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  • 1
    Language: English
    In: The Journal of chemical physics, 28 August 2012, Vol.137(8), pp.084108
    Description: Analytic second derivatives of the relativistic energy for the calculation of electric response properties are derived utilizing the normalized elimination of the small component (NESC) method. Explicit formulas are given for electric static dipole polarizabilities and infrared intensities by starting at the NESC representation of electric dipole moments. The analytic derivatives are implemented in an existing NESC program and applied to calculate dipole moments, polarizabilities, and the infrared spectra of gold- and mercury-containing molecules as well as some actinide molecules. Comparison with experiment reveals the accuracy of NESC second order electric response properties.
    Keywords: Chemistry ; Physics;
    ISSN: 00219606
    E-ISSN: 1089-7690
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  • 2
    Language: English
    In: The Journal of Chemical Physics, 07 October 2012, Vol.137(13)
    Description: The dependence of the nuclear quadrupole coupling constants (NQCC) on the interaction between electrons and a nucleus of finite size is theoretically analyzed. A deviation of the ratio of the NQCCs obtained from two different isotopomers of a molecule from the ratio of the corresponding bare nuclear electric quadrupole moments, known as quadrupole anomaly, is interpreted in terms of the logarithmic derivatives of the electric field gradient at the nuclear site with respect to the nuclear charge radius. Quantum chemical calculations based on a Dirac-exact relativistic methodology suggest that the effect of the changing size of the Au nucleus in different isotopomers can be observed for Au-containing molecules, for which the predicted quadrupole anomaly reaches values of the order of 0.1%. This is experimentally detectable and provides an insight into the charge distribution of non-spherical nuclei.
    Keywords: Communications
    ISSN: 0021-9606
    E-ISSN: 1089-7690
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  • 3
    Language: English
    In: The Journal of Chemical Physics, 07 July 2013, Vol.139(1)
    Description: A new algorithm for the two-component Normalized Elimination of the Small Component (2cNESC) method is presented and tested in the calculation of spin-orbit (SO) splittings for a series of heavy atoms and their molecules. The 2cNESC is a Dirac-exact method that employs the exact two-component one-electron Hamiltonian and thus leads to exact Dirac SO splittings for one-electron atoms. For many-electron atoms and molecules, the effect of the two-electron SO interaction is modeled by a screened nucleus potential using effective nuclear charges as proposed by Boettger [ Phys. Rev. B 62 , 7809 ( 2000 ) 10.1103/PhysRevB.62.7809 ] . The use of the screened nucleus potential for the two-electron SO interaction leads to accurate spinor energy splittings, for which the deviations from the accurate Dirac Fock-Coulomb values are on the average far below the deviations observed for other effective one-electron SO operators. For hydrogen halides HX (X = F, Cl, Br, I, At, and Uus) and mercury dihalides HgX 2 (X = F, Cl, Br, I) trends in spinor energies and SO splittings as obtained with the 2cNESC method are analyzed and discussed on the basis of coupling schemes and the electronegativity of X.
    Keywords: Articles
    ISSN: 0021-9606
    E-ISSN: 1089-7690
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  • 4
    Language: English
    In: The Journal of Chemical Physics, 07 June 2015, Vol.142(21)
    Description: The analytical gradient for the two-component Normalized Elimination of the Small Component (2c-NESC) method is presented. The 2c-NESC is a Dirac-exact method that employs the exact two-component one-electron Hamiltonian and thus leads to exact Dirac spin-orbit (SO) splittings for one-electron atoms. For many-electron atoms and molecules, the effect of the two-electron SO interaction is modeled by a screened nucleus potential using effective nuclear charges as proposed by Boettger [Phys. Rev. B 62 , 7809 (2000)]. The effect of spin-orbit coupling (SOC) on molecular geometries is analyzed utilizing the properties of the frontier orbitals and calculated SO couplings. It is shown that bond lengths can either be lengthened or shortened under the impact of SOC where in the first case the influence of low lying excited states with occupied antibonding orbitals plays a role and in the second case the jj -coupling between occupied antibonding and unoccupied bonding orbitals dominates. In general, the effect of SOC on bond lengths is relatively small (≤5% of the scalar relativistic changes in the bond length). However, large effects are found for van der Waals complexes Hg 2 and Cn 2 , which are due to the admixture of more bonding character to the highest occupied spinors.
    Keywords: Articles
    ISSN: 0021-9606
    E-ISSN: 1089-7690
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  • 5
    Language: English
    In: The Journal of Chemical Physics, 28 February 2014, Vol.140(8)
    Description: The formic acid dimer in its C 2h -symmetrical cyclic form is stabilized by two equivalent H-bonds. The currently accepted interaction energy is 18.75 kcal/mol whereas the experimental binding energy D 0 value is only 14.22 ±0.12 kcal/mol [ F. Kollipost, R. W. Larsen, A. V. Domanskaya, M. Nörenberg, and M. A. Suhm, J. Chem. Phys. 136 , 151101 ( 2012 ) ]. Calculation of the binding energies D e and D 0 at the CCSD(T) (Coupled Cluster with Single and Double excitations and perturbative Triple excitations)/CBS (Complete Basis Set) level of theory, utilizing CCSD(T)/CBS geometries and the frequencies of the dimer and monomer, reveals that there is a 3.2 kcal/mol difference between interaction energy and binding energy D e , which results from (i) not relaxing the geometry of the monomers upon dissociation of the dimer and (ii) approximating CCSD(T) correlation effects with MP2. The most accurate CCSD(T)/CBS values obtained in this work are D e = 15.55 and D 0 = 14.32 kcal/mol where the latter binding energy differs from the experimental value by 0.1 kcal/mol. The necessity of employing augmented VQZ and VPZ calculations and relaxing monomer geometries of H-bonded complexes upon dissociation to obtain reliable binding energies is emphasized.
    Keywords: Articles
    ISSN: 0021-9606
    E-ISSN: 1089-7690
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  • 6
    Language: English
    In: The Journal of Chemical Physics, 14 November 2016, Vol.145(18)
    Description: The analytical energy gradient and Hessian of the two-component Normalized Elimination of the Small Component (2c-NESC) method with regard to the components of the electric field are derived and used to calculate spin-orbit coupling (SOC) corrected dipole moments and dipole polarizabilities of molecules, which contain elements with high atomic number. Calculated 2c-NESC dipole moments and isotropic polarizabilities agree well with the corresponding four-component-Dirac Hartree–Fock or density functional theory values. SOC corrections for the electrical properties are in general small, but become relevant for the accurate prediction of these properties when the molecules in question contain sixth and/or seventh period elements (e.g., the SO effect for At 2 is about 10% of the 2c-NESC polarizability). The 2c-NESC changes in the electric molecular properties are rationalized in terms of spin-orbit splitting and SOC-induced mixing of frontier orbitals with the same j = l + s quantum numbers.
    Keywords: Articles
    ISSN: 0021-9606
    E-ISSN: 1089-7690
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  • 7
    Language: English
    In: The Journal of chemical physics, 28 June 2011, Vol.134(24), pp.244117
    Description: The analytical energy gradient of the normalized elimination of the small component (NESC) method is derived for the first time and implemented for the routine calculation of NESC geometries and other first order molecular properties. Essential for the derivation is the correct calculation of the transformation matrix U relating the small component to the pseudolarge component of the wavefunction. The exact form of ∂U/∂λ is derived and its contribution to the analytical energy gradient is investigated. The influence of a finite nucleus model and that of the picture change is determined. Different ways of speeding up the calculation of the NESC gradient are tested. It is shown that first order properties can routinely be calculated in combination with Hartree-Fock, density functional theory (DFT), coupled cluster theory, or any electron correlation corrected quantum chemical method, provided the NESC Hamiltonian is determined in an efficient, but nevertheless accurate way. The general applicability of the analytical NESC gradient is demonstrated by benchmark calculations for NESC/CCSD (coupled cluster with all single and double excitation) and NESC/DFT involving up to 800 basis functions.
    Keywords: Articles;
    ISSN: 00219606
    E-ISSN: 1089-7690
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  • 8
    Language: English
    In: The Journal of Chemical Physics, 07 August 2012, Vol.137(5)
    Description: Based on the analytic derivatives formalism for the spin-free normalized elimination of the small component method, a new computational scheme for the calculation of the electric field gradient at the atomic nuclei was developed and presented. The new computational scheme was tested by the calculation of the electric field gradient at the mercury nucleus in a series of Hg-containing inorganic and organometallic compounds. The benchmark calculations demonstrate that the new formalism is capable of reproducing experimental and theoretical reference data with high accuracy. The method developed can be routinely applied to the calculation of large and very large molecules and holds considerable promise for the interpretation of the experimental data of biologically relevant compounds containing heavy elements.
    Keywords: Articles
    ISSN: 0021-9606
    E-ISSN: 1089-7690
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  • 9
    Language: English
    In: The Journal of Chemical Physics, 04/07/2017, Vol.146(13), p.134109
    Description: A new method for calculating nuclear magnetic resonance shielding constants of relativistic atoms based on the two-component (2c), spin-orbit coupling including Dirac-exact NESC (Normalized Elimination of the Small Component) approach is developed where each term of the diamagnetic and paramagnetic contribution to the isotropic shielding constant σiso is expressed in terms of analytical energy derivatives with regard to the magnetic field B and the nuclear magnetic moment 𝝁. The picture change caused by renormalization of the wave function is correctly described. 2c-NESC/HF (Hartree-Fock) results for the σiso values of 13 atoms with a closed shell ground state reveal a deviation from 4c-DHF (Dirac-HF) values by 0.01%–0.76%. Since the 2-electron part is effectively calculated using a modified screened nuclear shielding approach, the calculation is efficient and based on a series of matrix manipulations scaling with (2M)3 (M: number of basis functions).
    Keywords: Spin-Orbit Interactions ; Basis Functions ; Mathematical Analysis ; Magnetic Shielding ; Magnetic Moments ; Constants ; Diamagnetism ; Nuclei ; Nuclear Magnetic Resonance–NMR;
    ISSN: 0021-9606
    E-ISSN: 1089-7690
    Source: CrossRef
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  • 10
    Language: English
    In: The Journal of Chemical Physics, 28 August 2012, Vol.137(8)
    Description: Information on the electronic structure of a molecule and its chemical bonds is encoded in the molecular normal vibrational modes. However, normal vibrational modes result from a coupling of local vibrational modes, which means that only the latter can provide detailed insight into bonding and other structural features. In this work, it is proven that the adiabatic internal coordinate vibrational modes of Konkoli and Cremer [ Int. J. Quantum Chem. 67 , 29 ( 1998 )] 10.1002/(SICI)1097-461X(1998)67:1〈29::AID-QUA3〉3.0.CO;2-0 represent a unique set of local modes that is directly related to the normal vibrational modes. The missing link between these two sets of modes are the compliance constants of Decius, which turn out to be the reciprocals of the local mode force constants of Konkoli and Cremer. Using the compliance constants matrix, the local mode frequencies of any molecule can be converted into its normal mode frequencies with the help of an adiabatic connection scheme that defines the coupling of the local modes in terms of coupling frequencies and reveals how avoided crossings between the local modes lead to changes in the character of the normal modes.
    Keywords: Articles
    ISSN: 0021-9606
    E-ISSN: 1089-7690
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