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1.
The theory for the calculation of the frequency-dependent hyperpolarizabilities β(?2ω; 0, ω), β(?ω; 0, ω), and β(0; ω, ?ω) is discussed. New relations between these tensors are derived for those wave functions that obey the time-dependent Hellmann–Feynman theorem (e.g., the self-consistent field [SCF] or the exact wave function). Using second-order Møller–Plesset perturbation theory (MP2), expressions are obtained for the hyperpolarizabilities in terms of derivatives of appropriately defined linear polarizability tensors with respect to a static electric field. Results are presented for ammonia and formaldehyde for the optical Kerr effect and for secondharmonic generation. These results indicate that it is desirable to determine the frequency-dependent contribution to the hyperopolarizability at the MP2 rather than the SCF level of theory, in cases where the static hyperpolarizability has a large contribution from electron correlation and/or where the frequency-dependent contribution may be more significant, such as for secondharmonic generation. 相似文献
2.
N. C. Handy 《Theoretical chemistry accounts》1973,31(3):201-204
Boys and Handy [1] have discussed the solution of the bivariational equations with restricted numerical integration. One of the weaknesses of the method was that in the numerical summations over points, some points arose with r
ij= 0 and non-zero weights. This makes the method quite impractical for the Schrodinger Hamiltonian (because of the singularity at r
ij= 0), and it cannot be advantageous for the transcorrelated Hamiltonian C–1HC because there will be some discontinuous higher derivatives at r
ij=0. Here it is shown how the symmetry of cylindrically symmetric molecules can be used to eliminate such points, without losing any of the advantages of the overall method, such as the convergence of the eigensolutions. It is also shown how the primary numerical integration points (z
i, ri) may be chosen in any calculation such that each is associated with an equal amount of one-electron density. The choice of the angular coordinates are governed by the removal of the r
ij=0 points and maintaining the natural orthogonality between orbitals of different symmetry types. The method has been programmed and found to be practical, although no new molecular calculations have yet been performed. It is to be hoped that these points will give a basis for new transcorrelated calculations on diatomic molecules.This paper was presented during the session on numerical integration methods for molecules of the 1970 Quantum Theory Conference in Nottingham. It has been revised in the light of the interesting discussion which followed. 相似文献
3.
Using recently developed theoretical techniques it has been possible to achieve an exact variational solution of the Schrödinger equation within a modest basis set or one-eleltron functions. The full configuration interaction for this system included a total of 256473 1A1 spin-and space-adapted configurations. Comparison with many-body perturbation theory proves to be quite interesting. 相似文献
4.
In this paper we extend our density-functional theory calculations, with generalized gradient approximation and hybrid functionals, using Slater-type orbitals (STOs), to the determination of second-order molecular properties. The key to the entire methodology involves the fitting of all STO basis function products to an auxiliary STO basis, through the minimization of electron-repulsion integrals. The selected properties are (i) dipole polarizabilities, (ii) nuclear magnetic shielding constants, and (iii) nuclear spin-spin coupling constants. In all cases the one-electron integrals involving STOs were evaluated by quadrature. The implementation for (ii) involved some complexity because we used gauge-including atomic orbitals. The presence of two-electron integrals on the right-hand side of the coupled equations meant that the fitting procedure had to be implemented. For (iii) in the hybrid case, fitting procedures were again required for the exchange contributions. For each property we studied a number of small molecules. We first obtained an estimate of the basis set limit using Gaussian-type orbitals (GTOs). We then showed how it is possible to reproduce these values using a STO basis set. For (ii) a regular TZ2P quality STO basis was adequate; for (i) the addition of one set of diffuse functions (determined by Slater's rules) gave the required accuracy; for (iii) it was necessary to add a set of 1s functions, including one very tight function, to give the desired result. In summary, we show that it is possible to predict second-order molecular properties using STO basis sets with an accuracy comparable with large GTO basis sets. We did not encounter any major difficulties with either the selection of the bases or the implementation of the procedures. Although the energy code (especially in the hybrid case) may not be competitive with a regular GTO code, for properties we find that STOs are more attractive. 相似文献
5.
We have performed large-scaleab initio calculations using second order Møller-Plesset perturbation theory (MP2) on the three van der Waals dimers formed from acetylene and carbon dioxide. Intermolecular geometrical parameters are reliably computed at this level of theory. Calculations of vibrational frequencies of the van der Waals modes, currently unobtainable by experimental means, give important information about the intermolecular potential and predict significant large-amplitude motion. Zero point energy contributions are shown to be vital in assessing the relative stability of conformations which are close in energy. Our studies suggest that the barrier to interconversion tunnelling in (CO2)2 is significantly smaller than previously inferred and is approximately the same as in (C2H2)2. The reason for the rigidity of (CO2)2 is the difference in monomer centre-of-mass separation between ground state and transition state. We also show that, in addition to the previously observedC
2v
form, the collinear form of C2H2-CO2 is a local minimum on its potential energy surface. 相似文献
6.
Deep eutectic solvents (such as the combination of either urea or glycerol with choline chloride) are effective solvents/organocatalysts for Pictet–Spengler condensations to form carbolines. The reaction conditions are quite mild and do not require additional Bronsted or Lewis acid catalyst. Given the inexpensive, non-toxic, and recyclable nature of the DES, these reaction conditions are simple and highly environmentally friendly. 相似文献
7.
8.
Duygu İNCİ 《应用有机金属化学》2020,34(12):e6016
NOO-type tridentate Schiff base, N-salicylidene-2-aminobenzoic acid, (H2L), and its ternary Cu (II) complex containing H2L Schiff base and 4,7-dimethyl-1,10-phenanthroline (4,7-dmphen), [Cu(4,7-dmphen)(H2L)]27H2O, have been synthesized and characterized by CHN analysis, ESI-MS, FTIR, and single-crystal X-ray diffraction techniques. The interaction of alone H2L Schiff base ligand and ternary Cu (II) complex with biomacramolecules {calf thymus DNA (CT-DNA) and bovine serum albumin (BSA)} has been investigated by electronic absorption and fluorescence spectroscopy. The experimental results indicate that H2L Schiff base ligand and ternary Cu (II) complex bind to CT-DNA by means of a moderate intercalation mode. Furthermore, the fluorescence quenching mechanism between H2L Schiff base ligand and ternary Cu (II) complex with BSA possesses a static quenching process. Radical scavenging activity of H2L Schiff base ligand and ternary Cu (II) complex was measured in terms of EC50, using the DPPH and H2O2 methods. Biomacromolecule interactions and scavenging activity studies revealed that ternary Cu (II) complex yielded better results than H2L Schiff base ligand alone. 相似文献
9.
Stuart Carter Nicholas C. Handy Cristina Puzzarini Riccardo Tarroni Paolo Palmieri 《Molecular physics》2013,111(21):1697-1712
A general method is presented for the evaluation of the spin rovibronic energy levels of triatomic molecules with up to three interacting potential energy surfaces. The full theory is outlined in detail, both for singlet and for doublet electronic states and the method is then applied to the benchmark example of C2H. High quality multireference configuration interaction calculations have been carried out to generate the 3-dimensional near-equilibrium adiabatic potential energy surfaces of the three lowest 12A'(X2Σ+), 22A'(A2Π), 12A''(A2Π) electronic states of C2H, and the pair of interacting states of A 0 symmetry have then been diabatized. Results are presented for J up to 7/2 and compared with gas-phase high resolution experimental results for energies up to 5600 cm1. 相似文献
10.
Jon Handy 《Journal d'Analyse Mathématique》2009,108(1):1-18
Let K be a square Cantor set, i.e., the Cartesian product K = E × E of two linear Cantor sets. Let δ
n
denote the proportion of the intervals removed in the nth stage of the construction of E. It is shown that if $
\delta _n = o(\frac{1}
{{\log \log n}})
$
\delta _n = o(\frac{1}
{{\log \log n}})
, then the corona theorem holds on the domain Ω = ℂ* \ K. 相似文献