Type Orbitals Research Articles

Efficient algorithm of the transcorrelated method for periodic systems

The transcorrelated (TC) method is one of the promising wave-function-based approaches for the first-principles electronic structure calculations. In this method, the many-body wave function is approximated as the Jastrow-Slater type and one-electron orbitals in the Slater determinant are optimized with a one-body self-consistent-field equation such as that in the Hartree-Fock (HF) method. Although the TC method has yielded good results for both molecules and solids, its computational cost in solid-state calculations, being of order O(N(k)(3)N(b)(3)) with N(k) and N(b) the respective numbers of k-points and bands, has for some years hindered its wide application in condensed matter physics. Although an efficient algorithm was proposed for a Gaussian basis set, that algorithm is not applicable to a plane-wave basis that is suited to and widely used in solid-state calculations. In this paper, we present a new efficient algorithm of the TC method for the plane-wave basis or an arbitrary basis function set expanded in terms of plane waves, with which the computational cost of the TC method scales as O(N(k)(2)N(b) (2)). This is the same as that of the HF method. We applied the TC method with the new algorithm to obtain converged band structure and cell parameters of some semiconductors.

Quantum Monte Carlo simulation of carbon monoxide reactivity when adsorbed at metal and oxide catalyst surfaces: Trial wave‐functions with exponential type basis and quasi‐exact three‐body correlation

AbstractReview publications show the advantages of using quantum Monte Carlo (QMC) methods when bonding interactions are modified and consequently, where the electron correlation energy varies and needs to be evaluated accurately. This article considers a model efficient metal catalyst for reactions of carbon monoxide. The ultimate aim is to help design industrially useful catalysts, since the reaction with water produces hydrogen gas selectively, that is, a clean fuel and a sustainable energy source. To narrow the gap between the industrial process and calculation, a model of platinum/oxide is studied. It is mimicked here by copper with and without adsorbed oxygen. Periodicity as well as a validated pseudo‐potential are used to limit the number of active electrons considered. A suitable code to carry out this task is CASINO. Furthermore, this code scales linearly to 100,000 processors and possesses a shared memory facility so that it is well‐suited to runs on the Blugene/P. It has been in production on such computers since early in 2011. A mixed plane‐wave/exponential type orbitals (ETO) basis is used for the systems studied. Plane waves are well‐suited to periodic solid substrates and a linear combination of ETOs for molecules. The atomic orbitals have direct physical interpretation, i.e., Coulomb Sturmians and hydrogen‐like orbitals. Their radial nodes are shown to be essential in obtaining the vitally important accurate QMC trial wave‐functions. Until 2008, ETO products on different atoms were difficult to manipulate for the evaluation of two‐electron integrals. Coulomb resolutions provide an excellent approximation that reduces these integrals to a sum of one‐electron overlap‐like integral products that each involve orbitals on at most two centers. They are thus readily evaluated. Only these integrals need to be re‐evaluated to change basis functions. In this article, QMC‐VMC variational optimisation is used with a quasi analytic two‐electron and nucleus correlation factor. The QMC diffusion Monte Carlo methodology is applied to adsorbed carbon monoxide and some of its reactions. © 2012 Wiley Periodicals, Inc.

Calculation of two-center nuclear attraction integrals of Slater type orbitals with noninteger principal quantum numbers using Guseinov’s one-center expansion formulas and Löwdin-α radial function

In this work, by the use of Guseinov’s one-center expansion formulas and Löwdin-α radial function, the series expansion relations in molecular coordinate system are established for the two-center nuclear attraction integrals of noninteger n∗ Slater type orbitals in terms of basic two-center nuclear attraction integrals over integer n Slater functions. The Löwdin α-radial function convoluted with the Guseinov’s one-center expansion formulas is one of the most important ingredients for accurate and efficient implementation of electronic structure calculation methods regardless of Hartree–Fock–Roothaan (HFR) method. The proposed algorithm shows better performance in arbitrary quantum numbers, screening constants and location of orbitals leading to significantly reduced run times.

Photophysical properties of [Cu(binap)2]+ and [Pd(binap)2] complexes: A theoretical study

A theoretical study of the electronic and molecular structure of [Cu(binap)2]+ (1) and [Pd(binap)2] (2) complexes (binap=2,20-bis(diphenylphosphino)-1,10-binaphthyl) was performed. We examined the ground states and the lowest excited states (S1 and T1) in order to get insights about the luminescence processes of these systems. Geometry optimizations were performed at density functional theory DFT (PW91 functional) employing Slater type orbitals (STO) including two polarization functions (TZ2P) and scalar relativistic corrections via the ZORA Hamiltonian. The UV–Vis absorption spectra were simulated employing time-dependent density functional theory (TD-DFT) and solvent effects were estimated using the COSMO model.The calculated excitation energies are in good agreement with experimental data, which is reflected by the calculated UV–Vis spectra. The results suggest that the lowest-energy excited state in each compound corresponds to a ML-LCT (metal–ligand to ligand charge transfer) state. We constructed Jablonsky diagrams for the luminescence phenom. In (1), this process consists of flourescence originated from the S1 state and the phosphorescence from the T1 state. In (2) the emission energy only results in phosphorescence.We found mainly differences in the geometrical parameters that envolve the Pd metal. The structural changes observed in the calculated geometries of the first excited states respect to those of the ground state have significative relevance in the values of the calculated Stokes shifts showed by the complexes in their UV–Vis/emission spectra.

Imaging of 3dMn orbitals in the ferromagnetic state for Ca-substituted manganite: Magnetic Compton investigation

The 3$d$ Mn orbitals in Pr${}_{0.25}$Ca${}_{0.25}$MnO${}_{3}$ (PCMO), in the ferromagnetic phase, were imaged by two-dimensional reconstruction of spin-polarized electron-momentum density projected along the [100] and [110] principal directions. The results were analyzed using a molecular-orbital scheme to understand the population distribution for the ${t}_{2g}$ and the ${e}_{g}$ states for Mn. The analysis shows that the ${t}_{2g}$ states are found to be half-filled, whereas, the ${e}_{g}$ states are dominated mainly by ${x}^{2}\ensuremath{-}{z}^{2}$-type orbitals for both projected [100] and [110] principal directions. The observance of preferential filling of the ${x}^{2}\ensuremath{-}{z}^{2}$-orbital type is consistent with a cooperative Jahn-Teller distortion of the MnO${}_{6}$ octahedra leading to a local tetragonal compression along the $y$ axis for this system. As a result of this distortion, the 3${y}^{2}\ensuremath{-}{r}^{2}$-type orbitals have a small population for PCMO; the ratio of the ${x}^{2}\ensuremath{-}{z}^{2}$-type orbitals to that of the 3${y}^{2}\ensuremath{-}{r}^{2}$-type orbitals is greater than 2, similar to that seen for bilayered manganites.

New tricks by very old dogs: predicting the catalytic hydrogenation of HMF derivatives using Slater-type orbitals

We report new experimental results on the hydrogenation of 5-ethoxymethylfurfural, an important intermediate in the conversion of sugars to industrial chemicals, using eight different M/Al2O3 catalysts (M = Au, Cu, Ni, Ir, Pd, Pt, Rh, and Ru) under various conditions. These data are then compared with the results for 48 bimetallic supported catalysts. The results are explained using a simple and effective model, applying catalyst descriptors based on Slater type orbitals (STOs). Each metal is described using four parameters: the height of the orbital peak, the distance of the peak from the metal atom centre, the peak width at half height, and the peak skewness. Importantly, all these parameters are derived from one simple equation, so the calculation is fast and robust. We then apply these descriptors for modeling the hydrogenation data using multivariate methods. Despite the inherent complexity of the reaction network, these simple models describe the catalysts' performance well. The general application of such descriptor models to in silico design and performance prediction of solid catalysts is discussed.

Synthesis and Characterization of (smif)2Mn(n= 0, M = V, Cr, Mn, Fe, Co, Ni, Ru;n= +1, M = Cr, Mn, Co, Rh, Ir; smif =1,3-di-(2-pyridyl)-2-azaallyl)

A series of Werner complexes featuring the tridentate ligand smif, that is, 1,3-di-(2-pyridyl)-2-azaallyl, have been prepared. Syntheses of (smif)(2)M (1-M; M = Cr, Fe) were accomplished via treatment of M(NSiMe(3))(2)(THF)(n) (M = Cr, n = 2; Fe, n = 1) with 2 equiv of (smif)H (1,3-di-(2-pyridyl)-2-azapropene); ortho-methylated ((o)Mesmif)(2)Fe (2-Fe) and ((o)Me(2)smif)(2)Fe (3-Fe) were similarly prepared. Metatheses of MX(2) variants with 2 equiv of Li(smif) or Na(smif) generated 1-M (M = Cr, Mn, Fe, Co, Ni, Zn, Ru). Metathesis of VCl(3)(THF)(3) with 2 Li(smif) with a reducing equiv of Na/Hg present afforded 1-V, while 2 Na(smif) and IrCl(3)(THF)(3) in the presence of NaBPh(4) gave [(smif)(2)Ir]BPh(4) (1(+)-Ir). Electrochemical experiments led to the oxidation of 1-M (M = Cr, Mn, Co) by AgOTf to produce [(smif)(2)M]OTf (1(+)-M), and treatment of Rh(2)(O(2)CCF(3))(4) with 4 equiv Na(smif) and 2 AgOTf gave 1(+)-Rh. Characterizations by NMR, EPR, and UV-vis spectroscopies, SQUID magnetometry, X-ray crystallography, and DFT calculations are presented. Intraligand (IL) transitions derived from promotion of electrons from the unique CNC(nb) (nonbonding) orbitals of the smif backbone to ligand π*-type orbitals are intense (ε ≈ 10,000-60,000 M(-1)cm(-1)), dominate the UV-visible spectra, and give crystals a metallic-looking appearance. High energy K-edge spectroscopy was used to show that the smif in 1-Cr is redox noninnocent, and its electron configuration is best described as (smif(-))(smif(2-))Cr(III); an unusual S = 1 EPR spectrum (X-band) was obtained for 1-Cr.

A study of the valence shell photoionisation dynamics of pyrimidine and pyrazine

The complete valence shell photoelectron spectra of pyrimidine and pyrazine have been recorded with synchrotron radiation and the observed structure has been interpreted with the aid of vertical ionisation energies and relative spectral intensities calculated using time-dependent density functional theory. The theoretical predictions for the single-hole ionic states due to outer valence shell ionisation agree satisfactorily with the experimental results. Ionisation from the inner valence orbitals is strongly influenced by many-body effects and the intensity associated with a particular orbital is spread amongst numerous satellites. Photoelectron angular distributions and partial cross sections have been determined both experimentally and theoretically, and demonstrate that shape resonances affect the valence shell photoionisation dynamics. In addition to shape resonances occurring a few eV above the ionisation threshold, the calculations indicate that many of the orbitals are influenced by shape resonant processes at much higher energies. Some of these higher energy resonances have been confirmed through a comparison between the relevant theoretical and experimental photoelectron asymmetry parameters. The spectral behaviour of asymmetry parameters associated with π-orbitals has been shown to differ from that of asymmetry parameters associated with σ-orbitals. These differences provide a means of distinguishing between the two types of orbitals even in heavily congested regions of the photoelectron spectrum suffering from band overlap.

Noninnocence in Metal Complexes: A Dithiolene Dawn

Noninnocence in inorganic chemistry traces its roots back half a century to work that was done on metal complexes containing unsaturated dithiolate ligands. In a flurry of activity in the early 1960s by three different research groups, homoleptic bis and tris complexes of these ligands, which came to be known as dithiolenes, were synthesized, and their structural, electrochemical, spectroscopic, and magnetic properties were investigated. The complexes were notable for facile one-electron transfers and intense colors in solution, and conventional oxidation-state descriptions could not account for their electronic structures. The bis complexes were, in general, found to be square-planar, including the first examples of this geometry for paramagnetic complexes and different formal d(n) configurations. Several of the neutral and monoanionic tris complexes were found to have trigonal-prismatic coordination, the first time that this geometry had been observed in molecular metal complexes. Electronic structural calculations employing extended Hückel and other semiempirical computational methods revealed extensive ligand-metal mixing in the frontier orbitals of these systems, including the observation of structures in which filled metal-based orbitals were more stable than ligand-based orbitals of the same type, suggesting that the one-electron changes upon oxidation or reduction were occurring on the ligand rather than on the metal center. A summary of this early work is followed with a brief section on the current interpretations of these systems based on more advanced spectroscopic and computational methods. The take home message is that the early work did indeed provide a solid foundation for what was to follow in investigations of metal complexes containing redox-active ligands.

Use of one-range addition theorems in terms of ϕα for ϕα-ETO and Coulomb- Yukawa like correlated interaction potentials with integer and noninteger indices in evaluation of multicenter multielectron integrals

Multicenter multielectron integrals appearing in the study of multielectron properties of atomic and molecular systems are evaluated using one-range addition theorems in terms of complete orthonormal sets of ϕα-exponential type orbitals (ϕα-ETO, α = 1, 0, −1, −2, …) for ϕα-ETO and Coulomb-Yukawa like correlated interaction potentials (CIP) introduced by the author. The final results are especially useful for the computation of arbitrary multicenter multielectron integrals that arise in the Hartree-Fock- Roothaan (HFR) approximation and also in the explicitly correlated methods based upon the use of ϕα-ETO as basis functions.

Use of noninteger n‐generalized exponential type orbitals with hyperbolic cosine in atomic calculations

AbstractThe efficiency of noninteger n‐generalized exponential type orbitals (NGETO) rn*−1 e with hyperbolic cosine (HC) cosh (βrμ) as radial basis functions in atomic ground state total energy calculations is studied. By the use of these functions, the combined Hartree‐Fock‐Roothaan calculations have been performed for some closed and open shell neutral atoms and their anions and cations with Z ≤ 21. The performance of new basis functions within the minimal basis framework has been compared with numerical Hartree‐Fock (NHF) results. Our total energy values are significantly close to NHF results. The presented minimal basis total energies obtained from the noninteger NGETO with HC are notably better than minimal basis functions total energies previously reported in the literature. It is found that the accuracy of new noninteger NGETO with HC almost correspond to the accuracy of the conventional double‐zeta functions. All the nonlinear parameters are fully optimized. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012

The general Gaussian product theorem

The Gaussian Product Theorem between two 1s Gaussian Type Orbitals (GTOs) is extended to an arbitrary number of s-type functions, giving a compact formula which permits to express the condensed GTO result. Then, this new formulation is combined with the product of arbitrary GTO Cartesian angular parts, obtaining a finite expansion expressing this product as a multilinear combination of such functions sharing a common center. The combination of both results constitutes the General Gaussian Product Theorem (GGPT), a final compact expression for the product of an arbitrary number of Cartesian GTOs. The notation provides an easy way to express algebraically any general multicenter GTO product expression. It is also shown how by means of Nested Summation Symbols the computational implementation can be easily and elegantly achieved. Computational parallelizable schemes of the GGPT are provided.

Ab initio large unit cell calculations of the electronic structure of diamond nanocrystals

In order to reduce computational efforts, and separate surface and core properties, diamond nanocrystals in the present model is represented by a heterojunction between the surface and the core in which the surface represents the outer most four layers and the core by the rest of the internal region of nanocrystal. Ab initio restricted Hartree-Fock (RHF) method coupled with the large unit cell method (LUC) is used to determine the electronic structure and physical properties of diamond nanocrystals core part with different sizes. The use of STO-3G basis choice is made to be able to compare to semiempirical methods using the complete neglect of differential overlap (CNDO) that uses Slater type orbitals (STO). The oxygenated (001)-(1 × 1) facet that expands with larger sizes of nanocrystals is also investigated to determine the rule of the surface in nanocrystals electronic structure. The results show that the present method agrees with semiempirical method contraction of lattice constant with increasing nanocrystal size but disagrees with energy gap variation with nanocrystal size in some regions. After nearly 1.4 nm the energy gap which is controlled by surface states begins to rise. The lowest unoccupied molecular orbital (LUMO) is attributed to surface states that largely reduce the value of energy gap. The sources of disagreement between semiempirical and ab initio results are discussed. The present method shows a maximum increment of the lattice constant by 3.3% over the calculated bulk for the smallest diamond nanocrystals. The surface states are found mostly non-degenerated because of the effect of surface discontinuity and oxygen atoms. Valance and conduction bands are wider on the surface due to splitting and oxygen atoms. The method also shows fluctuations in the converged energy gap, valence band width and cohesive energy of the core part of nanocrystal. These fluctuations might partially explain the controversial experimental results for diamond nanocrystals greater than 1.4 nm in size. The method of the present model has threefold results; it can be used to obtain the electronic structure of bulk, surface, and nanocrystals.

Cis,cis-1,3,5-Trihydroxynonamethylcyclohexasilane: A Cyclopolysilane with Unusual Properties

cis,cis-Trihydroxynonamethylcyclohexasilane (2) is easily accessible by the controlled hydrolysis of Cl3Si6Me9 in the presence of Et3N as an auxiliary base. The crystal structure of 2, as determined by single-crystal X-ray crystallography, exhibits “barrel-type” face-to-face dimeric aggregates held together by six intermolecular hydrogen bonds. NMR and IR spectra suggest that these OH-bonded aggregates are also present in nonpolar solutions. Full geometry optimization (B3LYP/TZVP) of the gas-phase structure of 2 further reveals unusually high energy differences between different conformers and a considerable stabilization of the molecule upon dimerization due to O−H hydrogen bonding. Time-dependent DFT B3LYP/TZVP calculations allow for a detailed interpretation of the UV absorption spectra of 2. The electronic transitions occur between occupied molecular orbitals with predominant σ(Si−Si) character and a small contribution of the oxygen lone pairs, and virtual MOs with contributions from σ*(Si−C), σ*(Si−O), and σ*(Si−Si) type orbitals. If 2 is reacted with MeSiCl3/Et3N, the adamantane-like cage MeSi(O3Si6Me9) (4) is obtained without the formation of considerable amounts of polymeric material, which is most likely a consequence of the preferred conformation of 2 with three adjacent OH groups in axial positions.

Analytical evaluation of Coulomb potential generated by multielectron molecule at arbitrary positions in space using one-range addition theorems of Slater type orbitals

By the use of unsymmetrical one-range addition theorems for Slater type orbitals (STO) and Coulomb potential introduced by the author, the analytical formulae in terms of two- and three-center nuclear attraction integrals, and linear combination coefficients of molecular orbitals are derived for the potential produced by the charges of molecule. These formulae can be useful for the study of interaction between atomic-molecular systems containing any number of closed and open shells when the STO are used in the combined Hartree-Fock-Roothaan (HFR) theory suggested by the author. It should be noted that the symmetry of the potential obtained is the same as the symmetry of the molecule. As an example of application, the calculations have been performed for the potential produced by the ground state of BH (3) molecule[Formula: see text].

Use of Guseinov's One-Center Expansion Formulae and Löwdin α Radial Function in Calculation of Two-Center Overlap Integrals over Slater Type Orbitals with Noninteger Principal Quantum Numbers

Use of Guseinov's One-Center Expansion Formulae and Löwdin α Radial Function in Calculation of Two-Center Overlap Integrals over Slater Type Orbitals with Noninteger Principal Quantum Numbers

Calculation of electric multipole transition radial matrix elements, oscillator strengths and Einstein coefficients over nonrelativistic radial wave function using Slater type orbitals

In this study, a new method is proposed for evaluating electric multipole transition (radial) matrix elements of the generalized type H nl , n ′ l ′ k in hydrogenic atom and ions using the Slater type orbitals (STOs). The formula obtained allows the determination of all multipole transition matrix elements between two different nonrelativistic radial wave functions R nl and R n ′ l ′ . A comparative study carried out between the results of analytical computations and other numerical simulations shows that the methods agree well and emphasizing thus the effectiveness and accuracy of the proposed analytical expressions. The simple equation thus obtained has been found to be remarkable accurate and has shown a wide range of applicability.

Use of combined Hartree–Fock–Roothaan theory in evaluation of lowest states of K[Ar]4s 03d 1 and Cr + [Ar]4s 03d 5 isoelectronic series over noninteger n-Slater type orbitals

By the use of integer and noninteger n-Slater Type Orbitals in combined Hartree-Fock-Roothaan method, self consistent field calculations of orbital and lowest states energies have been performed for the isoelectronic series of open shell systems K [Ar]4s^0 3d^1 2(D) (Z=19-30) and Cr+ [Ar] 4s^0 3d^5 6(S) (Z=24-30). The results of calculations for the orbital and total energies obtained from the use of minimal basis sets of integer- and noninteger n-Slater Type Orbitals are given in tables. The results are compared with the extended-basis Hartree-Fock computations. The orbital and total energies are in good agreement with those presented in the literature. The results are accurately and considerably can be useful in the application of non-relativistic and relativistic combined Hartree-Fock-Roothaan approach for heavy atomic systems.

The use of unsymmetrical one-range addition theorems of Slater type orbitals for the calculation of intermolecular Coulomb interaction energy

The formulae at Hartree–Fock level are derived for the energy of Coulomb interaction between molecules containing any number of closed and open shells. These formulae are expressed in terms of linear combination coefficients of molecular orbitals and multicenter integrals of Slater type orbitals and interaction potentials produced by the charges of the molecules. As an example of application, by the use of unsymmetrical one-range addition theorems of Slater type orbitals the Hartree–Fock–Roothaan calculations have been performed for the energy of interaction produced by the ground states of two molecules H2O.

Electronic Tuning of Ruthenium Complexes by 8‐Quinolate Ligands

A series of Ru(II) complexes were synthesized with the deprotonated forms of the ligands 8-hydroxyquinoline (quo(-)) and 5-NO(2)-8-hydroxyquinoline (5-NO(2)-quo(-)) as analogs to the prototypical complex [Ru(bpy)(3)](2+) (bpy = 2,2'-bipyridine). Electrochemistry, spectroscopy and density functional theory calculations were utilized to investigate the electronic tuning of the occupied t(2g)-type orbitals of the metal center with variation in the ligation sphere. The maximum of the lowest energy absorption of complexes containing one, two and three 8-quinolate ligands progressively redshifts from 452 nm in [Ru(bpy)(3)](2+) to 510 nm in [Ru(bpy)(2)(quo)](+), 515 nm in [Ru(bpy)(quo)(2)] and 540 nm in [Ru(quo)(3)](-) in water. This bathochromic shift results from the increase in energy of the occupied t(2g)-type orbital across the series afforded by coordination of each subsequent quo(-) ligand to the Ru(II) center. Time-dependent density functional theory calculations along with electrochemical analysis reveals that the lowest energy transition has contributions in the highest occupied molecular orbital from both the quo(-) ligand and the metal, such that the lowest energy transition is not from an orbital that is purely metal-centered in character as in [Ru(bpy)(3)](2+).