Gaussian integral programs

Integral Evaluation. We here confine our attention to the evaluation of integrals over Cartesian Gaussians (V7.) A seen in Table IV, the essentially unmodified FORTRAN source of the ATMOL3 Gaussian Integrals program compiled on the CRAY runs at approximately 6.2 times faster than the IBM 370/165 (circa. 2.4 times... 

In the CRAY-1 a Gaussian integrals program may be driven at 35 Mflops, a large closed shell SCF with a sparse list of integrals or Supermatrix at 10 Mflops, while a smaller SCF with a non-sparse Supermatrix may be driven at 135 Mflops. 

It was in 197 that we began development of our new series of Gaussian integral programs especially designed for large molecules MOLASYS (Molecular Orbital Calculations on Large Systems)... 

Popkie, H. E., "GIPSY (Gaussian Integral Program System) A... 

J. Almlof, Molecule, a vectorized Gaussian integral program. 

Gaussian 09 is the current integrated program including several molecular orbited methods, see Gaussian Inc. http //www.gaussian.com/... 

In the electronically excited state, all higher vibrational states are of importance and are given in Equations 4.63 and 4.64. To obtain the vibration overlap to the excited state, we have to use recursion formulas for Gaussian integrals (Appendix 6). The result is comparatively simple to obtain using these equations and Equations 4.63 and 4.64 in computer programs. The first one is... 

Here, n corresponds to the principal quantum number, the orbital exponent is termed and Ylm are the usual spherical harmonics that describe the angular part of the function. In fact as a rule of thumb one usually needs about three times as many GTO than STO functions to achieve a certain accuracy. Unfortunately, many-center integrals such as described in equations (7-16) and (7-18) are notoriously difficult to compute with STO basis sets since no analytical techniques are available and one has to resort to numerical methods. This explains why these functions, which were used in the early days of computational quantum chemistry, do not play any role in modem wave function based quantum chemical programs. Rather, in an attempt to have the cake and eat it too, one usually employs the so-called contracted GTO basis sets, in which several primitive Gaussian functions (typically between three and six and only seldom more than ten) as in equation (7-19) are combined in a fixed linear combination to give one contracted Gaussian function (CGF),... 

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