Biomedical subjects

Rodney J Bartlett

Publications and source records attributed to Rodney J Bartlett.

18 recordsLinked to original sources

PubMed2006

Addition by subtraction in coupled-cluster theory: a reconsideration of the CC and CI interface and the nCC hierarchy.

The nCC hierarchy of coupled-cluster approximations, where n guarantees exactness for n electrons and all products of n electrons are derived and applied to several illustrative problems. The condition of exactness for n=2 defines nCCSD=2CC, with nCCSDT=3CC and nCCSDTQ=4CC being exact for three and four electrons. To achieve this, the minimum number of diagrams is evaluated, which is less than in the corresponding CC model. For all practical purposes, nCC is also the proper definition of a size-extensive CI. 2CC is also an orbitally invariant coupled electron pair approximation. The numerical results of nCC are close to those for the full CC variant, and in some cases are closer to the full CI reference result. As 2CC is exact for separated electron pairs, it is the natural zeroth-order approximation for the correlation problem in molecules with other effects introduced as these units start to interact. The nCC hierarchy of approximations has all the attractive features of CC including its size extensivity, orbital invariance, and orbital insensitivity, but in a conceptually appealing form suited to bond breaking, while being computationally less demanding. Excited states from the equation of motion (EOM-2CC) are also reported, which show results frequently approaching those of EOM-CCSDT.

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PubMed2006

Ab initio correlation functionals from second-order perturbation theory.

Orbital-dependent exchange-correlation functionals are not limited by the explicit dependence on the density and present an attractive alternative to conventional functionals. With the successful implementation of the exact orbital-dependent exchange functional, the challenge lies in developing orbital-dependent approximations for the correlation functional. Ab initio many-body methods can provide such approximations. In particular, perturbation theory with the Kohn-Sham model as the reference [Görling and Levy, Phys. Rev. A 50, 196 (1994)] defines the exact correlation functional via an infinite perturbation series. The second-order term of these series gives the lowest-order approximation to the correlation functional. However, it has been suggested [Bartlett et al., J. Chem. Phys. 122, 034104 (2005)] that the Kohn-Sham Hamiltonian is not the optimal choice for the perturbation expansion and a different reference Hamiltonian may lead to an improved perturbation series and more accurate second-order approximation. Here, we demonstrate explicitly that the modified series can be used to define superior functional and potential. We present results of atomic and molecular calculations with both second-order functionals. Our results demonstrate that the modified functional offers a significantly improved description of the correlation effects as it does not suffer from convergence problems and results in energies and densities that are more accurate than those obtained with second-order Møller-Plesset perturbation theory or generalized-gradient approximation functionals.

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PubMed2006

High-level coupled-cluster methods for electron spin resonance spectra: on the experimental spectrum of the silacyclobutane radical cation.

The silacyclobutane radical cation is a prototype intermediate in chemical reactions involving Si based organic molecules. In the interest of its full characterization, the experimentally determined isotropic hyperfine coupling constants of the hydrogens in silacyclobutane radical cation (c-SiC(3)(+)) have raised some interesting questions, leading to different interpretations of the spectrum. To help resolve this discrepancy, we report very high-level theoretical results with coupled-cluster theory using its analytical, response density matrix procedure, and recently proposed basis sets that are specific to ESR. The detailed studies of geometries, basis set effects, and electron correlation tend to support the B3LYP/6-31G-based reassignment of the ESR spectrum of the c-SiC(3)(+) radical cation by Fängström et al.

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PubMed2006

Tailored coupled cluster singles and doubles method applied to calculations on molecular structure and harmonic vibrational frequencies of ozone.

To assess the separation of dynamic and nondynamic correlations and orbital choice, we calculate the molecular structure and harmonic vibrational frequencies of ozone with the recently developed tailored coupled cluster singles and doubles method (TCCSD). We employ the Hartree-Fock and complete active space (CAS) self-consistent field (SCF) orbitals to perform TCCSD calculations. When using the Hartree-Fock orbitals, it is difficult to reproduce the experimental vibrational frequency of the asymmetric stretching mode. On the other hand, the TCCSD based on the CASSCF orbitals in a correlation consistent polarized valence triple zeta basis yields excellent results with the two symmetric vibrations differing from the experimental harmonic values by 2 cm(-1) and the asymmetric vibration differing by 9 cm(-1).

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PubMed2005

Correlated one-particle method: numerical results.

In a previous paper a correlated one-particle method was formulated, where the effective Hamiltonian was composed of the Fock operator and a correlation potential. The objective was to define a correlated one-particle theory that would give all properties that can be obtained from a one-particle theory. The Fock-space coupled-cluster method was used to construct the infinite-order correlation potential, which yields correct ionization potentials (IP's) and electron affinities (EA's) as the negative of the eigenvalues. The model, however, was largely independent of orbital choice. To exploit the degree of freedom of improving the orbitals, the Brillouin-Brueckner condition is imposed, which leads to an effective Brueckner Hamiltonian. To assess its numerical properties, the effective Brueckner Hamiltonian is approximated through second order in perturbation. Its eigenvalues are the negative of IP's and EA's correct through second order, and its eigenfunctions are second-order Brueckner orbitals. We also give expressions for its energy and density matrix. Different partitioning schemes of the Hamiltonian are used and the intruder state problem is discussed. The results for ionization potentials, electron affinities, dipole moments, energies, and potential curves are given for some sample molecules.

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PubMed2005

Coupled-cluster method tailored by configuration interaction.

A method is presented which combines coupled cluster (CC) and configuration interaction (CI) to describe accurately potential-energy surfaces (PESs). We use the cluster amplitudes extracted from the complete active space CI calculation to manipulate nondynamic correlation to tailor a single reference CC theory (TCC). The dynamic correlation is then incorporated through the framework of the CC method. We illustrate the method by describing the PESs for HF, H2O, and N2 molecules which involve single, double, and triple bond-breaking processes. To the dissociation limit, this approach yields far more accurate PESs than those obtained from the conventional CC method and the additional computational cost is negligible compared with the CC calculation steps. We anticipate that TCC offers an effective and generally applicable approach for many problems.

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PubMed2005

Ab initio density functional theory: the best of both worlds?

Density functional theory (DFT), in its current local, gradient corrected, and hybrid implementations and their extensions, is approaching an impasse. To continue to progress toward the quality of results demanded by today's ab initio quantum chemistry encourages a new direction. We believe ab initio DFT is a promising route to pursue. Whereas conventional DFT cannot describe weak interactions, photoelectron spectra, or many potential energy surfaces, ab initio DFT, even in its initial, optimized effective potential, second-order many-body perturbation theory form [OEP (2)-semi canonical], is shown to do all well. In fact, we obtain accuracy that frequently exceeds MP2, being competitive with coupled-cluster theory in some cases. Furthermore, this is accomplished within a relatively fast computational procedure that scales like iterative second order. We illustrate our results with several molecular examples including Ne2,Be2,F2, and benzene.

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PubMed2005

Critical comparison of various connected quadruple excitation approximations in the coupled-cluster treatment of bond breaking.

To assess the limits of single-reference coupled-cluster (CC) methods for potential-energy surfaces, several methods have been considered for the inclusion of connected quadruple excitations. Most are based upon the factorized inclusion of the connected quadruple contribution (Qf) [J. Chem. Phys. 108, 9221 (1998)]. We compare the methods for the treatment of potential-energy curves for small molecules. These include CCSD(TQf), where the initial contributions of triple (T) and factorized quadruple excitations are added to coupled-cluster singles (S) and doubles (D), its generalization to CCSD(TQf), where instead of measuring their first contribution from orders in H, it is measured from orders in H=e(-(T1+T2))He(T1+T2); renormalized approximations of both, and CCSD2 defined in [J. Chem. Phys. 115, 2014 (2001)]. We also consider CCSDT, CCSDT(Qf), CCSDTQ, and CCSDTQP for comparison, where T, Q, and P indicate full triple, quadruple, and pentuple excitations, respectively. Illustrations for F2, the double bond breaking in water, and N2 are shown, including effects of quadruples on equilibrium geometries and vibrational frequencies. Despite the fact that no perturbative approximation, as opposed to an iterative approximation, should be able to separate a molecule correctly for a restricted-Hartree-Fock reference function, some of these higher-order approximations have a role to play in developing new, more robust procedures.

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PubMed2005

Molecular applications of the intermediate Hamiltonian Fock-space coupled-cluster method for calculation of excitation energies.

The intermediate Hamiltonian Fock-space coupled-cluster (FS-CC) method with singles and doubles is applied to calculate vertical excitation energies (EEs) for some molecular systems. The calculations are performed for several small molecules, such as H2O, N2, and CO, and for larger systems, such as C2H4, C4H6, and C6H6. Due to the intermediate Hamiltonian formulation, which provides a robust computational scheme for solving the FS-CC equations, and the efficient factorization strategy, relatively large basis sets and model spaces are employed permitting a comparison of the calculated vertical EEs with the experimental data.

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PubMed2005

Quantum chemical study of the electronic structure of NiCH2 + in its ground state and low-lying electronic excited states.

The electronic structure of NiCH(2) (+), representative of transition metal carbene ions, is investigated by means of several methods of quantum chemistry. The relative stabilities of the four low-lying doublet electronic states ((2)A(1), (2)A(2), (2)B(1), and (2)B(2)) are determined at the coupled cluster singles and doubles level (CCSD) and triples level [CCSD(T) and CCSDT-3] with both a Hartree-Fock and density functional theory (Kohn-Sham) reference. The equation-of-motion coupled cluster for treatment of excited states in singles and doubles approximation (EOM-CCSD) is used to characterize the transition energies from the (2)A(1) electronic ground state to the low-lying doublet excited states. The (2)A(2) and (2)B(1) states are nearly degenerate, found to be separated by 940 cm(-1) at the EOM-CCSD level, in agreement with the CASSCF energy ordering. The (2)B(2) state is calculated to be higher in energy by more than 1.0 eV. The spin purity of the low-lying doublet and quadruplet states described by CCSD calculations based on the unrestricted open-shell Hartree-Fock reference is discussed.

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PubMed2005

The exchange-correlation potential in ab initio density functional theory.

From coupled-cluster theory and many-body perturbation theory we derive the local exchange-correlation potential of density functional theory in an orbital dependent form. We show the relationship between the coupled-cluster approach and density functional theory, and connections and comparisons with our previous second-order correlation potential [OEP-MBPT(2) (OEP-optimized effective potential)] [I. Grabowski, S. Hirata, S. Ivanov, and R. J. Bartlett, J. Chem. Phys. 116, 4415 (2002)]. Starting from a general theoretical framework based on the density condition in Kohn-Sham theory, we define a rigorous exchange-correlation functional, potential and orbitals. Specifying initially to second-order terms, we show that our ab initio correlation potential provides the correct shape compared to those from reference quantum Monte Carlo calculations, and we demonstrate the superiority of using Fock matrix elements or more general infinite-order semicanonical transformations. This enables us to introduce a method that is guaranteed to converge to the right answer in the correlation and basis set limit, just as does ab initio wave function theory. We also demonstrate that the energies obtained from this generalized second-order method [OEP-MBPT2-f] and [OEP-MBPT2-sc] are often of coupled-cluster accuracy and substantially better than ordinary Hartree-Fock based second-order MBPT=MP2.

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PubMed2004

A natural linear scaling coupled-cluster method.

It is shown that using an appropriate localized molecular orbital (LMO) basis, one is able to calculate coupled-cluster singles and doubles (CCSD) wave functions and energies for very large systems by performing full CCSD calculations on small subunits only. This leads to a natural linear scaling coupled-cluster method (NLSCC), in which total correlation energies of extended systems are evaluated as the sum of correlation energy contributions from individual small subunits within that system. This is achieved by defining local occupied orbital correlation energies. These are quantities, which in the LMO basis become transferable between similar molecular fragments. Conventional small scale existing molecular CCSD codes are all that is needed, the local correlation effect being simply transmitted via the appropriate LMO basis. Linear scaling of electronic correlation energy calculations is thus naturally achieved using the NLSCC approach, which in principle can treat nonperiodic extended systems of infinite basis set size. Results are shown for alkanes and several polyglycine molecules and the latter compared to recent results obtained via an explicit large scale LCCSD calculation. (c) 2004 American Institute of Physics.

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PubMed2004

Fock space multireference coupled cluster method with full inclusion of connected triples for excitation energies.

We report the initial Fock space multireference coupled cluster method with the full inclusion of single, double, and triple excitations (FS-CCSDT) for the (1,1) sector. We present pilot applications for calculating excitation energies for the N(2) molecule and the Ne atom. The performance of the current model, along with the FS-CCSD one, has been studied in comparison with the equation-of-motion coupled-cluster and the similarity transformed methods.

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PubMed2004

Singular value decomposition applied to the compression of T3 amplitude for the coupled cluster method.

We apply the singular value decomposition to compress the degrees of freedom of T3 amplitude for the CCSDT-1 method (compressed CCSDT-1). This method enables us to make the number of the T3 amplitudes less than that of the T2 amplitudes, making CCSDT-1 calculations much less expensive without losing accuracy. We perform test calculations on some atoms and molecules to investigate the applicability of this method. Computational results for the electronic energies as well as timings of these calculations are presented.

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PubMed2004

Independent particle theory with electron correlation.

We formulate an effective independent particle model where the effective Hamiltonian is composed of the Fock operator and a correlation potential. Within the model the kinetic energy and the exchange energy can be expressed exactly leaving the correlation energy functional as the remaining unknown. Our efforts concentrate on finding a correlation potential such that exact ionization potentials and electron affinities can be reproduced as orbital energies. The equation-of-motion coupled-cluster approach enables us to define an effective Hamiltonian from which a correlation potential can be extracted. We also make the connection to electron propagator theory. The disadvantage of the latter is the inherit energy dependence of the potential resulting in a different Hamiltonian for each orbital. Alternatively, the Fock space coupled-cluster approach employs an effective Hamiltonian which is energy independent and universal for all orbitals. A correlation potential is extracted which yields the exact ionization potentials and electron affinities and a set of associated molecular orbitals. We also describe the close relationship to Brueckner theory.

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PubMed2004

Coupled-cluster singles and doubles for extended systems.

Coupled-cluster theory with connected single and double excitation operators (CCSD) and related approximations, such as linearized CCSD, quadratic configuration interaction with single and double excitation operators, coupled-cluster with connected double excitation operator (CCD), linearized CCD, approximate CCD, and second- and third-order many-body perturbation theories, are formulated and implemented for infinitely extended one-dimensional systems (polymers), on the basis of the periodic boundary conditions and distance-based screening of integrals, density matrix elements, and excitation amplitudes. The variation of correlation energies with the truncation radii of short- and long-range lattice sums and with the number of wave vector sampling points in the first Brillouin zone is examined for polyethylene, polyacetylene, and polyyne, and is shown to be a function of the degree of pi-electron conjugation or the fundamental band gaps. The t2 and t1 amplitudes in the atomic orbital (AO) basis are obtained by first computing the t amplitudes in the Bloch-orbital basis and subsequently back-transforming them into the AO basis. The plot of these AO-based t amplitudes as a function of unit cells also indicates that the t2 amplitudes of polyacetylene and polyyne exhibit appreciably slower decay than those of polyethylene, although the asymptotic decay behavior is invariably 1/r3. The AO-based t1 amplitudes appear to correlate strongly with the electronic structure, and they decay seemingly exponentially for polyethylene whereas they stay at a constant magnitude across the seventh nearest neighbors of polyacetylene and polyyne, which attests to far reaching effects of nondynamical electron correlation mediated by orbital rotation. Nonetheless, the unit cell contributions to the correlation energies taper below 10(-6) hartree after 15 A for all three polymers. The basis set dependence of the decay behavior of t2 amplitudes is also examined for linear hydrogen fluoride polymer (HF)infinity and linear beryllium polymer (Be)infinity employing the STO-3G, 6-31G, and 6-31G* basis sets, and proves to be rather small.

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PubMed2004

Toward a computational description of nitrile hydratase: studies of the ground state bonding and spin-dependent energetics of mononuclear, non-heme Fe(III) complexes.

The metal coordination and spin state of the Fe(III) center in nitrile hydratase (NHase) has stimulated the synthesis of model complexes in efforts to understand the reactivity and spectroscopic properties of the enzyme. We report density functional theory (DFT) calculations on a number of Fe(III) complexes that have been prepared as models of the NHase metal center, together with others having similar ligands but different ground state spin multiplicities. Our results suggest that a DFT description of specific spin configurations in these systems does not suffer from significant amounts of spin contamination. In particular, B3LYP calculations not only reproduce the observed spin state preferences of these Fe(III) complexes but also predict spin-dependent structural properties consistent with those expected on the basis of ligand field models. An analysis of the natural bond orbital (NBO) transformation of the Kohn-Sham wave functions has enabled quantitation of the overall contribution to covalency of ligand-to-metal sigma-donation and pi-donation, and metal-to-ligand pi-back-bonding in these Fe(III) complexes at their BLYP-optimized geometries. Although sulfur ligands are the primary source of covalency in the Fe(III) complexes, our quantitative analysis suggests that hyperbonding between metal-bound nitrogens and an Fe-S bond represents a mechanism by which Fe-N covalency may arise. These studies establish the computational methodology for future theoretical investigations of the NHase Fe(III) center.

Chemical Phenomena↗

PubMed2002

(3h)J((15)N-(31)P) spin-spin coupling constants across N[bond]H....O[bond]P hydrogen bonds.

Equation-of-motion coupled cluster singles and doubles (EOM-CCSD) calculations have been performed to evaluate three-bond (15)N-(31)P coupling constants ((3h)J(N[bond]P)) across N[bond]H....O[bond]P hydrogen bonds in model cationic and anionic complexes including NH(4)(+):OPH, NH(4)(+):OPH(3), NH(3):(-)O(2)PH(2), NFH(2):(-)O(2)PH(2), and NF(2)H:(-)O(2)PH(2). Three-bond coupling constants can be appreciable when the phosphorus is P(V), but are negligible with P(III). (3h)J(N[bond]P) values in complexes with cyclic or open structures are less than 1 Hz, a consequence of the nonlinear arrangement of N, H, O, and P atoms. For complexes with these structures, (3h)J(N[bond]P) may not be experimentally measurable. In contrast, complexes in which the N, H, O, and P atoms are collinear or nearly collinear have larger values of (3h)J(N[bond]P), even though the N[bond]P distances are longer than N[bond]P distances in cyclic and open structures. In linear complexes, (3h)J(N[bond]P) is dominated by the Fermi-contact term, which is distance dependent. Therefore, N[bond]P (and hydrogen-bonding N[bond]O) distances in these complexes can be determined from experimentally measured (15)N-(31)P coupling constants.

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