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Adding projection operator for NH3 and ethylene
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,71 @@ | ||
| { | ||
| "name":"d2h", | ||
| "classes": [ | ||
| { | ||
| "symbol": "E", | ||
| "multiplicity": 1 | ||
| }, | ||
| { | ||
| "symbol": "C2(z)", | ||
| "multiplicity": 1 | ||
| }, | ||
| { | ||
| "symbol": "C2(y)", | ||
| "multiplicity": 1 | ||
| }, | ||
| { | ||
| "symbol": "C2(x)", | ||
| "multiplicity": 1 | ||
| }, | ||
| { | ||
| "symbol": "i", | ||
| "multiplicity": 1 | ||
| }, | ||
| { | ||
| "symbol": "sigma(xy)", | ||
| "multiplicity": 1 | ||
| }, | ||
| { | ||
| "symbol": "sigma(xz)", | ||
| "multiplicity": 1 | ||
| }, | ||
| { | ||
| "symbol": "sigma(yz)", | ||
| "multiplicity": 1 | ||
| } | ||
| ], | ||
| "symmetry_groups": [ | ||
| { | ||
| "symbol": "Ag", | ||
| "characters": [1,1,1,1,1,1,1,1] | ||
| }, | ||
| { | ||
| "symbol": "B1g", | ||
| "characters": [1,1,-1,-1,1,1,-1,-1] | ||
| }, | ||
| { | ||
| "symbol": "B2g", | ||
| "characters": [1,-1,1,-1,1,-1,1,-1] | ||
| }, | ||
| { | ||
| "symbol": "B3g", | ||
| "characters": [1,-1,-1,1,1,-1,-1,1] | ||
| }, | ||
| { | ||
| "symbol": "Au", | ||
| "characters": [1,1,1,1,-1,-1,-1,-1] | ||
| }, | ||
| { | ||
| "symbol": "B1u", | ||
| "characters": [1,1,-1,-1,-1,-1,1,1] | ||
| }, | ||
| { | ||
| "symbol": "B2u", | ||
| "characters": [1,-1,1,-1,-1,1,-1,1] | ||
| }, | ||
| { | ||
| "symbol": "B3u", | ||
| "characters": [1,-1,-1,1,-1,1,1,-1] | ||
| } | ||
| ] | ||
| } |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,101 @@ | ||
| # -*- coding: utf-8 -*- | ||
|
|
||
| import numpy as np | ||
| from collections import Counter | ||
|
|
||
| class ProjectionOperator: | ||
|
|
||
| def __init__(self, ct, so): | ||
| # | ||
| # ToDo: assert that the objects have the right type | ||
| # | ||
|
|
||
| self.ct = ct # character table | ||
| self.so = so # symmetry operations | ||
| self.groups = None | ||
| self.irreps = None | ||
|
|
||
| def collect(self): | ||
| """ | ||
| Construct groups of basis functions that can transform among each | ||
| other and figure out which irreps these span | ||
| """ | ||
| # create one logical matrix that shows the interaction | ||
| groupmatrix = np.zeros_like(self.so.operation_matrices[0], dtype=np.bool8) | ||
| for m in self.so.operation_matrices: | ||
| bm = np.abs(m) > 1e-9 | ||
| groupmatrix = np.logical_or(groupmatrix, bm) | ||
|
|
||
| #print(groupmatrix) | ||
|
|
||
| # collect the groups | ||
| self.groups = [] | ||
| for i,row in enumerate(groupmatrix): | ||
| if np.sum(row) > 1: | ||
| idx = np.where(row)[0] | ||
| self.groups.append(np.array(idx, dtype=np.int64)) | ||
| else: | ||
| self.groups.append(np.array([i], dtype=np.int64)) | ||
|
|
||
| # create unique list | ||
| self.groups = np.array(self.groups, dtype=object) | ||
| res = Counter(map(tuple, self.groups)) | ||
| self.groups = [r for r in res] | ||
|
|
||
| # determine irreps per lips | ||
| self.irreps = [] | ||
| for g in self.groups: | ||
| chars = [np.sum(np.take(np.diagonal(m),g)) for m in self.so.operation_matrices] | ||
| self.irreps.append(self.ct.lot(chars)) | ||
|
|
||
| def build_mos(self): | ||
| # check if groups have been collected | ||
| if self.groups is None: | ||
| self.collect() | ||
|
|
||
| # build molecular orbitals | ||
| self.mos = np.zeros((len(self.so.mol.basis), len(self.so.mol.basis)), | ||
| dtype=np.float64) | ||
| mo_idx = 0 | ||
| for g,irreplist in zip(self.groups,self.irreps): | ||
| for j,irrep in enumerate(irreplist): # loop over irreps | ||
|
|
||
| # early exit if there are no irreps of this type | ||
| if irrep == 0: | ||
| continue | ||
|
|
||
| irrep_e = self.ct.get_character(j,0) # get dimensionality of irrep | ||
|
|
||
| irrepres = np.zeros((int(irrep * irrep_e), len(self.so.mol.basis))) | ||
| for k in range(int(irrep * irrep_e)): # loop over times the irrep is present | ||
| #label = self.ct.get_label_irrep(j) | ||
| res = self.apply_projection_operator(g[k], j) | ||
| irrepres[k,:] = res | ||
|
|
||
| # perform orthogonalization if the irrep space is larger than 1 | ||
| if len(irrepres) > 1: | ||
| S = irrepres @ irrepres.transpose() | ||
| e,v = np.linalg.eigh(S) | ||
| X = v @ np.diag(1.0 / np.sqrt(e)) @ v.transpose() | ||
| irrepres = X @ irrepres | ||
|
|
||
| for mo in irrepres: | ||
| self.mos[mo_idx] = mo | ||
| mo_idx += 1 | ||
| else: | ||
| self.mos[mo_idx] = irrepres[0,:] | ||
| mo_idx += 1 | ||
|
|
||
| return self.mos | ||
|
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||
|
|
||
| def apply_projection_operator(self, bf_idx, irrep_idx): | ||
| """ | ||
| Apply the projection operator to a basis function | ||
| """ | ||
| res = np.zeros(len(self.so.mol.basis)) | ||
| for i,m in enumerate(self.so.operation_matrices): | ||
| res += self.ct.get_character(irrep_idx, i) * m[bf_idx,:] | ||
|
|
||
| # return result and normalize it | ||
| return np.array(res, dtype=np.float64) / np.linalg.norm(res) |
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