100,471 research outputs found
Non-perturbative magnetic phenomena in closed-shell paramagnetic molecules
No full textBy means of non-perturbative ab initio calculations, it is shown that paramagnetic closed-shell molecules are characterized by a strongly non-linear magnetic response, whose main feature consists of a paramagnetic-to-diamagnetic transition in a strong magnetic field. The physical origin of this phenomenon is rationalised on the basis of an analytical model based on molecular orbital theory. For the largest molecules considered here, the acepleiadylene dianion and the corannulene dianion, the transition field is of the order of 10 3 T, about one order of magnitude larger than the magnetic field strength currently achievable in experimental settings. However, our simple model suggests that the paramagnetic-to-diamagnetic transition is a universal property of paramagnetic closed-shell systems in strong magnetic fields, provided no singlet-triplet level crossing occurs for fields smaller than the critical transition field. Accordingly, fields weaker than 100 T should suffice to trigger the predicted transition for systems whose size is still well within the (medium-large) molecular domain, such as hypothetical antiaromatic rings with less than one hundred carbon atoms. © 2009 the Owner Societies
Accurate calculation and modeling of the adiabatic connection in density functional theory
No full textUsing a recently implemented technique for the calculation of the adiabatic connection (AC) of density functional theory (DFT) based on Lieb maximization with respect to the external potential, the AC is studied for atoms and molecules containing up to ten electrons: the helium isoelectronic series, the hydrogen molecule, the beryllium isoelectronic series, the neon atom, and the water molecule. The calculation of AC curves by Lieb maximization at various levels of electronic-structure theory is discussed. For each system, the AC curve is calculated using Hartree–Fock (HF) theory, second-order Møller–Plesset (MP2) theory, coupled-cluster singles-and-doubles (CCSD) theory, and coupled-cluster singles-doubles-perturbative-triples [CCSD(T)] theory, expanding the molecular orbitals and the effective external potential in large Gaussian basis sets. The HF AC curve includes a small correlation-energy contribution in the context of DFT, arising from orbital relaxation as the electron-electron interaction is switched on under the constraint that the wave function is always a single determinant. The MP2 and CCSD AC curves recover the bulk of the dynamical correlation energy and their shapes can be understood in terms of a simple energy model constructed from a consideration of the doubles-energy expression at different interaction strengths. Differentiation of this energy expression with respect to the interaction strength leads to a simple two-parameter doubles model (AC-D) for the AC integrand (and hence the correlation energy of DFT) as a function of the interaction strength. The structure of the triples-energy contribution is considered in a similar fashion, leading to a quadratic model for the triples correction to the AC curve (AC-T). From a consideration of the structure of a two-level configuration-interaction (CI) energy expression of the hydrogen molecule, a simple two-parameter CI model (AC-CI) is proposed to account for the effects of static correlation on the AC. When parametrized in terms of the same input data, the AC-CI model offers improved performance over the corresponding AC-D model, which is shown to be the lowest-order contribution to the AC-CI model. The utility of the accurately calculated AC curves for the analysis of standard density functionals is demonstrated for the BLYP exchange-correlation functional and the interaction-strength-interpolation (ISI) model AC integrand. From the results of this analysis, we investigate the performance of our proposed two-parameter AC-D and AC-CI models when a simple density functional for the AC at infinite interaction strength is employed in place of information at the fully interacting point. The resulting two-parameter correlation functionals offer a qualitatively correct behavior of the AC integrand with much improved accuracy over previous attempts. The AC integrands in the present work are recommended as a basis for further work, generating functionals that avoid spurious error cancellations between exchange and correlation energies and give good accuracy for the range of densities and types of correlation contained in the systems studied here
Range-dependent adiabatic connections
No full textRecently, we have implemented a scheme for the calculation of the adiabatic connection linking the Kohn–Sham system to the physical, interacting system. This scheme uses a generalized Lieb functional, in which the electronic interaction strength is varied in a simple linear fashion, keeping the potential or the density fixed in the process. In the present work, we generalize this scheme further to accommodate arbitrary two-electron operators, allowing the calculation of adiabatic connections following alternative paths as outlined by Yang [J. Chem. Phys. 109, 10107 (1998)] . Specifically, we examine the error-function and Gaussian-attenuated error-function adiabatic connections. It is shown that while the error-function connection displays some promising features, making it amenable to the possible development of new exchange-correlation functionals by modeling the adiabatic connection integrand, the Gaussian-attenuated error-function connection is less promising. We explore the high-density and strong static correlation regimes for two-electron systems. Implications of this work for the utility of range-separated schemes are discussed
Nonperturbative ab initio calculations in strong magnetic fields using London orbitals
No full textA self-consistent field (SCF) London-orbital computational scheme to perform gauge-origin independent nonperturbative calculations for molecules in strong magnetic fields is presented. The crucial difference in the proposed approach with respect to common-origin finite-field SCF implementations consists in the evaluation of molecular integrals over the field-dependent molecular basis functions, which is tantamount to computing molecular integrals in a hybrid Gaussian and plane-wave basis set. The implementation of a McMurchie-Davidson scheme for the calculation of the molecular integrals over London orbitals is discussed, and preliminary applications of the newly developed code to the calculation of fourth-rank hypermagnetizabilities for a set of small molecules, benzene, and cyclobutadiene are presented. The nonperturbative approach is particularly useful for studying the highly nonlinear response of paramagnetic closed-shell systems such as boron monohydride, or the π -electron response of cyclobutadiene. © 2008 American Institute of Physics
The equilibrium structure of ferrocene
No full textThe molecular structures of ferrocene in the eclipsed (equilibrium) and staggered (saddle-point) conformations have been determined by full geometry optimizations at the levels of second-order Møller–Plesset (MP2) theory, coupled-cluster singles-and-doubles (CCSD) theory and CCSD theory with a perturbative triples correction [CCSD(T)] in a TZV2P+f basis set. Existing experimental results are reviewed. The agreement between the CCSD(T) results and experiment is in all cases excellent; the calculated structure parameters and the barrier to internal rotation of the ligand rings differ from the most accurate experimental values by calculations for single-configuration-dominated transition metal complexes such as ferrocene thus appear to have an accuracy comparable to that observed for molecules containing only first- and second-row atoms, and to be of a quality similar to that obtained experimentally. A comparison with previous DFT results indicates that the B3LYP model gives overall the overall the best DFT results,
with a deviation of around 2 pm for the metal–carbon distance
and smaller errors for the cyclopentadienyl rings
The calculation of adiabatic-connection curves from fullconfiguration-interaction (FCI) densities: two-electronsystems
No full textHartree-Fock and Kohn-Sham time-dependent response theory in a second-quantization atomic-orbital formalism suitable for linear scaling
No full textWe present a second-quantization based atomic-orbital method for the computation of
time-dependent response functions within Hartree-Fock and Kohn-Sham density-functional
theories. The method is suited for linear scaling. Illustrative results are presented for excitation
energies, one- and two-photon transition moments, polarizabilities, and hyperpolarizabilities for
hexagonal BN sheets with up to 180 atoms
A closed-shell coupled-cluster treatment of the Breit--Paulifirst-order relativistic energy correction
No full textCalculation of electric dipole hypershieldings at the nuclei in the Hellmann--Feynman approximation.
No full textThe third-rank electric hypershieldings at the nuclei of four small molecules have been evaluated atthe Hartree–Fock level of theory in the Hellmann–Feynman approximation. The nuclear electrichypershieldings are closely related to molecular vibrational absorption intensities and ageneralization of the atomic polar tensors ~expanded in powers of the electric field strength! isproposed to rationalize these intensities. It is shown that the sum rules for rototranslationalinvariance and the constraints imposed by the virial theorem provide useful criteria for basis-setcompleteness and for near Hartree–Fock quality of nuclear shieldings and hypershieldingsevaluated in the Hellmann–Feynman approximation. Twelve basis sets of different size and qualityhave been employed for the water molecule in an extended numerical test on the practicality of theproposed scheme. The best results are obtained with the R12 and R121 basis sets, designed for thecalculation of electronic energies by the explicitly correlated R12 method. The R12 basis set issubsequently used to investigate three other molecules, CO, N2 , and NH3 , verifying that the R12basis consistently performs very well
Range-dependent adiabatic connections
No full textRecently, we have implemented a scheme for the calculation of the adiabatic connection linking the Kohn–Sham
system to the physical, interacting system. This scheme uses a generalized Lieb functional, in which the electronic-interaction
strength is varied in a simple linear fashion, keeping the potential or the density fixed in the process. In the present work,
we generalize this scheme further to accommodate arbitrary two-electron operators, allowing the calculation of adiabatic
connections following alternative paths as outlined by Yang [J. Chem. Phys. 109, 10107 (1998)]. Specifically, we examine the
error-function and Gaussian-attenuated error-function adiabatic connections. We explore the high-density and strong staticcorrelation
regimes for two-electron systems. The resulting adiabatic connections give an alternative view of the exchange–
correlation problem and their utility for the development of new exchange–correlation functionals in Kohn–Sham and rangeseparated
hybrid schemes is discussed
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