Theoretical study of valance photoelectron spectra of hypoxanthine, xanthine, and caffeine using direct symmetry-adapted cluster/configuration interaction methodology

UV photoelectron spectra of hypoxanthine, xanthine, and caffeine, up to 20 eV, were calculated and compared with the experimental spectra reported in literature. The calculations were performed using a novel version of the quantum mechanical symmetry-adapted cluster/configuration interaction (SAC-CI) method termed, direct SAC-CI. The Duning/Huzinaga valance double-zeta D95+(d,p) Gaussian basis set was also employed with this method. The ionization energies and intensities were calculated, and the corresponding spectral bands were assigned. Natural bonding orbital (NBO) calculations were employed for better spectral band assignment. The calculated ionization energies and intensities reasonably produced the experimental photoelectron spectra.     

The Photoelectron Spectrum of Tetrafluorobutatriene

The He(I_α) and He(II_α) spectra of tetrafluorobutatriene 3 (F) have been recorded for comparison with those of butatriene 3 (H). Ab initio double-zeta basis self-consistent field (SCF) and configuration interaction calculations on butatriene show that, contrary to previous assignment, no shake-up band is expected to appear in the 9–10 eV energy range of the photoelectron spectrum. Further, such SCF calculations on tetrafluorobutatriene support the use of the perfluoro effect in assigning the purely π orbital ionizations. It is argued that 3 (F) is a key compound for the study of the perfluoro effect. This is supported by a qualitative comparison of its photoelectron-spectroscopic results with those of other perfluoro systems.     

The effect of bond functions on molecular dissociation energies

Multi-reference Cl calculations are reported for the ground states of HCl and N₂ at their equilibrium distances, and for their separated atoms. Basis sets of double-zeta and double-zeta plus polarization quality are systematically augmented by additional sets of functions located at the bond centers. It is shown that use of bond functions can lead to either an underestimate or an overestimate of the the bond energy. Optimum basis sets for each molecule were obtained, giving D_e values of 4.59 eV for HCl (expt. 4.62 eV) and 9.96 eV for N₂ (expt. 9.905 eV) at the estimated full Cl level. The quality of the potential curves obtained with these basis sets is discussed.     

Valence band structure of cellulose and lignin studied by XPS and DFT

In this report, X-ray induced photoelectron spectroscopy (XPS) measurements of the valence band structure of cellulose and lignin are combined with a theoretical reconstruction of the spectra based on density functional theory (DFT) calculations. These calculations involve an analysis of the valence band structures and their respective orbitals in which basic units of cellulose and lignin are considered. In addition, photoionization cross sections are incorporated for reconstruction of the XPS spectra. This combination of theoretical calculations and experimental measurements revealed that an emission present up to 10 eV in the valence band structure is dominated by oxygen rather than by carbon, as reported in literature. Furthermore, a quantitative elemental analysis shows significant carbon contributions at binding energies above 13 eV. The valence band analysis supported by DFT provides a powerful basis for a detailed interpretation of spectroscopic data and enables a profound insight into application relevant processes in future.     

Binding energies at different momenta for the valence orbitals of HCl by the binary (e, 2e) method

The binding energy spectra for the valence orbitals of hydrogen chloride have been obtained using the binary (e,2e) method at 1200 eV. The strength of the innermost valence orbital (4σ) is severely split among several ion states in the energy range 25 to 41 eV. The measured cross sections are compared with results of calculations using contracted Gaussian basis sets of double-zeta quality, and with a one-particle Green's function calculation.     

Correlation corrected band structures of homopolypeptides v. B3LYP band structures of 19 homopolypeptides

Ab initio B3LYP crystal orbital (CO) calculations have been performed on the 19 homopolypeptides (PolyGly, PolyAla, PolySer, PolyThre, PolyLeu, PolyiLeu, PolyVal, PolyAspAc, PolyAsp, PolyGlutAc, PolyGlut, PolyHist, PolyProl, PolyCyst, PolyMeth, PolyTyr, PolyPhenAla, PolyArg, and PolyLys) in their β pleated sheet conformation. Keeping the main chain conformation fixed as in PolyGly, the side chain geometries were optimized. For the calculation 2n+1 different k points were used with n = 8 for the case of simpler and n = 10 for more complicated side chains. The basis set applied was the double ζ one of Clementi. According to the results obtained, the conduction bands are shifted upward and the valance band downward, compared with the results of previous BLYP 1 and LDA 7 CO calculations. The bandwidths are similar to the previous cases. The band edges are in many cases not at the endpoints of the first Brillouin zones, causing nonmonotonous dispersion of both the conduction bands (CB) and the valance bands (VB), respectively. The fundamental gap values due to the upward shifts of the CB and downward shifts of the VB are substantially larger than in the case of our previous DFT CO calculations (values 6.0–7.0 eV). They are very close to the gap values, which can be estimated on the basis of experimental ultraviolet (UV) spectra of some homopolypeptides and on the basis of intermediate exciton theoretical calculations (6.5–7.5 eV). These surprisingly good results for the gaps are due to the compensation of errors (LDA or BLYP gives too small and simple HF provides too large gap values) in the B3LYP method. The admixture of the exact HF exchange with a weight of 0.19 obviously compensates the self interaction error occurring in the LDA or BLYP methods. This article discusses whether/how this result could be established by other B3LYP CO calculations on simple polymer chains and on stacked systems (e.g., nucleotide base stacks). Furthermore, a comparative analysis of the ground state DFT methods, the HF method and of the optimized effective potential method could throw more light on our successful theoretical results for the gaps of the homopolypeptides. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Energy band gaps and lattice parameters evaluated with the Heyd-Scuseria-Ernzerhof screened hybrid functional

This work assesses the Heyd-Scuseria-Ernzerhof (HSE) screened Coulomb hybrid density functional for the prediction of lattice constants and band gaps using a set of 40 simple and binary semiconductors. An extensive analysis of both basis set and relativistic effects is given. Results are compared with established pure density functionals. For lattice constants, HSE outperforms local spin-density approximation (LSDA) with a mean absolute error (MAE) of 0.037 A for HSE vs 0.047 A for LSDA. For this specific test set, all pure functionals tested produce MAEs for band gaps of 1.0-1.3 eV, consistent with the very well-known fact that pure functionals severely underestimate this property. On the other hand, HSE yields a MAE smaller than 0.3 eV. Importantly, HSE correctly predicts semiconducting behavior in systems where pure functionals erroneously predict a metal, such as, for instance, Ge. The short-range nature of the exchange integrals involved in HSE calculations makes their computation notably faster than regular hybrid functionals. The current results, paired with earlier work, suggest that HSE is a fast and accurate alternative to established density functionals, especially for solid state calculations.     

Calculation of electron detachment energies for water cluster anions: an appraisal of electronic structure methods, with application to (H2O)20- AND (H2O)24-

We present benchmark calculations of vertical electron detachment energies (VDEs) for various conformers of (H2O)n-, using both wave function and density functional methods, in sequences of increasingly diffuse Gaussian basis sets. For small clusters (n < or = 6), a systematic examination of VDE convergence reveals that it is possible to converge this quantity to within approximately 0.01 eV of the complete-basis limit, using a highly diffuse but otherwise economical Pople-style basis set of double-zeta quality, with 28 atom-centered basis functions per water molecule. Floating-center basis functions can be useful but are not required to obtain accurate VDEs. Second-order M?ller-Plesset perturbation (MP2) theory suffices to obtain VDEs that are within 0.05 eV of the results from both experiment and coupled-cluster theory, and which always err toward underbinding the extra electron. In contrast to these consistent predictions, VDEs calculated using density functional theory (DFT) vary widely, according to the fraction of Hartree-Fock exchange in a given functional. Common functionals such as BLYP and B3LYP overestimate the VDE by 0.2-0.5 eV, whereas a variant of Becke's "half and half" functional is much closer to coupled-cluster predictions. Exploratory calculations for (H2O)20- and (H2O)24- cast considerable doubt on earlier calculations that were used to assign the photoelectron spectra of these species to particular cluster isomers.     

On the electronic band structure of periodic β-pleated sheet polypeptides in the presence of water and ions

The structure of the possible water surroundings of several periodic polypeptides in the -pleated sheet conformation has been determined by Monte-Carlo calculations. The resulting water positions have been used to calculate the band structure of the polymers in the effective field of these water molecules. In addition, similar calculations have been performed with sodium ions in the solution. It has been found that the changes of the band widths and of the band gaps are less than 1.8 eV in the presence of water and less than 1.1 eV in the presence of water and ions. The band positions themselves are, however, shifted by up to 3.7 eV in the presence of water and by up to 6 eV in the presence of water and ions.Dedicated to Professor J. Koutecký on the occasion of his 65th birthday     

Approximate STO functions for the first-row transition metal atoms

Slater type orbital (STO) basis sets for the atoms Sc-Zn have been derived using a technique based on the distance between subspaces. The accuracy for several properties of these basis sets has been tested. Basis sets studied are of both single- and double-zeta sizes, although this technique can be generalized for any size. Uniform quality criteria through the series of atoms Sc-Zn are difficulty to establish due to the varying number of d electrons. A comparative study at the atomic level of the quality of STO basis sets (both the two new basis sets and Clementi's basis sets) for the first-row transition elements has been carried out. Results show that the new basis sets provide better simulation for several properties. Molecular calculations on compounds with these atoms using a Gaussian expansion fitted according to the new values of optimized STOs are also included. The results obtained are similar to those reported when STO-3G basis set is used.     

The photoelectron spectrum of HCP and comments on the first photoelectron band of HCN

The photoelectron spectrum of HCP has been obtained, Ionization potentials are found at 10.79 ± 0.01 eV (X² Π) and 12.86 ± 0.01 eV (A ² Σ). By comparison with HCP, a new interpretation of the first photoelectron band of HCN has been proposed which involves a Renner-Teller interaction in the Σ⁺ vibronic states of the molecular ion.     

Equation-of-motion coupled-cluster study on exciton states of polyethylene with periodic boundary condition

Equation-of-motion coupled cluster with singles and doubles (EOM-CCSD) method has been applied to exciton states of polyethylene using ab initio crystal Hartree-Fock method with one-dimensional periodic boundary condition. Full transformation of two-electron integrals from atomic-orbital basis to crystal-orbital basis has been performed for EOM-CCSD calculations. In order to make transformed integrals to have correct properties of translational symmetry, a lattice summation scheme has been proposed. The EOM-CCSD excitation energies have been obtained for the lowest singlet and triplet exciton states of polyethylene. The excitation energies converge with system size much faster than oligomer calculations using n-alkanes. Quasiparticle energy-level calculations by second-order many-body perturbation theory and by solving the inverse Dyson equation have also been performed to obtain exciton binding energies. Basis set dependencies on excitation energy, quasiparticle band gap, and exciton binding energy have been investigated. At the 6-31+G level, the excitation energy of the lowest singlet-exciton state and its binding energy are calculated to be 8.1 and 3.2 eV, respectively. The calculated excitation energy is well comparable with the corresponding experimental value, 7.6 eV.     

A CI non-empirical pseudopotential calculation of the vertical valence excited states of the iodine molecule

The non-empirical atomic pseudopotential proposed by Durand and Barthelat has been used, together with the CIPSI algorithm for large scale CI, to calculate the vertical transition energies of the iodine molecule, in a valence extended (double-zeta + d) basis set. All the valence excited states were considered. The mixing of configurations is very important especially for the Σ⁺_g, Π_g and Π_u symmetries. The experimentally known transition energies are calculated within a 1 eV error, despite the lack of diffuse orbitals and spin-orbit interaction. Some qualitative Mulliken's estimates are discussed. A new ³Σ⁺_g state from the 10 σ_u → 11 σ_u single excitation is predicted in the 9 eV region.     

Configuration interaction calculation of the potential curves for the C3 molecule in its ground and lowest-lying Πu states

Ab initio SCF and Cl calculations are reported for the C₃ molecule using a basis set of double-zeta plus polarization quality. Potential curves are obtained for the symmetric stretch and bending and antisymmetric stretch vibrational coordinates for the ground and 3σ_u → l π_g^3,1Π_u excited states of this system in order to calculate the intensity distributions for the associated electronic transitions. The calculated T₀ value for the ¹Π_u ← X?¹ ∑⁺_g transition of 3.03 eV is in quite good agreement with the location of the origin of the 4050 Å (3.06 eV) band system in C₃, confirming its previous assignment to this electronic transition; the lifetime of the ¹H_u upper state is also obtained in the CI treatment. A value of 2.04 eV is calculated for the corresponding ³Π_u ← X?¹ ∑⁺_g origin, which result in turn suggests that the weak feature starting at 2.10 eV (5900 Å) should be assigned thereto.     

A constrained variational approach to the designing of low transport band gap materials: A multiobjective random mutation hill climbing method

Neutral polythiophene (PT) and polyselenophene (PSe) are semiconductors with band gaps of about 2 eV. We have proposed and implemented a constrained variational method in which total energy of neutral PT or PSe oligomers is minimized under the constraint that the band gap measured by HOMO–LUMO energy difference is also a minimum in each case. The constrained (bimodal) minimization has been carried out by an adaptive random mutation hill climbing method within the basic framework of Su‐Schrieffer‐Heeger type of model. We show that the “band‐gap constrained minimization” automatically creates electron deficient quinoid regions (QR) in the PT or PSe chains, embedded in aromatic regions (ARs), on both sides. We have investigated how the number and distribution of such QRs can reduce the band gap. Band gap constrained electronic structure calculations thus provide designing clues for low transport band gap materials based on molecular chromophores. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

A scheme for the economical use of numerical basis sets in calculations with SIESTA

We demonstrate the effectiveness of an economical scheme that uses numerical basis sets in computations with SIESTA. The economical basis sets demonstrated, in which high-level double-zeta basis plus polarization orbitals (DZP) are applied only for atoms of strong electronegativity and metal atoms while a double-zeta basis is applied to the rest of the atoms of small proton-bound carboxylic acid clusters and sodium–organic compounds, predict correct geometric structures very close to those obtained using DZP for all atoms. The use of economical basis sets can save about 30–50% of the CPU time that is used for calculations with large basis sets. This study provides a general guideline for basis set selection in SIESTA computations of large systems.Acknowledgement. The work described in this paper was fully supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (project no. CityU 1033/00P).     

The two-dimensional band structure of (polyphthalocyaninato)Ni(II)

The two-dimensional (2D) band structure of (polyphthalocyaninato)Ni(II), Ni(ppc), has been analyzed by a self-consistent field (SCF ) Hartree–Fock (HF ) crystal orbital (CO ) formalism based on an INDO (intermediate neglect of differential overlap) type Hamiltonian. The calculated HF band gap of Ni(ppc) amounts to 0.24 eV. The highest filled band is a ringlike a_1u combination (D_4h symmetry label) localized at the carbon sites of the organic fragment. Remarkable hybridization in the valence band leads to the considerable band width Δ?_v of 2.92 eV. This value is close to the Δ?_v numbers which are conventionally encountered in one-dimensional metallomacrocycles. The effective width of the states in Ni(ppc) is 13.8 eV. In graphite a net π interval of 13.0 eV is predicted by the present CO formalism; i.e., the energetic distribution of the π electrons is roughly comparable in both 2D solids. The Ni 3d states in Ni(ppc) are far below the Fermi level which is calculated at ?4.9 eV; they are predicted between ?12.2 and ?16.4 eV in the mean-field approximation. Quasi-particle corrections lead to a significant shift of these strongly metal-centered states. Important electronic structure properties of Ni(ppc) are compared with those of 1D metallomacrocycles with similar molecular stoichiometry. The total density of states distribution of Ni(ppc) has been fragmented into projected (ligand π and σ, Ni 3d) contributions in order to allow for a transparent interpretation of the 2D band structure.     

Electrically polarized valence basis sets for the SBKJC effective core potential developed for calculations of dynamic polarizabilities and Raman intensities

Sadlej’s electric polarization method of Gaussian basis functions was applied to the double-zeta effective core potential basis sets of Stevens, Basch, Krauss, Jasien and Cundari to generate a new augmented polarized valence double-zeta set, named as pSBKJC, which is appropriate for the calculation of dynamic polarizabilities and Raman intensities. The pSBKJC basis set was developed for the atoms of families 14–17 (from C to F, Si to Cl, Ge to Br and Sn to I). In order to assess the performance of this new basis set, these properties were compared to those evaluated using Sadlej’s set, available in the EMSL online library under the name of Sadlej-pVTZ. In these tests, Hartree-Fock/pSBKJC calculations have proved to be less demanding of the computer than the Hartree-Fock/Sadlej-pVTZ ones but give results in excellent agreement with those from the Sadlej-pVTZ basis set. Since the Stevens et al. pseudopotential can represent the scalar relativistic effects, the results obtained at the Hartree-Fock/pSBKJC level show a better agreement with the results of Dirac-Hartree-Fock/Sadlej-pVTZ relativistic calculations using Dyall’s spin-free Hamiltonian. When comparing Hartree-Fock/pSBKJC data of Raman scattering activities, at the excitation wavelength of 488 nm, with those of spin-free Dirac-Hartree-Fock/Sadlej-pVTZ calculations, a very good agreement is observed, where the RMS error is 8.5 Å⁴a.m.u.^?1 and the averaged percentage error is 3.4%. In terms of computer savings in calculations of dynamic Raman intensities, a 20% reduction in the CPU time in the coupled cluster singles and doubles intensities of C₆H₆ and about 40% reduction in the time-dependent Hartree-Fock intensities for C₆F₆ molecules were attained.