Browsing by Subject "HARTREE-FOCK"

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  • Lehtola, Susi; Blockhuys, Frank; Van Alsenoy, Christian (2020)
    A uniform derivation of the self-consistent field equations in a finite basis set is presented. Both restricted and unrestricted Hartree-Fock (HF) theory as well as various density functional approximations are considered. The unitary invariance of the HF and density functional models is discussed, paving the way for the use of localized molecular orbitals. The self-consistent field equations are derived in a non-orthogonal basis set, and their solution is discussed also in the presence of linear dependencies in the basis. It is argued why iterative diagonalization of the Kohn-Sham-Fock matrix leads to the minimization of the total energy. Alternative methods for the solution of the self-consistent field equations via direct minimization as well as stability analysis are briefly discussed. Explicit expressions are given for the contributions to the Kohn-Sham-Fock matrix up to meta-GGA functionals. Range-separated hybrids and non-local correlation functionals are summarily reviewed.
  • Benkyi, Isaac; Sundholm, Dage (2019)
    Magnetically induced current densities are reported for porphycenes at the density functional theory level using gauge-including atomic orbitals, which ensure gauge-origin independence and a fast basis-set convergence of the current densities. We have analyzed the current densities by using the gauge-including magnetically induced current (GIMIC) method. The porphycenes are found to be aromatic. They sustain strong diatropic ring currents. The ring-current pathways have been obtained by integrating the strength of the current density passing selected bonds. The calculations show that the ring current of the porphycenes divides into an outer and inner pathways at the pyrrolic rings. Thus, the ring current involves all 26 pi electrons of the porphycenes, which is similar to the ring current of porphin. No significant local ring currents are sustained by the pyrrolic rings. Dihydroporphycene with four inner hydrogens is found to be antiaromatic with weakly aromatic pyrrolic rings. The six-membered rings in benzoporphycene sustain local paratropic ring currents. The global ring current of dibenzoporphycene divides into an outer and inner pathway at the benzoic rings. Interactions between the inner hydrogen and the neighbor nitrogen are found to be more significant for differences in the H-1 NMR shieldings than variations in global ring-current strengths. We found that the antiaromatic dihydroporphycene has a larger HOMO-LUMO gap but a smaller optical gap than the aromatic porphycene.
  • Lehtola, Susi (2019)
    Electronic structure calculations, such as in the Hartree-Fock or Kohn-Sham density functional approach, require an initial guess for the molecular orbitals. The quality of the initial guess has a significant impact on the speed of convergence of the self-consistent field (SCF) procedure. Popular choices for the initial guess include the one-electron guess from the core Hamiltonian, the extended Huckel method, and the superposition of atomic densities (SAD). Here, we discuss alternative guesses obtained from the superposition of atomic potentials (SAP), which is easily implementable even in real-space calculations. We also discuss a variant of SAD which produces guess orbitals by purification of the density matrix that could also be used in real-space calculations, as well as a parameter-free variant of the extended Huckel method, which resembles the SAP method and is easy to implement on top of existing SAD infrastructure. The performance of the core Hamiltonian, the SAD, and the SAP guesses as well as the extended Huckel variant is assessed in nonrelativistic calculations on a data set of 259 molecules ranging from the first to the fourth periods by projecting the guess orbitals onto precomputed, converged SCF solutions in single- to triple-zeta basis sets. It is shown that the proposed SAP guess is the best guess on average. The extended Huckel guess offers a good alternative, with less scatter in accuracy.
  • Popov, Georgi; Bačić, Goran; Mattinen, Miika; Manner, Toni; Lindström, Hannu; Seppänen, Heli; Suihkonen, Sami; Vehkamäki, Marko; Kemell, Marianna; Jalkanen, Pasi; Mizohata, Kenichiro; Räisänen, Jyrki; Leskelä, Markku; Koivula, Hanna Maarit; Barry, Seán T.; Ritala, Mikko (2020)
    Atomic layer deposition (ALD) is a viable method for depositing functional, passivating, and encapsulating layers on top of halide perovskites. Studies in that area have only focused on metal oxides, despite a great number of materials that can be made with ALD. This work demonstrates that, in addition to oxides, other ALD processes can be compatible with the perovskites. We describe two new ALD processes for lead sulfide. These processes operate at low deposition temperatures (45-155 degrees C) that have been inaccessible to previous ALD PbS processes. Our processes rely on volatile and reactive lead precursors Pb(dbda) (dbda = rac-N-2,N-3-di-tertbutylbutane-2,3-diamide) and Pb(btsa)(2) (btsa = bis(trimethylsilyl)amide) as well as H2S. These precursors produce high quality PbS thin films that are uniform, crystalline, and pure. The films exhibit p- type conductivity and good mobilities of 10-70 cm(2) V-1 s(-1). Low deposition temperatures enable direct ALD of PbS onto a halide perovskite CH3NH3PbI3 (MAPI) without its decomposition. The stability of MAPI in ambient air is greatly improved by capping with ALD PbS. More generally, these new processes offer valuable alternatives for PbS-based devices, and we hope that this study will inspire more studies on ALD of non-oxides on halide perovskites.
  • Mera-Adasme, Raul; Xu, Wen-hua; Sundholm, Dage; Mendizabal, Fernando (2016)
    Solar power is a strong alternative to the currently used fossil fuels in order to satisfy the world's energy needs. Among them, dye-sensitized solar cells (DSSC) represent a low-cost option. Efficient and cheap dyes are currently needed to make DSSCs competitive. Computational chemistry can be used to guide the design of new light-absorbing chromophores. Here, we have computationally studied the lowest excited states of ZnPBAT, which is a recently synthesized porphyrinoid chromophore with high light-absorption efficiency. The calculations have been performed at ab initio correlated levels of theory employing second-order coupled clusters (CC2) and algebraic diagrammatic construction using second order (ADC(2)) methods and by performing density functional theory (DFT) calculations using the time-dependent DFT (TDDFT) approach for excitation energies. The ultraviolet-visible (UV-vis) spectrum calculated at the ADC(2) and CC2 levels agrees well with the experimental one. The calculations show that ZnPBAT has six electronic transitions in the visible range of the absorption spectrum. The ab initio correlated calculations and previously reported experimental data have been used to assess the performance of several well-known density functionals that have been employed in the present TDDFT study. Solvent effects have been estimated by using the conductor-like screening model (COSMO). The influence of the addition of a TiO2 cluster to the chromophore systems has also been investigated. The results indicate that both CAM-B3LYP and Becke's "half-and-half'' (BHLYP) density functionals are appropriate for the studies of excitation energies in the blue range of the visible spectrum for these kinds of porphyrinoid chromophores, whereas the excitation energies of the Q band calculated at the ab initio correlated level are more accurate than those obtained in the present TDDFT calculations. The inclusion of solvent effects has a modest influence on the spectrum of the protonated form of the studied chromophores, whereas solvent models are crucial when studying the absorption spectrum of the anionic chromophore. The calculated UV-vis spectrum for the chromophore anion is not significantly affected by attaching a TiO2 cluster to it.
  • Valiev, Rashid R.; Fliegl, Heike; Sundholm, Dage (2017)
    Magnetizabilities and magnetically induced ring-current strength susceptibilities have been calculated at the Hartree-Fock, density functional theory and second order Moller-Plesset levels for a number of antiaromatic closed-shell carbaporphyrins, carbathia-porphyrins and isophlorins. The calculations yield a linear relation between magnetizabilities and ring-current strength susceptibilities. The calculations show that the porphyrinoids with the largest ring-current strength susceptibility are closed-shell paramagnetic molecules with positive magnetizabilities. The closed-shell paramagnetism is due to the large paramagnetic contribution to the magnetizability originating from the strong paratropic ring current in the antiaromatic porphyrinoids.
  • Lehtola, Susi; Dimitrova, Maria; Sundholm, Dage (2020)
    We present fully numerical electronic structure calculations on diatomic molecules exposed to an external magnetic field at the unrestricted Hartree-Fock limit, using a modified version of a recently developed finite-element programme, HelFEM. We have performed benchmark calculations on a few low-lying states of H-2, HeH+, LiH, BeH+, BH and CH+ as a function of the strength of an external magnetic field parallel to the molecular axis. The employed magnetic fields are in the range of B = [0, 10] B-0 atomic units, where B-0 approximate to 2.35 x 10(5) T. We have compared the results of the fully numerical calculations to ones obtained with the LONDON code using a large uncontracted gauge-including Cartesian Gaussian (GICG) basis set with exponents adopted from the Dunning aug-cc-pVTZ basis set. By comparison to the fully numerical results, we find that the basis set truncation error (BSTE) in the GICG basis is of the order of 1 kcal/mol at zero field, that the BSTE grows rapidly in increasing magnetic field strength, and that the largest BSTE at B = 10 B-0 exceeds 1000 kcal/mol. Studies in larger Gaussian-basis sets suggest that reliable results can be obtained in GICG basis sets at fields stronger than B = B-0, provided that enough higher-angular-momentum functions are included in the basis.
  • Rabaa, Hassan; Omary, Mohammad A.; Taubert, Stefan; Sundholm, Dage (2018)
    The molecular structure of stacked cyclic trinuclear gold(I) complexes [Au-3(RN=CR'(3)](n), with n = 1-4, where R = H, methyl (Me), cyclopentyl ((c)Pe), and phenyl (Ph) and R' = OH and methoxy (OMe) were studied computationally at the second-order Moller-Plesset (MP2) and density functional theory (DFT) levels of theory. At the DFT level, the aurophilic and dispersion interactions were accounted for by using the TPSS functional in combination with the semiempirical D3 correction. The structure optimizations yielded the lowest energy for a slided stacked structure of the [Au-3(HN=COH)(3)](2) dimer, where monomers are slightly shifted relative to one another. At the MP2 level, the slided structure is 32 kJ/mol more stable than the staggered dimer structure, which in turn is energetically 11 kJ/mol below the eclipsed structure. The calculations show that aromatic ligands lead to a planar and prismatic structure of [Au-3(PhN=COMe)(3)](4), whereas for [Au-3('PeN=COMe)(3)](4), a chair conformation is obtained due to steric effects. Excitation energies were calculated for [Au-3(RN=CR')(3)] and [Au-3(RN=CR'(3)](2) with R = H, Me, and 'Pe and R' = OH and OMe at the time-dependent DFT level using the optimized molecular structures of the singlet ground state. To simulate the luminescence spectra, the lowest triplet excitation energy was also calculated for the molecular structure of the lowest triplet state. The calculated excitation energies of [Au-3(HN=COH)(3)] and [Au-3(HN=COH)(3)](2) are compared with values obtained at the approximate singles and doubles coupled cluster (CC2) and the second-order algebraic diagrammatic construction (ADC(2)) levels of theory. The calculated absorption and emission energies reproduce the experimental trends, with extremely large Stokes shifts. A solvoluminescence mechanism is also proposed.
  • Solala, Eelis; Losilla, Sergio A.; Sundholm, Dage; Xu, Wenhua; Parkkinen, Pauli (2017)
    We present an integration scheme for optimizing the orbitals in numerical electronic structure calculations on general molecules. The orbital optimization is performed by integrating the Helmholtz kernel in the double bubble and cube basis, where bubbles represent the steep part of the functions in the vicinity of the nuclei, whereas the remaining cube part is expanded on an equidistant threedimensional grid. The bubbles' part is treated by using one-center expansions of the Helmholtz kernel in spherical harmonics multiplied with modified spherical Bessel functions of the first and second kinds. The angular part of the bubble functions can be integrated analytically, whereas the radial part is integrated numerically. The cube part is integrated using a similar method as we previously implemented for numerically integrating two-electron potentials. The behavior of the integrand of the auxiliary dimension introduced by the integral transformation of the Helmholtz kernel has also been investigated. The correctness of the implementation has been checked by performing Hartree-Fock self-consistent-field calculations on H-2, H2O, and CO. The obtained energies are compared with reference values in the literature showing that an accuracy of 10(-4) to 10(-7) E-h can be obtained with our approach. Published by AIP Publishing.
  • Frediani, Luca; Sundholm, Dage (2015)
  • Sun, Qiming; Zhang, Xing; Banerjee, Samragni; Bao, Peng; Barbry, Marc; Blunt, Nick S.; Bogdanov, Nikolay A.; Booth, George H.; Chen, Jia; Cui, Zhi-Hao; Eriksen, Janus Juul; Gao, Yang; Guo, Sheng; Hermann, Jan; Hermes, Matthew R.; Koh, Kevin; Koval, Peter; Lehtola, Susi; Li, Zhendong; Liu, Junzi; Mardirossian, Narbe; McClain, James D.; Motta, Mario; Mussard, Bastien; Pham, Hung Q.; Pulkin, Artem; Purwanto, Wirawan; Robinson, Paul J.; Ronca, Enrico; Sayfutyarova, Elvira; Scheurer, Maximilian; Schurkus, Henry F.; Smith, James E. T.; Sun, Chong; Sun, Shi-Ning; Upadhyay, Shiv; Wagner, Lucas K.; Wang, Xiao; White, Alec; Whitfield, James Daniel; Williamson, Mark J.; Wouters, Sebastian; Yang, Jun; Yu, Jason M.; Zhu, Tianyu; Berkelbach, Timothy C.; Sharma, Sandeep; Sokolov, Alexander; Chan, Garnet Kin-Lic (2020)
    PySCF is a Python-based general-purpose electronic structure platform that supports first-principles simulations of molecules and solids as well as accelerates the development of new methodology and complex computational workflows. This paper explains the design and philosophy behind PySCF that enables it to meet these twin objectives. With several case studies, we show how users can easily implement their own methods using PySCF as a development environment. We then summarize the capabilities of PySCF for molecular and solid-state simulations. Finally, we describe the growing ecosystem of projects that use PySCF across the domains of quantum chemistry, materials science, machine learning, and quantum information science. Published under license by AIP Publishing.
  • Fliegel, Helke; Dimitrova, Maria; Berger, Raphael J. F.; Sundholm, Dage (2021)
    A recently developed methodology for calculating, analyzing, and visualizing nuclear magnetic shielding densities is used for studying spatial contributions including ring-current contributions to 1H nuclear magnetic resonance (NMR) chemical shifts of aromatic and anti-aromatic free-base porphyrinoids. Our approach allows a visual inspection of the spatial origin of the positive (shielding) and negative (deshielding) contributions to the nuclear magnetic shielding constants. Diatropic and paratropic current-density fluxes yield both shielding and deshielding contributions implying that not merely the tropicity of the current density determines whether the contribution has a shielding or deshielding character. Instead the shielding or deshielding contribution is determined by the direction of the current-density flux with respect to the studied nucleus.
  • Solala, Eelis; Parkkinen, Pauli; Sundholm, Dage (2018)
    Canonical decomposition methods and the Tucker decomposition method have been applied to the cube part of the orbitals in the bubbles and cube framework for numerical electronic structure calculations on molecules. The iterative process of two variants of the alternating least squares method for performing canonical decomposition is found to converge rapidly to a given accuracy, whereas the accuracy is not significantly improved by continuing the iterations, implying that the studied canonical decomposition methods are not of practical use in our approach to numerical electronic structure calculations. The Tucker decomposition method of the orbitals is on the other hand found to have relative errors that are smaller than the numerical accuracy of the orbitals. The calculations also show that the reconstruction of the orbitals leads to errors that are well below the required accuracy.