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  • Parkkinen, Pauli; Losilla, Sergio A.; Solala, Eelis; Toivanen, Elias A.; Xu, Wen-Hua; Sundholm, Dage (2017)
    A grid-based fast multipole method (GB-FMM) for optimizing three-dimensional (3D) numerical molecular orbitals in the bubbles and cube double basis has been developed and implemented. The present GB-FMM method is a generalization of our recently published GB-FMM approach for numerically calculating electrostatic potentials and two-electron interaction energies. The orbital optimization is performed by integrating the Helmholtz kernel in the double basis. The steep part of the functions in the vicinity of the nuclei is represented by one-center bubbles functions, whereas the remaining cube part is expanded on an equidistant 3D grid The integration of 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 kind, analogously to the numerical inward and outward integration approach for calculating two-electron interaction potentials in atomic structure calculations. The expressions and algorithms for massively parallel calculations on general purpose graphics processing units (GPGPU) are described. The accuracy and the correctness of the implementation has been checked by performing Hartree-Fock self-consistent-field calculations (HF-SCF) on H-2, H2O, and CO. Our calculations show that an accuracy of 10(-4) to 10(-7) E-h can be reached in HF-SCF calculations on general molecules.
  • Ridley, Michael; Talarico, Walter; Karlsson, Daniel; Lo Gullo, Nicola; Tuovinen, Riku (2022)
    We review one of the most versatile theoretical approaches to the study of time-dependent correlated quantum transport in nano-systems: the non-equilibrium Green's function (NEGF) formalism. Within this formalism, one can treat, on the same footing, inter-particle interactions, external drives and/or perturbations, and coupling to baths with a (piece-wise) continuum set of degrees of freedom. After a historical overview on the theory of transport in quantum systems, we present a modern introduction of the NEGF approach to quantum transport. We discuss the inclusion of inter-particle interactions using diagrammatic techniques, and the use of the so-called embedding and inbedding techniques which take the bath couplings into account non-perturbatively. In various limits, such as the non-interacting limit and the steady-state limit, we then show how the NEGF formalism elegantly reduces to well-known formulae in quantum transport as special cases. We then discuss non-equilibrium transport in general, for both particle and energy currents. Under the presence of a time-dependent drive-encompassing pump-probe scenarios as well as driven quantum systems-we discuss the transient as well as asymptotic behavior, and also how to use NEGF to infer information on the out-of-equilibrium system. As illustrative examples, we consider model systems general enough to pave the way to realistic systems. These examples encompass one- and two-dimensional electronic systems, systems with electron-phonon couplings, topological superconductors, and optically responsive molecular junctions where electron-photon couplings are relevant.
  • 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.
  • Baryshnikov, G. V.; Valiev, R. R.; Cherepanov, V. N.; Karaush-Karmazin, N. N.; Minaeva, V. A.; Minaev, B. F.; Ågren, H. (2019)
    The electronic structure, absorption and emission spectra, aromaticity and photophysical behavior of the recently synthesized tetrasilatetrathia[8]circulene and tetragermatetrathia[8]circulene compounds have been studied computationally. Both compounds demonstrate a specific bifacial aromaticity, which is unusual for hetero[8]circulenes; the inner eight-membered core sustains an expected strong paratropic magnetically-induced ring current, while the outer perimeter contains saturated Si(Et)2 and Ge(Et)2 moieties which break the conjugation between the thiophene rings. The overall magnetically-induced ring current for both studied circulenes is close to zero because of the strong local diatropic currents in each thiophene ring that compensate the paratropic counterpart. The electronic absorption and emission spectra of tetrasilatetrathia[8]circulene and tetragermatetrathia[8]circulene demonstrate a clear visible vibronic progression. The 0–0 band is the most active one in the absorption spectra, while in the fluorescence spectra the 0–1 band composed of several normal vibrations is more intense compared with the 0–0 band in excellent agreement with experiment. Accounting for spin–orbit coupling effects, an analysis of the photophysical constants for the two compounds demonstrates: (1) a clear manifestation of the internal heavy atom effect on the inter-system crossing efficiency; (2) one to two order domination of non-radiative rates over the fluorescence rate; and (3) that the S1–S0 internal conversion is extremely slow and can not compete with the fluorescence, while the S1–Tn inter-system crossing is a main deactivation channel of the S1 excited state. These results provide new insight into the electronic structure and photophysics of tetrasilatetrathia[8]circulene and tetragermatetrathia[8]circulene as novel standalone representatives of hetero[8]circulenes – tetraannelated derivatives of tetrathienylene.
  • Molina, V.; Rauhalahti, M.; Hurtado, J.; Fliegl, H.; Sundholm, D.; Munoz-Castro, A. (2017)
    [trans-Cu(mu-OH)(mu-dmpz)](6) (1) exhibits six Cu(II) centers effectively coupled through a ligand mediated mechanism leading to a diamagnetic ground state over a wide temperature range. Here we investigate further magneto-structural correlations based on the possible free electron precession along such a copper-based ring-like nanocoil mediated by bridging ligands. We find that in 1, mediated antiferro-magnetic coupling leads to characteristics that induce aromatic ring behavior through evaluation of both induced currents and shielding of cones from a relativistic density functional theory level. According to our gauge calculations including magnetically induced current densities and an induced magnetic field, a sizable ring current strength susceptibility is obtained for the cyclic Cu-N-N-Cu and Cu-O-Cu pathways, allowing a magnetic exchange between the copper centers. Our study suggests that [Cu-6(dmPz)(6)(OH)(6)] consisting of an aromatic ring structure displays aromaticity and superexchange along the Cu-O-Cu and Cu-N-N-Cu backbones, which accounts for 80% and 20% of the overall ring current strength susceptibility, respectively. This reveals the presence of particular aromatic ring characteristics in coordination compounds without a direct metal-metal bond, where several formally paramagnetic centers are antiferromagnetically-coupled through supporting ligands. We envisage that our findings can be extended to other examples depicting ligand-mediated interaction between metal centers.
  • Benkyi, Isaac; Tapavicza, Enrico; Fliegl, Heike; Sundholm, Dage (2019)
    The absorption spectra of naphthalene, anthracene, pentacene and pyrene in the ultraviolet-visible (UV-Vis) range have been simulated by using an efficient real-time generating function method that combines calculated adiabatic electronic excitation energies with vibrational energies of the excited states. The vertical electronic excitation energies have been calculated at the density functional theory level using the PBE0 functional and at the second-order approximate coupled-cluster level (CC2). The absorption spectra have been calculated at the PBE0 level for the studied molecules and at the CC2 level for naphthalene. The transition probabilities between vibrationally resolved states were calculated by using the real-time generating function method employing the full Duschinsky formalism. The absorption spectrum for naphthalene calculated at the PBE0 and CC2 levels agrees well with the experimental one after the simulated spectra have been blue-shifted by 0.48 eV and 0.12 eV at the PBE0 and CC2 level, respectively. The absorption spectra for anthracene, pentacene and pyrene simulated at the PBE0 level agree well with the experimental ones when they are shifted by 0.49 eV, 0.57 eV and 0.46 eV, respectively. The strongest transitions of the main vibrational bands have been assigned.
  • Hirvonen, Viivi; Myllys, Nanna; Kurtén, Theo; Elm, Jonas (2018)
    The role of covalently bound dimer formation is studied using highlevel quantum chemical methods. Reaction free energy profiles for dimer formation between common oxygen-containing functional groups are calculated, and based on the Gibbs free energy differences between transition states and reactants, we show that none of the studied two-component gas-phase reactions are kinetically feasible at 298.15 K and 1 atm. Therefore, the catalyzing effect of water, base, or acid molecules is calculated, and sulfuric acid is identified to lower the activation free energies significantly. We find that the reactions yielding hemiacetal, peroxyhemiacetal, alpha-hydroxyester, and geminal diol products occur with activation free energies of less than 10 kcal/mol with sulfuric acid as a catalyst, indicating that these reactions could potentially take place on the surface of sulfuric acid clusters. Additionally, the formed dimer products bind stronger onto the pre-existing cluster than the corresponding reagent monomers do. This implies that covalent dimerization reactions stabilize the existing cluster thermodynamically and make it less likely to evaporate. However, the studied small organic compounds, which contain only one functional group, not able to form dimer are products that are stable against evaporation at atmospheric conditions. Calculations of dimer formation onto a cluster surface and the clustering ability of dimer products should be extended to large terpene oxidation products in order to estimate the real atmospheric significance.
  • 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.
  • Liu, Ling; Kupiainen-Maatta, Oona; Zhang, Haijie; Li, Hao; Zhong, Jie; Kurten, Theo; Vehkamaki, Hanna; Zhang, Shaowen; Zhang, Yunhong; Ge, Maofa; Zhang, Xiuhui; Li, Zesheng (2018)
    The formation of atmospheric aerosol particles from condensable gases is a dominant source of particulate matter in the boundary layer, but the mechanism is still ambiguous. During the clustering process, precursors with di↵erent reactivities can induce various chemical reactions in addition to the formation of hydrogen bonds. However, the clustering mechanism involving chemical reactions is rarely considered in most of the nucleation process models. Oxocarboxylic acids are common compositions of secondary organic aerosol, but the role of oxocarboxylic acids in secondary organic aerosol formation is still not fully understood. In this paper, glyoxylic acid, the simplest and the most abundant atmospheric oxocarboxylic acids, has been selected as a representative example of oxocarboxylic acids in order to study the clustering mechanism involving hydration reaction using Density Functional Theory combined with the Atmospheric Clusters Dynamic Code. The hydration reaction of glyoxylic acid can occur either in the gas phase or during the clustering process. In atmospheric conditions, the total conversion ratio of glyoxylic acid to its hydration reaction product (2,2-dihydroxyacetic acid) in both gas phase and clusters can be up to 85%, andthe product can further participate in the clustering process. The di↵erences in cluster structures and properties induced by the hydration reaction lead to significant di↵erences in cluster formation rates and pathways at relatively low temperatures.
  • Elm, Jonas; Passananti, Monica; Kurten, Theo; Vehkamäki, Hanna (2017)
    Recent experimental evidence suggests that diamines can enhance atmospheric new particle formation more efficiently compared to monoamines such as dimethylamine Here we investigate the molecular interactions between sulfuric acid (sa) and the diamine putrescine (put) using computational methods. The molecular structure of up to four sulfuric acid molecules and up to four putrescine molecules were obtained, at the omega B97X-D/6-31++G(d,p) level of theory. We utilized a domain local pair natural orbital coupled cluster method (DLPNO-CCSD(T)/aug-cc-pVTZ) to obtain highly accurate binding energies of the clusters. We find that the (sa)(1-4)(put)(1-4) clusters show more ionic character than clusters consisting of sulfuric acid and dimethylamine (dma) by readily forming several sulfate ions in the cluster. To estimate the stability of the clusters, we calculate the evaporation rates and compare them to ESI-APi-TOF measurements. Using the atmospheric cluster dynamics code (ACDC), we simulate and compare the new particle formation rates between the (sa)(1-4)(put)(1-4) and (sa),(1-4)(dma)(1-4) cluster systems. We find that putrescine significantly enhances the formation of new particles compared to dimethylamine. Our findings suggest that a large range of amines with different basicity is capable of explaining various regions of the observed new particle formation events. These results indicate that diamines, or related compounds with high basicity, might be important species in forming the initial cluster with sulfuric acid and subsequently more abundant amines with lower basicity can assist in the new particle formation process by attaching to the sulfuric acid-diamine nucleus.
  • Mendizabal, Fernando; Mera-Adasme, Raul; Xu, Wen-Hua; Sundholm, Dage (2017)
    Dye-sensitized solar-cell (DSSC) systems have been investigated by calculating light-absorption and electron-injection processes of the LD13 ([5,15-bis(2,6-(1,1-dimethylethyl)-phenyl)-10-4-dimethylaminophenylethynyl-20-4-carboxy phenylethynyl porphyrinato]zinc-(II)) and YD2-o-C8 ([5,15bis( 2,6-dioctoxyphenyl)-10-(bis(4-hexylphenyl)amino-20-4-carboxyphenylethynyl)porphyrinato]zinc-(II)) dyes adsorbed on a TiO2 cluster simulating the semiconductor. The binding energy of the dyes with the TiO2 clusters has been calculated at the density functional theory (DFT) level using the B3LYP and CAM-B3LYP functionals. The electronic excitation energies have been calculated at the time-dependent DFT (TDDFT) level for the dyes in the gas and solvent phase employing the B3LYP, CAM-B3LYP and BHLYP functionals. The calculated excitation energies have been compared to values obtained at the algebraic diagrammatic construction through second order (ADC(2)) level of theory. The TDDFT calculations with the B3LYP in tetrahydrofuran solvent with the dye and dye-TiO2 models yield excitation energies that agree well with the transitions in the experimental absorption spectra. Changes in the free energy for electron injection support the better performance of the dyes on the TiO2 clusters.
  • Leverentz, Hannah R.; Siepmann, J. Ilja; Truhlar, Donald G.; Loukonen, Ville; Vehkamäki, Hanna (2013)
  • Nordlund, K. (2019)
    In this Article, I review the development of computer simulation techniques for studying radiation effects in materials from 1946 until 2018. These developments were often closely intertwined with associated experimental developments, which are also briefly discussed in conjunction with the simulations. The focus is on methods that either deal directly with the primary radiation damage generation event, or with such defects or phase changes that typically occur due to radiation. The methods discussed at some length are, in order of historical appearance: Reaction rate theory or rate equations (RE), Monte Carlo neutronics calculations (MCN), Metropolis Monte Carlo (MMC), Molecular Dynamics (MD), Binary Collision Approximation (BCA), Kinetic Monte Carlo (KMC), Discrete Dislocation Dynamics (DDD), Time-Dependent Density Functional Theory (TDDFT), and Finite Element Modelling (FEM). For each method, I present the origins of the methods, some key developments after this, as well as give some opinions on possible future development paths. (C) 2019 The Author. Published by Elsevier B.V.
  • 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.
  • Johansson, Mikael P.; Swart, Marcel (2013)
    By analysing the properties of the electron density in the structurally simple perhalogenated ethanes, X3C–CY3 (X, Y = F, Cl), a previously overlooked non-covalent attraction between halogens attached to opposite carbon atoms is found. Quantum chemical calculations extrapolated towards the full solution of the Schrödinger equation reveal the complex nature of the interaction. When at least one of the halogens is a chlorine, the strength of the interaction is comparable to that of hydrogen bonds. Further analysis shows that the bond character is quite different from standard non-covalent halogen bonds and hydrogen bonds; no bond critical points are found between the halogens, and the σ-holes of the halogens are not utilised for bonding. Thus, the nature of the intramolecular halogen···halogen bonding studied here appears to be of an unusually strong van der Waals type.
  • Taubert, Stefan; Sundholm, Dage; Pichierri, Fabio (2010)
  • Taubert, Stefan; Sundholm, Dage; Pichierri, Fabio (2010)
  • Taubert, Stefan; Sundholm, Dage; Pichierri, Fabio (2010)
  • Mkrtchyan, Satenik; Jakubczyk, Michal; Lanka, Suneel; Yar, Muhammad; Ayub, Khurshid; Shkoor, Mohanad; Pittelkow, Michael; Iaroshenko, Viktor O. (2021)
    We communicate two mild, solvent-free mechanochemical coupling transformations of CF3 group with nitro compounds into amides or Schiff bases employing Ytterbia as a catalyst. This process proceeds via C-F bond activation, accompanied with utilisation of Si-based reductants/oxygen scavengers - reductants of the nitro group. The scope and limitations of the disclosed methodologies are thoroughly studied. To the best of our knowledge, this work is the first example of mechanical energy promoted transformation of the inert CF3 group into other functionalities.