Gaussian bases

Lehtomaki, N.A., Sandell, Jr., N.R. and Athans, M. (1981) Robustness Results in Linear-Quadratic Gaussian Based Multivariable Control Designs, IEEE Trans, on Automat. Contr., AC-26(1), pp. 75-92. 

The accuracy of the results obtained here using gaussian bases - and the usefulness of the numerical tests based on these results - can be seen from the values given in the Table 1. It is seen that the dissociation energy De obtained in the largest basis used here is excellent (error equal to 0.01 eV). On the other hand, the error on the value obtained using the minimum basis is as high as 1.35 eV (or 48% in relative value). This proves, if need be, the importance of the orbital optimisation studied in the present article. 

The calculations performed with gaussian bases have been checked employing also the STOCOS bases which include, beside Slater and Hydrogenic orbitals, a large number of STOCOS functions... 

In Section V we derived several Gaussian-based models for estimating the mean concentration resulting from point source releases of material. We have seen that the conditions under which the equation is valid are highly idealized and therefore that it should not be expected to be applicable to very many actual ambient situations. Because of its simplicity. 

In Table 2.8 we show a comparison of the EGSO weights for the two full MCVB calculations we have made with orthogonalized Gaussian bases. These are quite close to one another. We have only listed functions with weights > 0.001, and in each case there are five. 

Sim, F., Salahub, D.R., and Chin, S. (1992) The accurate calculation of dipole moments and dipole polarizabilities using Gaussian-based density functional methods. Int. J. Quantum Chem., 43 (4), 463-479. 

Universal pulses act equally on any initial magnetisation state whereas excitation and inversion pulses are designed to act on longitudinal magnetisation only. The bandwidth factor is the product of the pulse duration. At, and the excitation bandwidth, Af, which is here defined as the excitation window over which the pulse is at least 70% effective (net pulse amplitude within 3 dB of the maximum other publications may define this value for higher levels and so quote smaller bandwidth factors). Use this factor to estimate the appropriate pulse duration for the desired bandwidth. The attenuation factor is used for approximate power calibration and represents the amount by which the transmitter output should be increased over that of a soft rectangular pulse of equal duration. The Gaussian based profiles are truncated at the 1% level. 

The assumption for the measurement of peak widths in Eqs. (8)—(10) is that the peak is Gaussian. Unfortunately, few peaks are truly Gaussian and, in general, for asymmetrical peaks, N, calculated by a Gaussian-based equation, increases the higher up on the peak the width is measured. Figure 3 shows the error in plate-count determinations for asymmetrical peaks as a function of the peak height at which the width is measured. A more accurate approach to efficiency measurement has been presented by Foley and Dorsey (7), which takes into account the peak asymmetry. 

Constrained optimization procedure for finding transition states and reaction pathways in the framework of gaussian based density functional method the case of isomerization reactions. 

We have seen that under certain idealized conditions the mean concentration of a species emitted from a point source has a Gaussian distribution. This fact, although strictly true only in the case of stationary, homogeneous turbulence, serves as the basis for a large class of atmospheric diffusion formulas in common use. The collection of Gaussian-based formulas is sufficiently important in practical application that we devote a portion of this chapter to them. The focus of these formulas is the expression for the mean concentration of a species emitted from a continuous, elevated point source, the so-called Gaussian plume equation. 

We have derived several Gaussian-based models for estimating the mean concentration resulting from point source releases of material. We have noted that the conditions under... 

Calculation of Dipole Moments and Dipole Polarizabilities Using Gaussian-Based Density Functional Methods. 

I. P. Hamilton and J. C. Light, "On Distributed Gaussian Bases for Multi-dimenslonal Vibrational Problems," preprint. 

Passive dispersion The passive regime is described by the partial reflection model, which is a Gaussian-based model that accounts for gravitational settling and deposition effects (Overcamp, 1976). 

At intermediate values of a (and hence of n l), equation (9.70) predicts a sharp upturn in the stress at a s greater than 4, as observed in experiments. Because of the complexity of equation (9.70), the Gaussian-based (9.34) is preferred where possible. 

J. D. Augspurger and C. . Dykstra,/. Comput. Chem., 11,105 (1990). General Quantum Mechanical Operators. An Open-Ended Approach for One-Electron Integrals with Gaussian Bases. 

Functional Methods in Chemistry J. K. Labanowskl and J. W. Andzelm, Eds., Springer-Vsrlag, New York, 1991, pp. 77-100. Gaussian-Based Density Functional Methodology, Software, and Applications. 

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