What's this?

How to install?

Requirements

This package needs some third-part package to ensure fundamental functions.

• Python 3.x
• Numpy
• Numba

$ conda install numpy numba sympy

• Basis_set_exchange ¹: (Without in conda distribution by April, 2020.)

$ pip install basis_set_exchange

Get this soft

Now For Source only.

$ git clone [$the git Repository URL]

Fast Start

Code Structure

/QuanChemComp:

/core

• file math.py

  • Some important math functions.
    Offering:\
    • Func Factorial(n) Factorial of integer. Also called $N!$
      • No Error will raise.
    • Func DoubleFactorial(n) Double Factorial of integer. Also called $N!!$
      • No Error will raise.
    • Func Comb(n: int, m: int) Combination of m in n. Notice 0<=m<=n.
      • No Error will raise.

/core/AnalyticInteg

Most Integration Func use numpy.array values a_array and b_array. And ***notice the unit*** of distance data.

Most methods here using numba.njit to accelerate. # TODO: GPU numba and other Parallel.

• file gtoMath.py

  Focus on Common Dependency, eg. Constant, coefficients

  • Offering some Common math functions for GTO.
    Offering:
    • Func K_GTO(a, b, dAB_2), dAB_2:x^2+y^2+z^2, not |AB|,but |AB|^2
    • Func norm_GTO(a: float, la=0, ma=0, na=0) for Normalization of GTO |aAlmn> if necessary. (Most always.)

• file GammaFunc.py

  Focus on particular Gamma Functions: Boys Func $F_m(w)$

  • Func $F_m(w)$.
    Offering:
    • Analytical Func _Fm(m,w): use bultin function from sympy package.
    • - Default & Prefer - Approximate Func FmDefold(m,w): use Pade approximate, data from the book ²

• file overlap.py

  Focus on $\left<aAlmn\mid bBlmn\right>$

  • The Realization of Overlap Integration in Quantum Chemistry.\
    Offering:
    • FuncSxyzDefold(a, b, a_array, b_array, la, ma, na, lb, mb, nb)
      • for l,m,n<4,there are builtin Functions by values.

• file kinetic.py

  Focus on $\left<aAlmn\mid -\frac{1}{2} \nabla^2 \mid bBlmn\right>$

  • Depended on FuncSxyzDefold in overlap.py
  • The Realization of Kinetic Integration in Quantum Chemistry.\
    Offering:
    • FunckinetDefold(a, b, a_array, b_array, la, ma, na, lb, mb, nb)
      • Use Values Sxyz from overlap.py

• file potential/potential.py

  Focus on $\left<aAlmn\mid \frac{1}{r_{C}}\mid bBlmn\right>$ and $\left<aAlmn bBlmn\mid \frac{1}{r_{C}}\mid cClmn dDlmn \right>$

  • The Realization of Potential Integration in Quantum Chemistry. Including one-electron Integrate and two-electron Integrate. Most algorithm is from book ³
    Offering:
    • Func _Eijt(i: int, j: int, t: int, p, PAx, PBx)
      • return the expansion coefficients $E_t^{ij}/E_0^{00}$ of McMurchine-Davidson scheme.
      • Require Func Comb from ../math.py
    • Func _Rtuvn(t, u, v, n, p, PCx, PCy, PCz, PC2)
      • return the Hermite Coulomb integrals $R_{tuv}$
      • Require Func FmDefold from ../GammaFunc.py
    • Func V_tuvab(i, j, k, l, m, n, p, Kab, rPA, rPB, rPC, PC2)
      • return the basic integrate V^{000}_ab
    • Func phi_2c1e_nNorm(t, u, v, i, j, k, l, m, n, p, Kab, rPA, rPB, rPC, PC2)
      • Warning: NOT NORMALIZED.
      • return all kinds of one-electron integrate with differential operators.
      • Require Func V_tuvab(i, j, k, l, m, n, p, Kab, rPA, rPB, rPC, PC2) in the same .py file.
    • Func phi_2c1e(t, u, v, i, j, k, l, m, n, p, Kab, rPA, rPB, rPC, PC2)
      • NORMALIZED version of Func phi_2c1e_nNorm
    • Func gabcd(la, lb, lc, ld, ma, mb, mc, md, na, nb, nc, nd, a, b, c, d, Kab_Kcd, rPA, rPB, rQC, rQD, rPQ, PQ2)
      • NORMALIZED
      • return two-electron integrate <aAbB|1/r_{12}|cCdD>.
      • Require Func _Rtuvn and _Eijt

/core

• file elements.py

Author: Christoph Gohlke https://www.lfd.uci.edu/~gohlke/

License in file.

Frequently Q&A

Rerferences

Footnotes

1. A New Basis Set Exchange: An Open, Up-to-date Resource for the Molecular Sciences Community. Benjamin P. Pritchard, Doaa Altarawy, Brett Didier, Tara D. Gibson, Theresa L. Windus. J. Chem. Inf. Model. 2019, 59(11), 4814-4820, doi:10.1021/acs.jcim.9b00725. ↩

2. 徐光宪; 黎乐民; 王德民. 量子化学：基本原理和从头计算法, 第二版.; 科学出版社: 北京, 2007. C.2 p.67 ↩

3. Helgaker T., Jørgensen P., Olsen J. (2000). Molecular Electronic-Structure Theory . Chichester: Wiley; doi:10.1002/9781119019572 ↩