53#ifndef _math_symmetry_pointgrp_h
54#define _math_symmetry_pointgrp_h
58#include <util/class/class.h>
59#include <util/state/state.h>
60#include <util/keyval/keyval.h>
61#include <math/scmat/vector3.h>
70class SymmetryOperation {
76 SymmetryOperation(
const SymmetryOperation &);
80 double trace()
const {
return d[0][0]+d[1][1]+d[2][2]; }
96 void zero() { memset(d,0,
sizeof(
double)*9); }
99 SymmetryOperation
operate(
const SymmetryOperation& r)
const;
102 SymmetryOperation
transform(
const SymmetryOperation& r)
const;
105 void unit() {
zero(); d[0][0] = d[1][1] = d[2][2] = 1.0; }
111 void i() {
zero(); d[0][0] = d[1][1] = d[2][2] = -1.0; }
159 inline double trace()
const;
176 void zero() { memset(d,0,
sizeof(
double)*25); }
186 zero(); d[0][0] = d[1][1] = d[2][2] = d[3][3] = d[4][4] = 1.0;
193 void i() {
zero(); d[0][0] = d[1][1] = d[2][2] = d[3][3] = d[4][4] = -1.0;}
222 for (
int i=0;
i < n;
i++)
239class IrreducibleRepresentation {
240 friend class CharacterTable;
254 IrreducibleRepresentation();
255 IrreducibleRepresentation(
const IrreducibleRepresentation&);
261 ~IrreducibleRepresentation();
263 IrreducibleRepresentation& operator=(
const IrreducibleRepresentation&);
266 void init(
int =0,
int =0,
const char* =0,
const char* =0);
278 int nproj()
const {
return degen*degen; }
281 int nrot()
const {
return nrot_; }
287 const char *
symbol()
const {
return symb; }
292 const char *
symbol_ns()
const {
return (csymb?csymb:symb); }
297 return complex_ ? 0.5*rep[i].trace() : rep[i].trace();
301 double p(
int x1,
int x2,
int i)
const {
return rep[i](x1,x2); }
305 double p(
int d,
int i)
const {
306 int dc=d/degen;
int dr=d%degen;
307 return rep[i](dr,dc);
325class CharacterTable {
327 enum pgroups {C1, CS, CI, CN, CNV, CNH, DN, DND, DNH, SN, T, TH, TD, O,
364 CharacterTable(
const CharacterTable&);
367 CharacterTable& operator=(
const CharacterTable&);
374 const char *
symbol()
const {
return symb; }
384 if (pg==CN || pg==SN || pg==CNH || pg==T || pg==TH)
394 for (
int i=0; i < nirrep_; i++) {
395 int nc = (gamma_[i].
complex()) ? 1 : gamma_[i].degen;
403 for (
int ir=0, cn=0; ir < nirrep_; ir++) {
404 int nc = (gamma_[ir].complex()) ? 1 : gamma_[ir].degen;
405 for (
int c=0; c < nc; c++,cn++)
414 for (
int ir=0, cn=0; ir < nirrep_; ir++) {
415 int nc = (gamma_[ir].complex()) ? 1 : gamma_[ir].degen;
416 for (
int c=0; c < nc; c++,cn++)
436class PointGroup:
public SavableState {
490 PointGroup(
const PointGroup&);
494 PointGroup& operator=(
const PointGroup&);
502 const char *
symbol()
const {
return symb; }
The CharacterTable class provides a workable character table for all of the non-cubic point groups.
Definition pointgrp.h:325
IrreducibleRepresentation & gamma(int i)
Returns the i'th irrep.
Definition pointgrp.h:376
int order() const
Returns the order of the point group.
Definition pointgrp.h:372
int which_irrep(int i)
Returns the irrep component i belongs to.
Definition pointgrp.h:402
CharacterTable(const char *)
This constructor takes the Schoenflies symbol of a point group as input.
void print(std::ostream &=ExEnv::out0()) const
This prints the irrep to the given file, or stdout if none is given.
SymmetryOperation & symm_operation(int i)
Returns the i'th symmetry operation.
Definition pointgrp.h:378
const char * symbol() const
Returns the Schoenflies symbol for the point group.
Definition pointgrp.h:374
int complex() const
Cn, Cnh, Sn, T, and Th point groups have complex representations.
Definition pointgrp.h:383
int inverse(int i) const
Returns the index of the symop which is the inverse of symop[i].
Definition pointgrp.h:390
int which_comp(int i)
Returns which component i is.
Definition pointgrp.h:413
CharacterTable(const char *, const SymmetryOperation &)
This is like the above, but it also takes a reference to a SymmetryOperation which is the frame of re...
int nirrep() const
Returns the number of irreps.
Definition pointgrp.h:370
static std::ostream & out0()
Return an ostream that writes from node 0.
The IrreducibleRepresentation class provides information associated with a particular irreducible rep...
Definition pointgrp.h:239
int ntrans() const
Returns the number of translations associated with the irrep.
Definition pointgrp.h:284
const char * symbol_ns() const
Returns the Mulliken symbol for the irrep without special characters.
Definition pointgrp.h:292
int order() const
Returns the order of the group.
Definition pointgrp.h:269
IrreducibleRepresentation(int, int, const char *, const char *=0)
This constructor takes as arguments the order of the point group, the degeneracy of the irrep,...
void init(int=0, int=0, const char *=0, const char *=0)
Initialize the order, degeneracy, and Mulliken symbol of the irrep.
int nproj() const
Returns the number of projection operators for the irrep.
Definition pointgrp.h:278
double p(int d, int i) const
Returns the character for the d'th contribution to the i'th representation matrix.
Definition pointgrp.h:305
int degeneracy() const
Returns the degeneracy of the irrep.
Definition pointgrp.h:272
double p(int x1, int x2, int i) const
Returns the element (x1,x2) of the i'th representation matrix.
Definition pointgrp.h:301
int complex() const
Returns the value of complex_.
Definition pointgrp.h:275
int nrot() const
Returns the number of rotations associated with the irrep.
Definition pointgrp.h:281
double character(int i) const
Returns the character for the i'th symmetry operation of the point group.
Definition pointgrp.h:296
const char * symbol() const
Returns the Mulliken symbol for the irrep.
Definition pointgrp.h:287
void print(std::ostream &=ExEnv::out0()) const
This prints the irrep to the given file, or stdout if none is given.
int equiv(const Ref< PointGroup > &, double tol=1.0e-6) const
Returns 1 if the point groups are equivalent, 0 otherwise.
PointGroup(const char *, SymmetryOperation &)
Like the above, but this constructor also takes a frame of reference as an argument.
void set_symbol(const char *)
Sets (or resets) the Schoenflies symbol.
const char * symbol() const
Returns the Schoenflies symbol for this point group.
Definition pointgrp.h:502
void print(std::ostream &o=ExEnv::out0()) const
Print the object.
SCVector3 & origin()
Returns the origin of the symmetry frame.
Definition pointgrp.h:508
PointGroup(const char *)
This constructor takes a string containing the Schoenflies symbol of the point group as its only argu...
CharacterTable char_table() const
Returns the CharacterTable for this point group.
const SymmetryOperation & symm_frame() const
A const version of the above.
Definition pointgrp.h:506
void save_data_state(StateOut &so)
Save the base classes (with save_data_state) and the members in the same order that the StateIn CTOR ...
PointGroup(const Ref< KeyVal > &)
The PointGroup KeyVal constructor looks for three keywords: symmetry, symmetry_frame,...
SymmetryOperation & symm_frame()
Returns the frame of reference for this point group.
Definition pointgrp.h:504
PointGroup(const char *, SymmetryOperation &, const SCVector3 &)
Like the above, but this constructor also takes a point of origin as an argument.
A template class that maintains references counts.
Definition ref.h:332
Restores objects that derive from SavableState.
Definition statein.h:70
Serializes objects that derive from SavableState.
Definition stateout.h:61
The SymRep class provides an n dimensional matrix representation of a symmetry operation,...
Definition pointgrp.h:145
void c2_y()
Set equal to C2 about the x axis.
const double * operator[](int i) const
const version of the above
Definition pointgrp.h:167
SymRep operate(const SymRep &r) const
This operates on this with r (i.e. return r * this).
double & operator()(int i, int j)
returns a reference to the (i,j)th element of the transformation matrix
Definition pointgrp.h:171
void E()
Set equal to the identity.
Definition pointgrp.h:190
void set_dim(int i)
set the dimension of d
Definition pointgrp.h:162
void rotation(int n)
Set equal to a clockwise rotation by 2pi/n.
void unit()
Set equal to a unit matrix.
Definition pointgrp.h:185
void sigma_h()
Set equal to reflection in xy plane.
void sigma_yz()
Set equal to reflection in yz plane.
void c2_x()
Set equal to C2 about the x axis.
void zero()
zero out the symop
Definition pointgrp.h:176
double * operator[](int i)
returns the i'th row of the transformation matrix
Definition pointgrp.h:165
void print(std::ostream &=ExEnv::out0()) const
print the matrix
void sigma_xz()
Set equal to reflection in xz plane.
void i()
Set equal to an inversion.
Definition pointgrp.h:193
double trace() const
returns the trace of the transformation matrix
Definition pointgrp.h:219
double operator()(int i, int j) const
const version of double& operator()(int i, int j)
Definition pointgrp.h:173
SymRep transform(const SymRep &r) const
This performs the transform r * this * r~.
The SymmetryOperation class provides a 3 by 3 matrix representation of a symmetry operation,...
Definition pointgrp.h:70
void unit()
Set equal to a unit matrix.
Definition pointgrp.h:105
double operator()(int i, int j) const
const version of the above
Definition pointgrp.h:93
void c2_x()
Set equal to C2 about the x axis.
Definition pointgrp.h:127
SymmetryOperation operate(const SymmetryOperation &r) const
This operates on this with r (i.e. return r * this).
void rotation(int n)
Set equal to a clockwise rotation by 2pi/n.
double * operator[](int i)
returns the i'th row of the transformation matrix
Definition pointgrp.h:83
double & operator()(int i, int j)
returns a reference to the (i,j)th element of the transformation matrix
Definition pointgrp.h:90
void c2_y()
Set equal to C2 about the x axis.
Definition pointgrp.h:130
double trace() const
returns the trace of the transformation matrix
Definition pointgrp.h:80
SymmetryOperation transform(const SymmetryOperation &r) const
This performs the transform r * this * r~.
void zero()
zero out the symop
Definition pointgrp.h:96
void E()
Set equal to E.
Definition pointgrp.h:108
void sigma_h()
Set equal to reflection in xy plane.
Definition pointgrp.h:114
void i()
Set equal to an inversion.
Definition pointgrp.h:111
void sigma_xz()
Set equal to reflection in xz plane.
Definition pointgrp.h:117
void print(std::ostream &=ExEnv::out0()) const
print the matrix
void sigma_yz()
Set equal to reflection in yz plane.
Definition pointgrp.h:120
const double * operator[](int i) const
const version of the above
Definition pointgrp.h:86