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  • 1
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 95 (1991), S. 6723-6733 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The Brueckner doubles variant of coupled cluster theory has recently been reintroduced by the authors. The use of Brueckner orbitals means that the governing equations for Tˆ2 take a particularly simple form. Here we give the details for the evaluation of the gradient of the Brueckner doubles energy for (a) the unrestricted spin–orbital formalism and (b) the closed-shell restricted formalism. Applications are presented for H2O, NH3, CH4, H2CO, C2H2, HCN, and CO2 and comparisons are made with the Hartree–Fock, second order Møller–Plesset and quadratic configuration interaction models and with experiment.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 94 (1991), S. 118-132 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The potential energy surfaces of the two lowest-lying singlet electronic states of methylene (CH2) are determined by internally contracted multireference configuration interaction calculations, using a full-valence reference space, with an extended Gaussian basis set. The rotation–vibration levels on these surfaces are calculated by diagonalizing the rovibrational Hamiltonian matrix in a contracted basis. The rovibronic mixing due to the strong Renner–Teller interaction in this system is treated through the Coriolis term in the kinetic energy operator, using geometry-dependent electronic angular momentum matrix elements calculated from ab initio wave functions. The agreement between experiment and this high-quality ab initio calculation is sufficiently good that the calculation can be used to assign the observed vibronic bands in this very complex spectrum, where 90% of the observed lines remain unassigned. Many of the previous vibronic band labels are found to be incorrect. Most of the K>0 bands previously labeled b˜ 1B1 are actually predominantly a˜ 1A1 in character, and the vibrational numbering of their b˜ 1B1 components are also incorrect. This work demonstrates the importance of supplementing experimental data with good quality ab initio calculations.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 93 (1990), S. 4123-4128 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The removal of spin contamination from unrestricted Hartree–Fock Møller–Plesset calculations is now recognized to be important. Here the Handy–Knowles formulation, previously presented, is studied. An evaluation of the energy and the energy gradient, for the removal of one- and two-spin contaminants, is described. The cost of the algorithm for the gradient is proportional to n2v3, where n and v are the number of occupied and virtual orbitals, respectively. Applications of this algorithm are presented for CN, Li3, and the abstraction of H from CH4.
    Type of Medium: Electronic Resource
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  • 4
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Methods for the determination of the frequency dependent hyperpolarizabilities, β(−2ω;ω,ω), β(−ω;ω,0), and β(0;ω,−ω) at the self-consistent field (SCF) level of theory are discussed and compared. Two efficient alternatives are proposed; one involves determination of appropriate response vectors which arise in first-order perturbation theory at frequency ω, and the other involves solving first-order perturbation theory equations at frequency 0 (static), ω and 2ω. Neither approach involves solution of the second-order perturbation theory equations. The method is illustrated with application to formaldehyde and methyl fluoride using large one-particle basis sets. The basis set requirement for convergence of this property at the SCF level of theory is investigated. Basis sets including up to d functions on first row atoms and p functions on hydrogen incorporating diffuse functions appear to be adequate. The effect of electron correlation on the static hyperpolarizability is estimated using second-order Møller–Plesset theory. Comparison is made with experimental values where available.
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  • 5
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 91 (1989), S. 2396-2398 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: In very large full configuration interaction (full CI), nearly all of the CI coefficients are very small. Calculations, using a newly developed algorithm which exploits this fact, on NH3 with a DZP basis are reported, involving 2×108 Slater determinants. Such calculations are impossible with other existing full CI codes. The new algorithm opens up the opportunity of full CI calculations which are unlimited in size.
    Type of Medium: Electronic Resource
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  • 6
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The high resolution rovibrational spectrum of H2S has been evaluated from three-dimensional ab initio potential energy and electric dipole moment functions and variational rovibrational eigenfunctions, which took full account of anharmonicity effects and rotation–vibration coupling. The quality of the near equilibrium theoretical potential energy function has been checked by comparisons with experimental equilibrium structure, empirical quartic force fields, vibrational band origins, centrifugal distortion constants, and rotational energy levels. All parameters agree well with the available experimental data. Vibrational band intensities for the ν2, 2ν2, ν1, and ν3 bands have been calculated from empirical and ab initio dipole moment functions and compared with experimental and theoretical integrated band intensities. The difficulties arising by the derivation of such data from the experimental intensities of H2S are discussed. The theoretical results strongly suggest that higher than first derivatives are needed for a proper description of the dipole moment function. The room temperature absorption spectra have been evaluated ab initio for the pure rotational and the ν2, 2ν2, ν1, and ν3 transitions. The unusual intensity pattern of the P, Q, and R branches attributed to the rotational–vibrational coupling has been well reproduced. Absolute line intensities calculated previously by perturbation theory are compared with variational results. The purely theoretical line intensities agree satisfactorily with experiment for the bending transitions, however, the extremely flat regions of the dipole moment functions along the bond stretching displacements make the transition intensities very sensitive to the values of the dipole moment derivatives.
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  • 7
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 89 (1988), S. 2107-2115 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The value of the Møller–Plesset third order calculations is examined. An efficient method for the evaluation of the gradient of the MP3 energy is reported, and it has been programmed for both restricted and unrestricted Hartree–Fock wave functions. Large basis set calculations (TZ2P or better) are reported for the optimization of geometries and the determination of harmonic frequencies (which are obtained by finite differences of analytic gradients). The molecules selected are NH2, PH2, AsH2, H2O, NH3, H2CO, HCN, and C2H2. For the closed shell systems, the RMP3 predictions for bond lengths are inferior ((approximate)0.006 A(ring)) to RMP2 predictions ((approximate)0.003 A(ring)) for single bonds, and for multiple bonds the RMP3 bond lengths are too short by approximately the same amount ((approximate)0.01 A(ring)) that RMP2 are too long. For the open shell systems, the UMP3 geometrical parameters show only a marginal improvement over UMP2, except for PH2 where the bond length error is reduced to 0.003 A(ring). The results for harmonic frequencies show a similar comparison between MP2 and MP3. On the basis of this experience, it appears that large scale calculations at the MP3 level are not recommended; MP2 calculations with a large basis set are much cheaper and provide results with a similar, if not superior, accuracy.
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  • 8
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We present an efficient reformulation of the analytic configuration interaction (CI) energy second derivative. Specifically, the Z-vector method of Handy and Schaefer is used to avoid solving the second order coupled perturbed Hartree–Fock (CPHF) equations. We have incorporated translational–rotational invariance into the new method. We present a more efficient method for the evaluation of the Y matrix contribution. The procedure which has been implemented can accommodate very large basis sets and CI expansions for any general restricted Hartree–Fock (RHF) reference wave function. As a test case, we apply the new procedure to the HSOH molecule using a double zeta plus polarization basis set. This leads to 50 contracted Gaussian basis functions and 116 403 configurations in the CI expansion. Harmonic vibrational frequencies and infrared intensities are predicted for HSOH and its deuterated isotopomers. The analytic method described herein requires only 56% of the central processor unit time used by a numerical method.
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  • 9
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Full configuration-interaction (FCI) calculations are performed at selected geometries for the 1∑+ state of HF and the 2B1 and 2A1 states of NH2 using both DZ and DZP Gaussian basis sets. Higher excitations become more important when the bonds are stretched and the SCF reference becomes a poorer zeroth-order description of the wave function. The CASSCF-MRCI procedure gives excellent agreement with the FCI potentials, especially when corrected with a multireference analog of the Davidson correction.
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  • 10
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 117 (2002), S. 1470-1478 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The most common form of density functional calculations on molecular systems used generalized gradient approximation exchange-correlation functionals (such calculations can be applied to larger systems because no exact exchange is included). The most efficient and fastest such codes use an auxiliary basis set to fit the density so that only three-center integrals need to be evaluated. The codes DGAUSS and TURBOMOL use Gaussian basis sets, whereas the long-established ADF code uses Slater basis sets. We here examine the use of Slater basis sets. Our new code evaluates all required integrals numerically by quadrature. We report calculations on the G2 molecular set, contrasting them with similar calculations using Gaussian basis sets. Our conclusion, as far as energetics and structure are concerned, is that very similar predictions may be obtained from basis sets of the same size, and at approximately the same cost. © 2002 American Institute of Physics.
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