely used in modern optical instruments operating in the infrared and visible wavelengths of electromagnetic radiation. In particular, due to its anisotropic properties, calcite is used in polarization optics devices. Ab initio quantum mechanical modeling of the Raman and infrared spectra of calcite makes it possible to better understand the structure and nature of the chemical bonds of the compound, and find the optimal conditions for the effective use of unique properties of calcite in photonics tools. The calculations are performed within the framework of the density functional theory in the CRYSTAL program, using the “hybrid” B3LYP functional and the all-electronic bases of the STO-6G, PO-TZVP and BSD atomic orbitals of the Gaussian type. The obtained results for the elastic constants, Raman and infrared spectra of calcite agree satisfactorily with the available experimental data for the basic sets of POB-TZVP and BSD.

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Toader, Ana Maria, Maria Cristina Buta, and Fanica Cimpoesu. "On the calculation of lanthanide systems. The spectral parameters of praseodymium trivalent ion." Chemistry Journal of Moldova 18, no. 2 (2023): 78–86. http://dx.doi.org/10.19261/cjm.2023.1146.

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In this work, taking the Pr(III) ion as a suitable case study, the authors test the capacity of a series of Gaussian Type Orbitals (GTOs) basis sets to account for the atomic spectra of lanthanide ions. An extended relevance of this assessment can be found in modeling the luminescence of lanthanide-based materials. It was selected the Pr(III) case because it shows a rather rich collection of experimental data, emerging from the f2 and fd configurations. The energy barycenters of spectral multiplets can be equated analytically in terms of the so-called Slater-Condon parameters. By multi-configurational ab initio procedures, with basis sets from existing GTO repositories, the calculated f→f transitions are moderately higher than the experimental values, while the relative energies of Fd states undergo both under- and over-estimation. The GTO shortcomings, that are impacting the accuracy, were debated, the critical perspective spreading the seeds of future development.

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Jursic, Branko S. "Computation of geometries and frequencies of singlet and triplet nitromethane with density functional theory using Gaussian-type orbitals." International Journal of Quantum Chemistry 64, no. 2 (1997): 263–69. http://dx.doi.org/10.1002/(sici)1097-461x(1997)64:2<263::aid-qua15>3.0.co;2-a.

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Ulian, Gianfranco, and Giovanni Valdrè. "Thermomechanical, electronic and thermodynamic properties of ZnS cubic polymorphs: an ab initio investigation on the zinc-blende–rock-salt phase transition." Acta Crystallographica Section B Structural Science, Crystal Engineering and Materials 75, no. 6 (2019): 1042–59. http://dx.doi.org/10.1107/s2052520619012630.

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In the present work, an extensive and detailed theoretical investigation is reported on the thermomechanical, electronic and thermodynamic properties of zinc-blende (sphalerite, zb-ZnS) and rock-salt zinc sulfide (rs-ZnS) over a wide range of pressure, by means of ab initio Density Functional Theory, Gaussian type orbitals and the well known B3LYP functional. For the first time, vibrational frequencies, phonon dispersion relations, elasto-piezo-dielectric tensor, thermodynamic and thermomechanical properties of rs-ZnS were calculated with a consistent approach that allows a direct comparison with the low-pressure polymorph. Special attention was paid to the evaluation of the thermodynamic pressure–temperature stability of the mineral phases between 0–25 GPa and 0–800 K. The static (T = 0 K) bulk moduli of sphalerite and rock-salt ZnS were 72.63 (3) GPa and 84.39 (5) GPa, respectively. The phase transition in static conditions calculated from the equation of state was about 15.5 GPa, whereas the elastic constants data resulted in P trans = 14.6 GPa. At room temperature (300 K), the zb-rs transition occurs at 14.70 GPa and a negative Clapeyron slope (dP)/(dT) = 0.0023 was observed up to 800 K. The electronic band structure showed a direct band gap for zb-ZnS (E g = 4.830 eV at equilibrium geometry), which became an indirect one by increasing pressure above 11 GPa. The results were found to be in good agreement with the available experimental and theoretical data, further extending the knowledge of important properties of zinc sulfide, in particular the thermomechanical ones of the rock-salt polymorph here extensively explored for the first time.

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Hu, Anguang, and Brett I. Dunlap. "Three-center molecular integrals and derivatives using solid harmonic Gaussian orbital and Kohn–Sham potential basis sets." Canadian Journal of Chemistry 91, no. 9 (2013): 907–15. http://dx.doi.org/10.1139/cjc-2012-0485.

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Three-center integrals over Gaussian orbital and Kohn–Sham (KS) basis sets are reviewed. An orbital basis function carries angular momentum about its atomic center. That angular momentum is created by solid harmonic differentiation with respect to the center of an s-type basis function. That differentiation can be brought outside any purely s-type integral, even nonlocal pseudopotential integrals. Thus the angular factors associated with angular momentum and differentiation with respect to atom position can be pulled outside loops over orbital and KS Gaussian exponents.

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Kotlyar, V. V., A. A. Kovalev, and A. P. Porfirev. "Measurement of the orbital angular momentum of an astigmatic Hermite–Gaussian beam." Computer Optics 43, no. 3 (2019): 356–67. http://dx.doi.org/10.18287/2412-6179-2019-43-3-356-367.

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Here we study three different types of astigmatic Gaussian beams, whose complex amplitude in the Fresnel diffraction zone is described by the complex argument Hermite polynomial of the order (n, 0). The first type is a circularly symmetric Gaussian optical vortex with and a topological charge n after passing through a cylindrical lens. On propagation, the optical vortex "splits" into n first-order optical vortices. Its orbital angular momentum per photon is equal to n. The second type is an elliptical Gaussian optical vortex with a topological charge n after passing through a cylindrical lens. With a special choice of the ellipticity degree (1: 3), such a beam retains its structure upon propagation and the degenerate intensity null on the optical axis does not “split” into n optical vortices. Such a beam has fractional orbital angular momentum not equal to n. The third type is the astigmatic Hermite-Gaussian beam (HG) of order (n, 0), which is generated when a HG beam passes through a cylindrical lens. The cylindrical lens brings the orbital angular momentum into the original HG beam. The orbital angular momentum of such a beam is the sum of the vortex and astigmatic components, and can reach large values (tens and hundreds of thousands per photon). Under certain conditions, the zero intensity lines of the HG beam "merge" into an n-fold degenerate intensity null on the optical axis, and the orbital angular momentum of such a beam is equal to n. Using intensity distributions of the astigmatic HG beam in foci of two cylindrical lenses, we calculate the normalized orbital angular momentum which differs only by 7 % from its theoretical orbital angular momentum value (experimental orbital angular momentum is –13,62, theoretical OAM is –14.76).

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Pinheiro da Silva, Braian, Wagner T. Buono, Leonardo J. Pereira, Daniel S. Tasca, Kaled Dechoum, and Antonio Z. Khoury. "Spin to orbital angular momentum transfer in frequency up-conversion." Nanophotonics 11, no. 4 (2021): 771–78. http://dx.doi.org/10.1515/nanoph-2021-0493.

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Abstract We demonstrate the spin to orbital angular momentum transfer in frequency upconversion with structured light beams. A vector vortex is coupled to a circularly polarized Gaussian beam in noncollinear second harmonic generation under type-II phase match. The second harmonic beam inherits the Hermite–Gaussian components of the vector vortex; however, the relative phase between them is determined by the polarization state of the Gaussian beam. This effect creates an interesting crosstalk between spin and orbital degrees of freedom, allowing the angular momentum transfer between them. Our experimental results match the theoretical predictions for the nonlinear optical response.

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Jursic, Branko S. "Density functional calculations of difluorodiazete structures with Gaussian-orbital-type approach." International Journal of Quantum Chemistry 57, no. 2 (1996): 213–17. http://dx.doi.org/10.1002/(sici)1097-461x(1996)57:2<213::aid-qua7>3.0.co;2-0.

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Lasar, Christian, and Thorsten Klüner. "Explicitly correlated orbital optimized contracted pair correlation methods: Foundations and applications." Journal of Theoretical and Computational Chemistry 17, no. 04 (2018): 1850024. http://dx.doi.org/10.1142/s0219633618500244.

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Pair correlation methods are able to achieve highly accurate solutions for chemical problems. Unfortunately, their applicability is generally restricted to medium-sized molecules due to storage requirements and computational costs. These restrictions can be partly overcome by local correlation methods. These methods use physical and mathematical criteria to decide which interactions are of such a long range that they do not have to be computed and saved. In our new ansatz, we define an alternative way towards local correlation. The range of interactions is strictly bound to the decay of integrals over Gaussian type geminals in the atomic orbital basis. The number of variables is reduced by orders of magnitude applying an efficient contraction scheme, leading to a naturally local representation of correlation effects. This scheme is extended by orbital optimization to describe multi-reference problems and explicit correlation to improve the basis set convergence.

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Saleev, Vladimir, and Alexandra Shipilova. "First-principles calculations of LiNbO3 optical properties: From far-infrared to ultraviolet." Modern Physics Letters B 32, no. 05 (2018): 1850063. http://dx.doi.org/10.1142/s021798491850063x.

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We perform first-principles calculations of optical properties for ferroelectric phase of LiNbO3 crystal using density functional theory (DFT) for wide range of wavelengths, from far-infrared (IR) to ultraviolet. We study frequency dependence of complex dielectric tensor and related quantities, such as refractive and reflection indices, absorption coefficients, etc. Our calculation incorporates advantages of numerical approaches based on atomic-orbital all-electron Gaussian-type basis sets, as it is realized in CRYSTAL14 program. We compared predictions obtained in general-gradient approach with PBESOL exchange-correlation functional and in hybrid approach with PBESOL0 functional, and we have found that hybrid PBESOL0 functional is more applicable to describe the wide set of the experimental data.

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Coursault, Delphine, and Etienne Brasselet. "Nanostructured silica spin–orbit optics for modal vortex beam shaping." Nanophotonics 11, no. 4 (2021): 805–12. http://dx.doi.org/10.1515/nanoph-2021-0579.

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Abstract Modality is a generic concept of wave-optics at the basis of optical information and communications. One of the challenges of photonics technologies based on optical orbital angular momentum consists in the production of a modal content for both the azimuthal and radial degrees of freedom. This basically requires shaping the complex amplitude of an incident light beam, which is usually made up from adaptive spatial light modulators or bespoke devices. Here, we report on the experimental attempt of a recent theoretical proposal [Opt. Lett. 42, 1966 (2017)] toward the production of various optical vortex modes of the Laguerre–Gaussian type relying on the spin–orbit interaction of light. This is done in the visible domain from optical elements made out of silica glass. The idea consists in exploiting the combined effects of azimuthally-varying geometric phase with that of radially-varying propagation features. The proposed approach can be readily extended to any wavelength as well as to other families of optical modes, although some dynamic phase problems remain to be solved to make it a turnkey technology.

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Ishimoto, Takayoshi, Masanori Tachikawa, and Umpei Nagashima. "Analytical optimization of exponent values in protonic and deuteronic Gaussian-type functions by elimination of translational and rotational motions from multi-component molecular orbital scheme." International Journal of Quantum Chemistry 108, no. 3 (2007): 472–81. http://dx.doi.org/10.1002/qua.21540.

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Jursic, Branko S., and Zoran Zdravkovski. "Theoretical investigation of the conrotatory ring opening of cyclobutene and 1, 2-dihydro-1, 2-diazacyclobutadienes with ab initio and density functional Gaussian-type-orbital approach." International Journal of Quantum Chemistry 56, no. 2 (1995): 115–23. http://dx.doi.org/10.1002/qua.560560206.

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Mathar, Richard J. "Erratum: Mutual conversion of three flavors of gaussian type orbitals." International Journal of Quantum Chemistry, 2009, NA. http://dx.doi.org/10.1002/qua.22353.

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Shaw, Robert A. "The completeness properties of Gaussian‐type orbitals in quantum chemistry." International Journal of Quantum Chemistry 120, no. 17 (2020). http://dx.doi.org/10.1002/qua.26264.

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Lehtola, Susi. "Importance profiles. Visualization of atomic basis set requirements." Electronic Structure, March 8, 2024. http://dx.doi.org/10.1088/2516-1075/ad31ca.

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Abstract Recent developments in fully numerical methods promise interesting opportunities for new, compact atomic orbital (AO) basis sets that maximize the overlap to fully numerical reference wave functions, following the pioneering work of Richardson and coworkers from the early 1960s. Motivated by this technique, we suggest a way to visualize the importance of AO basis functions employing fully numerical wave functions computed at the complete basis set (CBS) limit: the importance of a normalized AO basis function |α⟩ centered on some&#xD;nucleus can P be visualized by projecting |α⟩ on the set of numerically represented occupied orbitals |ψi ⟩ as I0 (α) = i ⟨α|ψi ⟩⟨ψi |α⟩. Choosing α to be a continuous parameter describing the orbital basis, such as the exponent of a Gaussian-type orbital (GTO) or Slater-type orbital (STO) basis function, one is then able to visualize the importance of various functions. The proposed visualization I0 (α) has the important property 0 ≤ I0 (α) ≤ 1 which allows unambiguous interpretation. We also propose a straightforward generalization of the importance profile for polyatomic appliations I(α), in which the importance of a test function |α⟩ is measured as the increase in projection from the atomic minimal basis. We exemplify the methods with importance profiles computed for atoms from the first three rows, and for a set of chemically diverse diatomic molecules. We find that the importance profile offers a way to visualize the atomic basis set requirements for a given system in an a priori manner, provided that a fully numerical reference wave function is available.

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38

Gangal, Krish, İpek Gerz, Tanvi Goyal, Ajeeth Iyer, Vaibhav Vaiyakarnam, and Larry McMahan. "Modeling Hartree-Fock approximations of the Schrödinger Equation for multielectron atoms from Helium to Xenon using STO-nG basis sets." Journal of Emerging Investigators, 2023. http://dx.doi.org/10.59720/22-211.

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The energy of an atom is extremely useful in nuclear physics and reaction mechanism pathway determination but is challenging to compute. Thus, we aimed to synthesize regression models for Pople Gaussian expansions of Slater-type Orbitals (STO-nG) atomic energy vs. atomic number scatter plots to allow for easy approximation of atomic energies without using computational chemistry methods. Using the Hartree-Fock method, we calculated atomic energies for elements helium to xenon (He to Xe) using STO-nG electron orbital basis set models. After calculating atomic energies for each basis set, we plotted them as tables of atomic energy (in Hartrees) versus the atomic number. We hypothesized that there would be a non-linear correlation in the scatter plot. We first formed the regressions using data from helium to krypton (He to Kr), and then we added new data from Kr to Xe. We then calculated the old and new coefficients of determination, and the difference between them. Due to their common use in modeling, exponential, sinusoidal, and quadratic regressions were tested to model the data. The data supported the hypothesis that the scatter plots had non-linear correlations. Sinusoidal and quadratic regressions had higher initial coefficients, suggesting higher viability, while sinusoidal regressions also had the highest average final coefficients, and the lowest change in coefficients. The data indicated that of the three regressions, sinusoidal regressions most aptly modeled the scatter plots.

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39

Qin, Xinming, Honghui Shang, and Jinlong Yang. "Efficient implementation of analytical gradients for periodic hybrid functional calculations within fitted numerical atomic orbitals from NAO2GTO." Frontiers in Chemistry 11 (July 27, 2023). http://dx.doi.org/10.3389/fchem.2023.1232425.

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The NAO2GTO scheme provides an efficient way to evaluate the electron repulsion integrals (ERIs) over numerical atomic orbitals (NAOs) with auxiliary Gaussian-type orbitals (GTOs). However, the NAO2GTO fitting will significantly impact the accuracy and convergence of hybrid functional calculations. To address this issue, here we propose to use the fitted orbitals as a new numerical basis to properly handle the mismatch between NAOs and fitted GTOs. We present an efficient and linear-scaling implementation of analytical gradients of Hartree-Fock exchange (HFX) energy for periodic HSE06 calculations with fitted NAOs in the HONPAS package. In our implementation, the ERIs and their derivatives for HFX matrix and forces are evaluated analytically with the auxiliary GTOs, while other terms are calculated using numerically discretized GTOs. Several integral screening techniques are employed to reduce the number of required ERI derivatives. We benchmark the accuracy and efficiency of our implementation and demonstrate that our results of lattice constants, bulk moduli, and band gaps of several typical semiconductors are in good agreement with the experimental values. We also show that the calculation of HFX forces based on a master-worker dynamic parallel scheme has a very high efficiency and scales linearly with respect to system size. Finally, we study the geometry optimization and polaron formation due to an excess electron in rutile TiO2 by means of HSE06 calculations to further validate the applicability of our implementation.

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40

Kim, Inkoo, Daun Jeong, Won-Joon Son, et al. "Kohn–Sham time-dependent density functional theory with Tamm–Dancoff approximation on massively parallel GPUs." npj Computational Materials 9, no. 1 (2023). http://dx.doi.org/10.1038/s41524-023-01041-4.

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AbstractWe report a high-performance multi graphics processing unit (GPU) implementation of the Kohn–Sham time-dependent density functional theory (TDDFT) within the Tamm–Dancoff approximation. Our algorithm on massively parallel computing systems using multiple parallel models in tandem scales optimally with material size, considerably reducing the computational wall time. A benchmark TDDFT study was performed on a green fluorescent protein complex composed of 4353 atoms with 40,518 atomic orbitals represented by Gaussian-type functions, demonstrating the effect of distant protein residues on the excitation. As the largest molecule attempted to date to the best of our knowledge, the proposed strategy demonstrated reasonably high efficiencies up to 256 GPUs on a custom-built state-of-the-art GPU computing system with Nvidia A100 GPUs. We believe that our GPU-oriented algorithms, which empower first-principles simulation for very large-scale applications, may render deeper understanding of the molecular basis of material behaviors, eventually revealing new possibilities for breakthrough designs on new material systems.

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41

Esteve-Paredes, Juan José, and Juan José Palacios. "A comprehensive study of the velocity, momentum and position matrix elements for Bloch states: Application to a local orbital basis." SciPost Physics Core 6, no. 1 (2023). http://dx.doi.org/10.21468/scipostphyscore.6.1.002.

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We present a comprehensive study of the velocity operator, \hat{\boldsymbol{v}}=\frac{i}{\hbar} [\hat{H},\hat{\boldsymbol{r}}]\,𝐯̂=iℏ[Ĥ,𝐫̂], when used in crystalline solids calculations. The velocity operator is key to the evaluation of a number of physical properties and its computation, both from a practical and fundamental perspective, has been a long-standing debate for decades. Our work summarizes the different approaches found in the literature, but never connected before in a comprehensive manner. In particular we show how one can compute the velocity matrix elements following two different routes. One where the commutator is explicitly used and another one where the commutator is avoided by relying on the Berry connection. We work out an expression in the latter scheme to compute velocity matrix elements, generalizing previous results. In addition, we show how this procedure avoids ambiguous mathematical steps and how to properly deal with the two popular gauge choices that coexist in the literature. As an illustration of all this, we present several examples using tight-binding models and local density functional theory calculations, in particular using Gaussian-type localized orbitals as basis sets. We show how the the velocity operator cannot be approximated, in general, by the k-gradient of the Bloch Hamiltonian matrix when a non-orthonormal basis set is used. Finally, we also compare with its real-space evaluation through the identification with the canonical momentum operator when possible. This comparison offers us, in addition, a glimpse of the importance of non-local corrections, which may invalidate the naive momentum-velocity correspondence.

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42

Kang, Byungkyun, Joshua Vincent, Yongbin Lee, Liqin Ke, Peter A. Crozier, and Qiang Zhu. "Modeling surface spin polarization on ceria-supported Pt nanoparticles." Journal of Physics: Condensed Matter, March 30, 2022. http://dx.doi.org/10.1088/1361-648x/ac62a3.

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Abstract In this work, we employ density functional theory simulations to investigate possible spin polarization of CeO$_2$-(111) surface and its impact on the interactions between a ceria support and Pt nanoparticles. With a Gaussian type orbital basis, our simulations suggest that the CeO$_2$-(111) surface exhibits a robust surface spin polarization due to the internal charge transfer between atomic Ce and O layers. In turn, it can lower the surface oxygen vacancy formation energy and enhance the oxide reducibility. We show that the inclusion of spin polarization can significantly reduce the major activation barrier in the proposed reaction pathway of CO oxidation on ceria-supported Pt nanoparticles. For metal-support interactions, surface spin polarization enhances the bonding between Pt nanoparticles and ceria surface oxygen, while CO adsorption on Pt nanoparticles weakens the interfacial interaction regardless of spin polarization. However, the stable surface spin polarization can only be found in the simulations based on the Gaussian type orbital basis. Given the potential importance in the design of future high-performance catalysts, our present study suggests a pressing need to examine the surface ferromagnetism of transition metal oxides in both experiment and theory.

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43

Mendoza-López, L. A., J. G. Acosta-Montes, J. A. Bernal-Orozco, et al. "Frequency Conversion of Optical Vortex Arrays Through Four-Wave Mixing in Hot Atomic Gases." Frontiers in Physics 10 (July 11, 2022). http://dx.doi.org/10.3389/fphy.2022.895023.

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Arrays of multiple vortices were transferred from infrared to the blue region of the optical spectrum. This demonstration was achieved by inducing four-wave mixing in an atomic gas with a Gaussian beam and a quasi-invariant propagation beam of the Mathieu type. The latter structure was analyzed in the Fourier space for the pump and the generated light. In both cases, the phase structure can be written with a compact mathematical expression by using the same parameters within experimental error bars. A Michelson–Morley interferometer was used to confirm that a phase singularity was present at each site as predicted by the theory. These studies add to the available control over orbital angular momentum in photons generated by atoms, which has a broad span of applications in quantum and classical information management.

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Slama, Marwa, Hela Habli, Soulef Jellali, and Mounir Ben El Hadj Rhouma. "Computational study of the electronic structure of the Sr^m+Kr (m=0, 1) van der Waals complexes." Physica Scripta, June 21, 2022. http://dx.doi.org/10.1088/1402-4896/ac7aea.

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Abstract A computational study of the electronic structure of the SrKr and Sr+Kr molecular systems is presented in this paper. The computational scheme is based on the Full Configuration Interaction (FCI) method and semi-empirical pseudo-potential approach of the atomic core Sr2+ with Gaussian-type-orbital (GTO) basis sets. We have calculated the potential energy surfaces (PESs), spectroscopic parameters, electric dipole moments, and the vibrational levels' spacing for the electronic states of the SrKr molecule and its Sr+Kr ion. The accuracy of the current spectroscopic results is discussed by comparing them tothe available experimental and theoretical data. It is interesting to note that the relevant data of the Sr+Kr molecular ion show significant shapes in the higher 2Σ+ electric states, which allows us to check the intense transition in electric dipole moment and to carry out a diabatic investigation in the future.

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45

Li, Shanggeng, Fanghua Zhu, Yawen Zhou та ін. "First theoretical probe for alkynyl bridged thiophene modified coumarin nonlinear optical materials with D-π-A and A-π-D-π-A structures". Journal of Nonlinear Optical Physics & Materials 31, № 02 (2022). http://dx.doi.org/10.1142/s0218863522500084.

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First-principles exploration is very important to molecular design. In this study, geometric structure, intramolecular charge transfer (ICT), energy levels, polar moment, and ultraviolet–visible (UV–Vis) spectroscopy of eight novel and different alkynyl bridged thiophene modified coumarin nonlinear optical molecules with [Formula: see text]-[Formula: see text]-[Formula: see text] and [Formula: see text]-[Formula: see text]-[Formula: see text]-[Formula: see text]-[Formula: see text] structures had been studied by density-functional theory (DFT) calculations within B3LYP hybrid functional using 6-31 [Formula: see text], [Formula: see text] Gaussian type molecular-orbital basis set. This has guiding significance for the design of nonlinear optical molecules and the development of coumarin-based photoelectric molecules.

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46

Ghavami Sabouri, Saeed. "Generation of vortex beams with non-uniform phase jumps azimuthal locations." Journal of Optics, March 1, 2023. http://dx.doi.org/10.1088/2040-8986/acc043.

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Abstract The phase angle of the vortex beam along a closed loop centered on the optical singularity changes 2πℓ where ℓ is the number of phase jumps (PJs) from 0 to 2 and indicates the topological charge (TC) of the vortex beam. In this paper, generation and specification of a new type of vortex beams that their PJs are asymmetrically embedded in the phase pattern are reported. In contrast to Laguerre-Gaussian (LG) vortex beams, where PJs are equally spaced azimuthally around the optical singularity, the presented vortex beams have PJs embedded at arbitrary azimuthal angles. By designing a particular forked grating and displaying it on a spatial light modulator, this type of vortex beam is experimentally generated. As with conventional forked grating, the designed grating produces vortex beams with opposite orbital angular momentum (OAM) sign in the first diffraction order. By measuring the relative orientation of the intensity profile of these OAM beams in the first diffraction order, the position of the PJs on the wavefront of a vortex beam with ℓ =2 can be determined. This type of vortex beam could have potential applications in various fields of photonics, especially in optical communications based on optical vortices.&#xD;

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