Gaussian-4 theory

Gaussian-4 theory.

The Gaussian-4 theory (G4 theory) for the calculation of energies of compounds containing first- (Li-F), second- (Na-Cl), and third-row main group (K, Ca, and Ga-Kr) atoms is presented. This theoretical procedure is the fourth in the Gaussian-n series of quantum chemical methods based on a sequence of single point energy calculations. The G4 theory modifies the Gaussian-3 (G3) theory in five wa...

Gaussian-4 theory using reduced order perturbation theory.

Two modifications of Gaussian-4 (G4) theory [L. A. Curtiss et al., J. Chem. Phys. 126, 084108 (2007)] are presented in which second- and third-order perturbation theories are used in place of fourth-order perturbation theory. These two new methods are referred to as G4(MP2) and G4(MP3), respectively. Both methods have been assessed on the G3/05 test set of accurate experimental data. The averag...

Tight Gaussian 4-Designs

A Gaussian t-design is defined as a finite set X in the Euclidean space Rn satisfying the condition: 1 V (Rn ) ∫ Rn f (x)e −α2||x ||2 dx = u∈X ω(u) f (u) for any polynomial f (x) in n variables of degree at most t , here α is a constant real number and ω is a positive weight function on X . It is easy to see that if X is a Gaussian 2e-design in Rn , then |X | ≥ (n+e e ) . We call X a tight Gaus...

Lecture 4 a Gaussian Elimination Example

To solve: 1 1 1 x 1 x 2 = 1 1 First factor the matrix to get: 1 0 1 1 1 0 1 − 1 x 1 x 2 = 1 1 Next solve: 1 0 1 1 y 1 y 2 = 1 1 To get: Which is the solution to the original system. When viewed this way, Gaussian elimination is just LU factorization of a matrix followed by some simple substitutions.

Multiresolution Gaussian Mixture Models: Theory and Applications