Base group: Getting Started (in update)

Term:basis Set

The concept of a base group:

The base group in quantum chemistry is a certain function which is used to describe the wave function of the system. Base Group is the basis of quantum chemistry ab initio calculation, which has very important meaning in quantum chemistry. The concept of the base group was first derived from the atomic orbit, and with the development of quantum chemistry, the concept of the base group has been greatly expanded and is now not confined to the original concept of atomic orbits. In the calculation of quantum chemistry, according to the different system, we need to choose different base groups, the more functions that make up the base group, the larger the base group, the higher the calculation precision, and the greater the computational amount. -Wikipedia

The basis set is the set of mathematical functions from which the wave function is constructed.--Essentials of Computa tional Chemistry 2nd Edition

"Sto–slater-type Orbital" \ (\large \varphi (r,\theta,\phi;\zeta,n,l,m) =\frac{(2\zeta) ^{n+1/2}}{[(2n)!] ^{1/2}} R^{n-1}e^{-\zeta r}y^m_l (\theta,\phi) \)

Named after the Slater function \ (\large E^{-\zeta r}\)

"Gto–gaussian-type Orbital" \ (\large \phi (x,y,z;\alpha,i,j,k) ={(\frac{2\alpha}{\pi})}^{3/4}{\frac{(8\alpha) ^{i+j+ k}i!j!k!} {(2i)! (2j)! (2k)!}} ^{1/2} x^i y^j z^k e^{-\alpha (x^2+y^2+z^2)}\)

Named after the Gaussian function \ (\large e^{-\alpha r^2}\)

Both good and bad: Sto can reflect the real shape of the electronic wave function; GTO facilitates fast computation.

"Primitive GTO," the original GTO, as on.

The "contracted GTO" compresses the gto/contraction GTO, even with several GTO linear combinations to simulate the STO shape.

Compression notation: eg: (3s)/[1s] Compresses 3 s-gto (written in parentheses parenthesis) into 1 s-sto (written in square brackets bracket)

Sto-mg:m said that the M-GTO compressed into a STO, through the measurement of m=3 when the balance between precision and speed to achieve optimal, that is sto-3g.

???? Example of a mark: sto-3g H (3s)/[1s];li (6s3p/3s)/[2s1p/1s]

"Single-\ (\large\zeta\)" refers to the use of a set of GTO compression to obtain a sto as an atomic orbital. Each atom orbit is represented by a STO base function (the GTO contained in STO as a whole), so there is only one \ (\large\zeta\) value, which is the smallest base group. Therefore, the accuracy of the calculation is poor. can be specifically sto-mg.

"Multiple-\ (\large\zeta\)" refers to the use of a set of GTO compression to obtain multiple STO as an atomic orbital. Each atom orbit is represented by multiple STO-based functions (which are obtained by the same GTO compression, but different compression methods), with multiple \ (\large\zeta\) values.

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Base group: Getting Started (in update)