High-pressure synthesis and superconductivity of a new binary barium germanide BaGe3

A new binary barium germanide BaGe(3) was prepared by high-pressure and high-temperature reactions using a Kawai type multi-anvil press. It crystallizes in a hexagonal unit cell with a = 6.814(1) ?, c = 5.027(8) ?, and V = 202.2(5) ?(3) (the space group P6(3)/mmc, No. 194). The unit cell contains two layers along the c axis composed of Ba atoms and Ge(3) triangular units. The triangular units stack along the c axis to form 1D columns in which the adjacent Ge(3) units turn to opposite directions. The columns, therefore, can be described as the face-sharing stacking of elongated Ge(6) octahedra. Each Ba atom is surrounded by six columns. BaGe(3) is metallic and shows superconductivity at 4.0 K. The band structure calculations revealed that there are four conduction bands mainly composed of Ge 4p and Ba 5d orbitals. From Fermi surface analysis, we confirmed that three of them have a large contribution of Ge 4pz orbitals in the vicinity of the Fermi level and show a simple 1D appearance. The remaining one contains Ge 4px, 4py, and Ba 5d contributions and shows a 2D property.     

Coupled-cluster with active space selected higher amplitudes: performance of seminatural orbitals for ground and excited state calculations

The active space approach for coupled-cluster models is generalized using the general active space concept and implemented in a string-based general coupled-cluster code. Particular attention is devoted to the choice of orbitals on which the subspace division is based. Seminatural orbitals are proposed for that purpose. These orbitals are obtained by diagonalizing only the hole-hole and particle-particle block of the one-electron density of a lower-order method. The seminatural orbitals are shown to be a good replacement for complete active space self-consistent field orbitals and avoid the ambiguities with respect to the reference determinant introduced by the latter orbitals. The seminatural orbitals also perform well in excited state calculations, including excited states with strong double excitation contributions, which usually are difficult to describe with standard coupled-cluster methods. A set of vertical excitation energies is obtained and benchmarked against full configuration interaction calculations, and alternative hierarchies of active space coupled-cluster models are proposed. As a simple application the spectroscopic constants of the C(2) B (1)Delta(g) and B(') (1)Sigma(g) (+) states are calculated using active space coupled-cluster methods and basis sets up to quadruple-zeta quality in connection with extrapolation and additivity schemes.     

Hartree-Fock orbitals for complex-scaled configuration interaction calculation of highly excited Feshbach resonances

We examine a complex-scaled configuration interaction [(CS)CI] for highly excited Feshbach resonances, where we study the 2s(2) resonance of helium as a test case. Sizable full-CI calculations are reduced by using a correctly defined minimum active space. We compare the convergence of the minimum active space for conventional Hartree-Fock (HF) orbitals obtained as solutions to Hermitian HF equations, to the convergence of minimum active space for complex orbitals obtained as solutions to complex-scaled HF equations. Ground-state optimized orbitals are compared to a simple modification of the HF method using the excited-state mean-field potential.     

Orbital signatures of methyl in L-alanine

Molecular orbital signatures of the methyl substituent in L-alanine have been identified with respect to those of glycine from information obtained in coordinate and momentum space, using dual space analysis. Electronic structural information in coordinate space is obtained using ab initio (MP2/TZVP) and density functional theory (B3LYP/TZVP) methods, from which the Dyson orbitals are simulated based on the plane wave impulse approximation into momentum space. In comparison to glycine, relaxation in geometry and valence orbitals in L-alanine is found as a result of the attachment of the methyl group. Five orbitals rather than four orbitals are identified as methyl signatures. That is, orbital 6a in the core shell, orbitals 11a and 12a in the inner valence shell, and orbitals 19a and 20a in the outer valence shell. In the inner valence shell, the attachment of methyl to glycine causes a splitting of its orbital 10a' into orbitals 11a and 12a of L-alanine, whereas in the outer valence shell the methyl group results in an insertion of an additional orbital pair of 19a and 20a. The frontier molecular orbitals, 24a and 23a, are found without any significant role in the methylation of glycine.     

Intramolecular interactions of L‐phenylalanine: Valence ionization spectra and orbital momentum distributions of its fragment molecules

Intramolecular interactions between fragments of L ‐phenylalanine, i.e., phenyl and alaninyl, have been investigated using dual space analysis (DSA) quantum mechanically. Valence space photoelectron spectra (PES), orbital energy topology and correlation diagram, as well as orbital momentum distributions (MDs) of L ‐phenylalanine, benzene and L ‐alanine are studied using density functional theory methods. While fully resolved experimental PES of L ‐phenylalanine is not yet available, our simulated PES reproduces major features of the experimental measurement. For benzene, the simulated orbital MDs for 1e_1g and 1a_2u orbitals also agree well with those measured using electron momentum spectra. Our theoretical models are then applied to reveal intramolecular interactions of the species on an orbital base, using DSA. Valence orbitals of L ‐phenylalanine can be essentially deduced into contributions from its fragments such as phenyl and alaninyl as well as their interactions. The fragment orbitals inherit properties of their parent species in energy and shape (ie., MDs). Phenylalanine orbitals show strong bonding in the energy range of 14‐20 eV, rather than outside of this region. This study presents a competent orbital based fragments‐in‐molecules picture in the valence space, which supports the fragment molecular orbital picture and building block principle in valence space. The optimized structures of the molecules are represented using the recently developed interactive 3D‐PDF technique. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2011     

Methylation of zebularine investigated using density functional theory calculations

Deoxyribonucleic acid (DNA) methylation is an epigenetic phenomenon, which adds methyl groups into DNA. This study reveals methylation of a nucleoside antibiotic drug 1‐(β‐D ‐ribofuranosyl)‐2‐pyrimidinone (zebularine or zeb) with respect to its methylated analog, 1‐(β‐D ‐ribofuranosyl)‐5‐methyl‐2‐pyrimidinone (d5) using density functional theory calculations in valence electronic space. Very similar infrared spectra suggest that zeb and d5 do not differ by types of the chemical bonds, but distinctly different Raman spectra of the nucleoside pair reveal that the impact caused by methylation of zeb can be significant. Further valence orbital‐based information details on valence electronic structural changes caused by methylation of zebularine. Frontier orbitals in momentum space and position space of the molecules respond differently to methylation. Based on the additional methyl electron density concentration in d5, orbitals affected by the methyl moiety are classified into primary and secondary contributors. Primary methyl contributions include MO8 (57a), MO18 (47a), and MO37 (28a) of d5, which concentrates on methyl and the base moieties, suggest certain connection to their Frontier orbitals. The primary and secondary methyl affected orbitals provide useful information on chemical bonding mechanism of the methylation in zebularine. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

Are there atomic orbitals in a molecule?

Effective atomic orbitals (AOs) have been calculated by the method of the "fuzzy atoms" analysis by using the numerical molecular orbitals (MOs) obtained from plane-wave DFT calculation, i.e., without introducing any atom-centered functions. The results show that in the case of nonhypervalent atoms there are as many effective AOs with non-negligible occupation numbers, as many orbitals are in the classical minimal basis set of the given atom. This means that, for nonhypervalent systems, it is possible to present the MOs as sums of effective atomic orbitals that resemble very much the atomic minimal basis orbitals of the individual atoms (or their hybrids). For hypervalent atoms some additional orbitals basically of d-type are also of some importance; they are necessary to describe the back-donation to these positive atoms. It appears that the d-type orbitals play a similar role also for strongly positive carbon atoms. The method employed here is also useful to decide whether the use of polarization functions of a given type is a matter of conceptual importance or has only a numerical effect.     

Exact wave functions for few-particle systems: The choice of expansion for coulomb potentials

We discuss a procedure for calculating numerical Hartree–Fock orbitals that can be applied to polyatomic systems. This approach is formulated in momentum space to avoid Coulomb singularities and uses fast Fourier transforms to solve integral convolutions. Results for a number of simple systems are presented.     

1,3-二氮杂薁类衍生物电子结构和光谱性质的理论研究

对1,3-二氮杂薁类衍生物采用密度泛函理论(DFT)在B3LYP/6-31G(d)的水平上进行了几何构型的全优化, 在此基础上探讨了分子结构和前线分子轨道能量等性质的变化规律, 采用含时密度泛函理论(TD-DFT)计算了分子的电子跃迁性质, 采用二维平面图和三维立体图来直观表示激发态的性质, 研究分子内电子转移特性. 跃迁密度矩阵的二维等高线图反映了电子-空穴相干性, 三维跃迁密度图反映了跃迁偶极矩的方向和强度, 三维电荷差异密度图说明了激发过程中分子内电子转移性质.     

Variationally optimized basis orbitals for biological molecules

Numerical atomic basis orbitals are variationally optimized for biological molecules such as proteins, polysaccharides, and deoxyribonucleic acid within a density functional theory. Based on a statistical treatment of results of a fully variational optimization of basis orbitals (full optimized basis orbitals) for 43 biological model molecules, simple sets of preoptimized basis orbitals classified under the local chemical environment (simple preoptimized basis orbitals) are constructed for hydrogen, carbon, nitrogen, oxygen, phosphorous, and sulfur atoms, each of which contains double valence plus polarization basis function. For a wide variety of molecules we show that the simple preoptimized orbitals provide well convergent energy and physical quantities comparable to those calculated by the full optimized orbitals, which demonstrates that the simple preoptimized orbitals possess substantial transferability for biological molecules.     

Multiple basis sets in calculations of triples corrections in coupled-cluster theory

Multiple basis sets are used in calculations of perturbational corrections for triples replacements in the framework of single-reference coupled-cluster theory. We investigate a computational procedure, where the triples correction is calculated from a reduced space of virtual orbitals, while the full space is employed for the coupled-cluster singles-and-doubles model. The reduced space is either constructed from a prescribed unitary transformation of the virtual orbitals (for example into natural orbitals) with subsequent truncation, or from a reduced set of atomic basis functions. After the selection of a reduced space of virtual orbitals, the singles and doubles amplitudes obtained from a calculation in the full space are projected onto the reduced space, the remaining set of virtual orbitals is brought into canonical form by diagonalizing the representation of the Fock operator in the reduced space, and the triples corrections are evaluated as usual. The case studies include the determination of the spectroscopic constants of N₂, F₂, and CO, the geometry of O₃, the electric dipole moment of CO, the static dipole polarizability of F⁻, and the Ne⋯Ne interatomic potential. Received: 28 December 1996 / Accepted: 8 April 1997     

Fourier transform general formula for systematic potentials

For calculating molecular integrals of systematic potentials, a three‐dimensional (3D) Fourier transform general formula can be derived, by the use of the Abel summation method. The present general formula contains all 3D Fourier transform formulas which are well known as Bethe–Salpeter formulas (Bethe and Salpeter, Handbuch der Physik, Bd. XXXV, 1957) as special cases. It is shown that, in several of the Bethe–Salpeter formulas, the integral does not converge in the meaning of the Riemann integral but converges in the meaning of a hyper function as the Schwartz distribution. For showing an effectiveness of the present general formula, the convergence condition of molecular integrals is derived generally for all of the present potentials. It is found that molecular integrals can be converged in the meaning of the Riemann integral for the present potentials, except for those for extra super singular potentials. It is also found that the convergence condition of molecular integrals over the Slater‐type orbitals is exactly the same as that of the corresponding integrals over the Gaussian‐type orbitals for the present systematic potentials. For showing more effectiveness, the molecular integral over the gauge‐including atomic orbitals is derived for the magnetic dipole‐same‐dipole interaction. © 2012 Wiley Periodicals, Inc.     

饱和烷烃分子C_nH_(2n+2)(n=4-6)的电子动量光谱(英文)

使用B3LYP/TZVP//B3LYP/aug-cc-pVTZ方法系统研究了饱和烷烃分子CnH2n+2(n=4-6)的轨道电子动量光谱,比较了同分异构体CnH2n+2(n=4-6)对轨道动量分布的影响.结合二维空间分析方法对电子在坐标空间中的密度分布进行了系统的研究.计算结果表明,最内价壳层电荷分布主要由s电子贡献,第二近邻芯价壳层则主要由p电子贡献,而其余的价壳层则为sp杂化.最内价轨道表现出最大的谱线强度并且远大于其它轨道的谱线强度,而且正烷烃的谱线强度要大于异烷烃等同分异构体的谱线强度,表现出了明显的与甲基移动的个数有关的性质.     

The unrestricted natural orbital-restricted active space method: methodology and implementation

The full configuration interaction method in the space of fractionally occupied unrestricted natural orbitals (UNO-CAS method) is extended to excited states as well as to strongly correlated and reactive systems with large active spaces. This is accomplished by␣using restricted active space (RAS) wave functions introduced by Olsen et al. [(1988) J Chem Phys 89: 2185] and using the UNOs without the expensive orbital optimization step. In RAS, the space of active orbitals is subdivided into three groups: a group with essentially doubly occupied orbitals (RAS1), the usual CAS space (RAS2), and a space with weakly occupied active orbitals (RAS3). We select these spaces on the basis of the occupation numbers of the UNOs. All possible electron distributions are allowed in the usual CAS space, but the number of vacancies is limited in RAS1 and the number of electrons is limited in RAS3. We discuss an efficient algorithm for generating a RAS wave function. This is based on the Handy-Knowles determinantal expansion with an addressing scheme adopted for the restricted expansion. Results for both ground and excited states of azulene and free base porphyrin are presented. Received: 16 July 1998 / Accepted: 7 August 1998 / Published online: 19 October 1998     

Thiepin‐Fused Heteroacenes: Simple Synthesis,Unusual Structure,and Semiconductors with Less Anisotropic Behavior

The simple one‐pot syntheses of sulfur‐rich thiepin‐fused heteroacences with an alkylidene–fluorene framework, THA1 and THA6 (thiepin‐fused heteroacene 1 or 6, in which the thiepin is conjugated at both ortho positions with S? CH₃ or S? C₆H₁₃, respectively), is reported. Based on electrochemical studies and theoretical calculations, their LUMO energies are relatively low (?3.26 eV), and their HOMO and HOMO?1 orbitals are nearly degenerate. The thiepin ring contributes mainly to HOMO?1 and LUMO orbitals, however, HOMO orbitals dominantly reside on thienoacence rings. Within the crystal of THA1, the molecules adopt a herringbone arrangement and multiple intermolecular interactions lead to the formation of a 2D network. Interestingly, THA6 shows totally different intermolecular arrangements. Organic field‐effect transistor (OFET) devices show both compounds exhibiting p‐type semiconducting behavior. Thin films or microcrystals of THA1 possess relatively high hole mobility. Moreover, the mobilities of the microcrystal of THA1 along three directions are in the same order, thus the hole‐carrier transporting within the hexagonal‐plane of microcrystal of THA1 exhibits less anisotropic behavior. In comparison, both thin films and microrods of THA6 show low hole mobilities. This agrees well with the intermolecular arrangements and interactions within crystal of THA6. Further theoretical calculations reveal that significant intermolecular electronic coupling among HOMO?1 orbitals and sulfur atoms play an important role in intermolecular electronic coupling for THA1.     

Scaling the Coulomb interaction in calculations of electron spectra of transition metal complexes

A simple technique of scaling two-electron integrals in ab initio calculations of the electronically excited states of transition metal complexes is proposed. This technique uses the fact that one-center two-electron integrals depend linearly on the scaling factor when Slater type functions are subjected to scaling transformation. This leads to a linear dependence of the d—d transition energy on the “scale” of Coulomb interaction, which allows one to affect the calculation result by varying the Slater exponential. To test the technique, ab initio configuration interaction and full active space calculations of the low excited states of the CrF ₆ ^3- , MnF ₆ ^2- , and VF ₆ ^3- complexes are performed. For transition elements, a basis of Slater type effective functions chosen from the optical spectra of the atoms and ions of transition elements is used. It is shown that in the STO-6G basis with effective exponentials, experimental transitions are reproduced with an accuracy of about 2000 cm^-1 even with the use of small active space determined by the orbitals localized on the central atom of the complex.     

Local Hartree–Fock orbitals using a three‐level optimization strategy for the energy

Using the three‐level energy optimization procedure combined with a refined version of the least‐change strategy for the orbitals—where an explicit localization is performed at the valence basis level—it is shown how to more efficiently determine a set of local Hartree–Fock orbitals. Further, a core–valence separation of the least‐change occupied orbital space is introduced. Numerical results comparing valence basis localized orbitals and canonical molecular orbitals as starting guesses for the full basis localization are presented. The results show that the localization of the occupied orbitals may be performed at a small computational cost if valence basis localized orbitals are used as a starting guess. For the unoccupied space, about half the number of iterations are required if valence localized orbitals are used as a starting guess compared to a canonical set of unoccupied Hartree–Fock orbitals. Different local minima may be obtained when different starting guesses are used. However, the different minima all correspond to orbitals with approximately the same locality. © 2013 Wiley Periodicals, Inc.     

6‐31G* basis set for third‐row atoms

Medium basis sets based upon contractions of Gaussian primitives are developed for the third‐row elements Ga through Kr. The basis functions generalize the 6‐31G and 6‐31G* sets commonly used for atoms up to Ar. A reexamination of the 6‐31G* basis set for K and Ca developed earlier leads to the inclusion of 3d orbitals into the valence space for these atoms. Now the 6‐31G basis for the whole third‐row K through Kr has six primitive Gaussians for 1s, 2s, 2p, 3s, and 3p orbitals, and a split‐valence pair of three and one primitives for valence orbitals, which are 4s, 4p, and 3d. The nature of the polarization functions for third‐row atoms is reexamined as well. The polarization functions for K, Ca, and Ga through Kr are single set of Cartesian d‐type primitives. The polarization functions for transition metals are defined to be a single 7f set of uncontracted primitives. Comparison with experimental data shows good agreement with bond lengths and angles for representative vapor‐phase metal complexes. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 976–984, 2001     

Theory of complete orthonormal relativistic vector wave function sets and Slater type relativistic vector orbitals in coordinate,momentum and four-dimensional spaces

The new analytical relations for the relativistic vector wave functions and Slater type relativistic vector orbitals in coordinate, momentum and four-dimensional spaces are derived using the properties of quasirelativistic vector spherical harmonics introduced by the author in previous paper (I.I. Guseinov, J. Math. Chem., 44, 197 (2008)) and complete orthonormal scalar basis sets of nonrelativistic ψ ^α -exponential type orbitals (ψ ^α -ETO), -momentum space orbitals (-MSO) and z ^α -hyperspherical harmonics (z ^α -HSH). The 6-component relativistic vector wave functions obtained are complete without the inclusion of the continuum. The relativistic vector wave function sets and Slater type relativistic vector orbitals are expressed through the corresponding quasirelativistic vector wave functions and Slater vector orbitals, respectively. The analytical formulas are also derived for overlap integrals over Slater type relativistic vector orbitals with the same screening constants in coordinate space.