2.1.1.1.3. moha.system.integral package

2.1.1.1.3.1. Submodules

2.1.1.1.3.2. moha.system.integral.angular_momentum module

moha.system.integral.angular_momentum.Lxyz(a, lmn1, A, b, lmn2, B)[source]

Evaluates kinetic energy integral between two Gaussians Returns a float. a: orbital exponent on Gaussian ‘a’ (e.g. alpha in the text) b: orbital exponent on Gaussian ‘b’ (e.g. beta in the text) lmn1: int tuple containing orbital angular momentum (e.g. (1,0,0))

for Gaussian ‘a’

lmn2: int tuple containing orbital angular momentum for Gaussian ‘b’ A: list containing origin of Gaussian ‘a’, e.g. [1.0, 2.0, 0.0] B: list containing origin of Gaussian ‘b’

moha.system.integral.angular_momentum.angular_momentum(a, b)[source]

Evaluates kinetic energy between two contracted Gaussians Returns float. Arguments: a: contracted Gaussian ‘a’, BasisFunction object b: contracted Gaussian ‘b’, BasisFunction object

2.1.1.1.3.3. moha.system.integral.differential module

moha.system.integral.differential.D(i, j, e, A, B, a, b)[source]

Recursive definition of Hermite Gaussian coefficients. Returns a float. a: orbital exponent on Gaussian ‘a’ (e.g. alpha in the text) b: orbital exponent on Gaussian ‘b’ (e.g. beta in the text) i,j: orbital angular momentum number on Gaussian ‘a’ and ‘b’ t: number nodes in Hermite (depends on type of integral,

e.g. always zero for overlap integrals)

Qx: distance between origins of Gaussian ‘a’ and ‘b’

moha.system.integral.differential.Dxyz(a, lmn1, A, b, lmn2, B, es)[source]

Evaluates overlap integral between two Gaussians Returns a float. a: orbital exponent on Gaussian ‘a’ (e.g. alpha in the text) b: orbital exponent on Gaussian ‘b’ (e.g. beta in the text) lmn1: int tuple containing orbital angular momentum (e.g. (1,0,0))

for Gaussian ‘a’

lmn2: int tuple containing orbital angular momentum for Gaussian ‘b’ A: list containing origin of Gaussian ‘a’, e.g. [1.0, 2.0, 0.0] B: list containing origin of Gaussian ‘b’

moha.system.integral.differential.differential(a, b, es)[source]

Evaluates overlap between two contracted Gaussians Returns float. Arguments: a: contracted Gaussian ‘a’, BasisFunction object b: contracted Gaussian ‘b’, BasisFunction object

2.1.1.1.3.4. moha.system.integral.electron_repulsion module

moha.system.integral.electron_repulsion.electron_repulsion(a, b, c, d)[source]

Evaluates overlap between two contracted Gaussians Returns float. Arguments: a: contracted Gaussian ‘a’, BasisFunction object b: contracted Gaussian ‘b’, BasisFunction object c: contracted Gaussian ‘b’, BasisFunction object d: contracted Gaussian ‘b’, BasisFunction object

moha.system.integral.electron_repulsion.gxyz(a, lmn1, A, b, lmn2, B, c, lmn3, C, d, lmn4, D)[source]

Evaluates kinetic energy integral between two Gaussians Returns a float. a,b,c,d: orbital exponent on Gaussian ‘a’,’b’,’c’,’d’ lmn1,lmn2 lmn3,lmn4: int tuple containing orbital angular momentum

for Gaussian ‘a’,’b’,’c’,’d’, respectively

A,B,C,D: list containing origin of Gaussian ‘a’,’b’,’c’,’d’

2.1.1.1.3.5. moha.system.integral.kinetic module

moha.system.integral.kinetic.T(i, j, A, B, a, b)[source]

Recursive definition of Hermite Gaussian coefficients. Returns a float. a: orbital exponent on Gaussian ‘a’ (e.g. alpha in the text) b: orbital exponent on Gaussian ‘b’ (e.g. beta in the text) i,j: orbital angular momentum number on Gaussian ‘a’ and ‘b’ t: number nodes in Hermite (depends on type of integral,

e.g. always zero for overlap integrals)

Qx: distance between origins of Gaussian ‘a’ and ‘b’

moha.system.integral.kinetic.Txyz(a, lmn1, A, b, lmn2, B)[source]

Evaluates kinetic energy integral between two Gaussians Returns a float. a: orbital exponent on Gaussian ‘a’ (e.g. alpha in the text) b: orbital exponent on Gaussian ‘b’ (e.g. beta in the text) lmn1: int tuple containing orbital angular momentum (e.g. (1,0,0))

for Gaussian ‘a’

lmn2: int tuple containing orbital angular momentum for Gaussian ‘b’ A: list containing origin of Gaussian ‘a’, e.g. [1.0, 2.0, 0.0] B: list containing origin of Gaussian ‘b’

moha.system.integral.kinetic.kinetic(a, b)[source]

Evaluates kinetic energy between two contracted Gaussians Returns float. Arguments: a: contracted Gaussian ‘a’, BasisFunction object b: contracted Gaussian ‘b’, BasisFunction object

2.1.1.1.3.6. moha.system.integral.linear_momentum module

moha.system.integral.linear_momentum.Pxyz(a, lmn1, A, b, lmn2, B)[source]

Evaluates kinetic energy integral between two Gaussians Returns a float. a: orbital exponent on Gaussian ‘a’ (e.g. alpha in the text) b: orbital exponent on Gaussian ‘b’ (e.g. beta in the text) lmn1: int tuple containing orbital angular momentum (e.g. (1,0,0))

for Gaussian ‘a’

lmn2: int tuple containing orbital angular momentum for Gaussian ‘b’ A: list containing origin of Gaussian ‘a’, e.g. [1.0, 2.0, 0.0] B: list containing origin of Gaussian ‘b’

moha.system.integral.linear_momentum.linear_momentum(a, b)[source]

Evaluates kinetic energy between two contracted Gaussians Returns float. Arguments: a: contracted Gaussian ‘a’, BasisFunction object b: contracted Gaussian ‘b’, BasisFunction object

2.1.1.1.3.7. moha.system.integral.multipole_moment module

moha.system.integral.multipole_moment.MM(i, j, e, A, B, C, a, b)[source]

Recursive definition of Hermite Gaussian coefficients. Returns a float. a: orbital exponent on Gaussian ‘a’ (e.g. alpha in the text) b: orbital exponent on Gaussian ‘b’ (e.g. beta in the text) i,j: orbital angular momentum number on Gaussian ‘a’ and ‘b’ t: number nodes in Hermite (depends on type of integral,

e.g. always zero for overlap integrals)

Qx: distance between origins of Gaussian ‘a’ and ‘b’

moha.system.integral.multipole_moment.MMxyz(a, lmn1, A, b, lmn2, B, lmn3, C)[source]

Evaluates overlap integral between two Gaussians Returns a float. a: orbital exponent on Gaussian ‘a’ (e.g. alpha in the text) b: orbital exponent on Gaussian ‘b’ (e.g. beta in the text) lmn1: int tuple containing orbital angular momentum (e.g. (1,0,0))

for Gaussian ‘a’

lmn2: int tuple containing orbital angular momentum for Gaussian ‘b’ A: list containing origin of Gaussian ‘a’, e.g. [1.0, 2.0, 0.0] B: list containing origin of Gaussian ‘b’

moha.system.integral.multipole_moment.multipole_moment(a, b, lmn, C)[source]

Evaluates overlap between two contracted Gaussians Returns float. Arguments: a: contracted Gaussian ‘a’, BasisFunction object b: contracted Gaussian ‘b’, BasisFunction object

2.1.1.1.3.8. moha.system.integral.nuclear_attraction module

moha.system.integral.nuclear_attraction.E(i, j, t, A, B, a, b)[source]

Recursive definition of Hermite Gaussian coefficients. Returns a float. a: orbital exponent on Gaussian ‘a’ (e.g. alpha in the text) b: orbital exponent on Gaussian ‘b’ (e.g. beta in the text) i,j: orbital angular momentum number on Gaussian ‘a’ and ‘b’ t: number nodes in Hermite (depends on type of integral,

e.g. always zero for overlap integrals)

Qx: distance between origins of Gaussian ‘a’ and ‘b’

moha.system.integral.nuclear_attraction.R(t, u, v, n, p, PCx, PCy, PCz, RPC)[source]

Returns the Coulomb auxiliary Hermite integrals Returns a float. Arguments: t,u,v: order of Coulomb Hermite derivative in x,y,z

(see defs in Helgaker and Taylor)

n: order of Boys function PCx,y,z: Cartesian vector distance between Gaussian

composite center P and nuclear center C

RPC: Distance between P and C

moha.system.integral.nuclear_attraction.Vxyz(a, lmn1, A, b, lmn2, B, C)[source]

Evaluates kinetic energy integral between two Gaussians Returns a float. a: orbital exponent on Gaussian ‘a’ (e.g. alpha in the text) b: orbital exponent on Gaussian ‘b’ (e.g. beta in the text) lmn1: int tuple containing orbital angular momentum (e.g. (1,0,0))

for Gaussian ‘a’

lmn2: int tuple containing orbital angular momentum for Gaussian ‘b’ A: list containing origin of Gaussian ‘a’, e.g. [1.0, 2.0, 0.0] B: list containing origin of Gaussian ‘b’ C: list containing origin of nuclear center ‘C’

moha.system.integral.nuclear_attraction.nuclear_attraction(a, b, C)[source]

Evaluates overlap between two contracted Gaussians Returns float. Arguments: a: contracted Gaussian ‘a’, BasisFunction object b: contracted Gaussian ‘b’, BasisFunction object C: center of nucleus

2.1.1.1.3.9. moha.system.integral.overlap module

moha.system.integral.overlap.S(i, j, A, B, a, b)[source]
Recursive definition of Hermite Gaussian coefficients.

Returns a float.

a

orbital exponent on Gaussian ‘a’ (e.g. alpha in the text)

b

orbital exponent on Gaussian ‘b’ (e.g. beta in the text)

i,j:

orbital angular momentum number on Gaussian ‘a’ and ‘b’

t:
number nodes in Hermite (depends on type of integral,

e.g. always zero for overlap integrals)

Qx: distance between origins of Gaussian ‘a’ and ‘b’

moha.system.integral.overlap.Sxyz(a, lmn1, A, b, lmn2, B)[source]
Evaluates overlap integral between two Gaussians

Returns a float.

a: orbital exponent on Gaussian ‘a’ (e.g. alpha in the text) b: orbital exponent on Gaussian ‘b’ (e.g. beta in the text) lmn1: int tuple containing orbital angular momentum (e.g. (1,0,0))

for Gaussian ‘a’

lmn2: int tuple containing orbital angular momentum for Gaussian ‘b’ A: list containing origin of Gaussian ‘a’, e.g. [1.0, 2.0, 0.0] B: list containing origin of Gaussian ‘b’

moha.system.integral.overlap.overlap(a, b)[source]

Evaluates overlap between two contracted Gaussians Returns float. Arguments: a: contracted Gaussian ‘a’, BasisFunction object b: contracted Gaussian ‘b’, BasisFunction object

2.1.1.1.3.10. Module contents