CheMPS2::FCI Class Reference

#include <FCI.h>

Public Member Functions
	FCI (CheMPS2::Hamiltonian *Ham, const unsigned int Nel_up, const unsigned int Nel_down, const int TargetIrrep, const double maxMemWorkMB=100.0, const int FCIverbose=2)
	Constructor. More...
virtual	~FCI ()
	Destructor.
unsigned int	getL () const
	Getter for the number of orbitals. More...
unsigned int	getNel_up () const
	Getter for the number of up or alpha electrons. More...
unsigned int	getNel_down () const
	Getter for the number of down or beta electrons. More...
unsigned int	getVecLength (const int irrep_center) const
	Getter for the number of variables in the vector " E_ij | FCI vector > " ; where irrep_center = I_i x I_j. More...
int	getTargetIrrep () const
	Get the target irrep. More...
int	getOrb2Irrep (const int orb) const
	Get an orbital irrep. More...
double	getERI (const int orb1, const int orb2, const int orb3, const int orb4) const
	Function which returns the electron repulsion integral (in chemists notation: integral dr1 dr2 orb1(r1) * orb2(r1) * orb3(r2) * orb4(r2) / |r1-r2|) More...
double	getGmat (const int orb1, const int orb2) const
	Function which returns the AUGMENTED one-body matrix elements ( G_{ij} = T_{ij} - 0.5 * sum_k ERI_{ikkj} ; see Chem. Phys. Lett. 111 (4-5), 315-321 (1984) ) More...
double	getEconst () const
	Function which returns the nuclear repulsion energy. More...
double	GSDavidson (double *inoutput=NULL, const int DVDSN_NUM_VEC=CheMPS2::DAVIDSON_NUM_VEC) const
	Calculates the FCI ground state with Davidson's algorithm. More...
unsigned int	LowestEnergyDeterminant () const
	Return the global counter of the Slater determinant with the lowest energy. More...
double	Fill2RDM (double *vector, double *TwoRDM) const
	Construct the (spin-summed) 2-RDM of a FCI vector: Gamma^2(i,j,k,l) = sum_sigma,tau < a^+_i,sigma a^+_j,tau a_l,tau a_k,sigma > = TwoRDM[ i + L * ( j + L * ( k + L * l ) ) ]. More...
void	Fill3RDM (double *vector, double *ThreeRDM) const
	Construct the (spin-summed) 3-RDM of a FCI vector: Gamma^3(i,j,k,l,m,n) = sum_sigma,tau,s < a^+_{i,sigma} a^+_{j,tau} a^+_{k,s} a_{n,s} a_{m,tau} a_{l,sigma} > = ThreeRDM[ i + L * ( j + L * ( k + L * ( l + L * ( m + L * n ) ) ) ) ]. More...
void	Fill4RDM (double *vector, double *FourRDM) const
	Construct the (spin-summed) 4-RDM of a FCI vector: Gamma^4(i,j,k,l,p,q,r,t) = sum_sigma,tau,s,z < a^+_{i,sigma} a^+_{j,tau} a^+_{k,s} a^+_{l,z} a_{t,z} a_{r,s} a_{q,tau} a_{p,sigma} > = FourRDM[ i + L * ( j + L * ( k + L * ( l + L * ( p + L * ( q + L * ( r + L * t ) ) ) ) ) ) ]. More...
void	Fock4RDM (double *vector, double *ThreeRDM, double *Fock, double *output) const
	Construct the (spin-summed) contraction of the 4-RDM with the Fock operator: output(i,j,k,p,q,r) = sum_{l,t} Fock(l,t) * Gamma^4(i,j,k,l,p,q,r,t) More...
void	Diag4RDM (double *vector, double *three_rdm, const unsigned int orbz, double *output) const
	Construct part of the 4-RDM: output(i,j,k,p,q,r) = Gamma^4(i,j,k,z,p,q,r,z) More...
double	CalcSpinSquared (double *vector) const
	Measure S(S+1) (spin squared) More...
void	RetardedGF (const double omega, const double eta, const unsigned int orb_alpha, const unsigned int orb_beta, const bool isUp, const double GSenergy, double *GSvector, CheMPS2::Hamiltonian *Ham, double *RePartGF, double *ImPartGF) const
	Calculate the retarded Green's function (= addition + removal amplitude) More...
void	RetardedGF_addition (const double omega, const double eta, const unsigned int orb_alpha, const unsigned int orb_beta, const bool isUp, const double GSenergy, double *GSvector, CheMPS2::Hamiltonian *Ham, double *RePartGF, double *ImPartGF, double *TwoRDMreal=NULL, double *TwoRDMimag=NULL, double *TwoRDMadd=NULL) const
	Calculate the addition part of the retarded Green's function: <GSvector| a_{alpha, spin(isUp)} [ omega - Ham + GSenergy + I*eta ]^{-1} a^+_{beta, spin(isUp)} |GSvector> More...
void	GFmatrix_addition (const double alpha, const double beta, const double eta, int *orbsLeft, const unsigned int numLeft, int *orbsRight, const unsigned int numRight, const bool isUp, double *GSvector, CheMPS2::Hamiltonian *Ham, double *RePartsGF, double *ImPartsGF, double **TwoRDMreal=NULL, double **TwoRDMimag=NULL, double **TwoRDMadd=NULL) const
	Calculate the addition Green's function: GF[i+numLeft*j] = <GSvector| a_{orbsLeft[i], spin} [ alpha + beta * Ham + I*eta ]^{-1} a^+_{orbsRight[j], spin} |GSvector> More...
void	RetardedGF_removal (const double omega, const double eta, const unsigned int orb_alpha, const unsigned int orb_beta, const bool isUp, const double GSenergy, double *GSvector, CheMPS2::Hamiltonian *Ham, double *RePartGF, double *ImPartGF, double *TwoRDMreal=NULL, double *TwoRDMimag=NULL, double *TwoRDMrem=NULL) const
	Calculate the removal part of the retarded Green's function: <GSvector| a^+_{beta, spin(isUp)} [ omega + Ham - GSenergy + I*eta ]^{-1} a_{alpha, spin(isUp)} |GSvector> More...
void	GFmatrix_removal (const double alpha, const double beta, const double eta, int *orbsLeft, const unsigned int numLeft, int *orbsRight, const unsigned int numRight, const bool isUp, double *GSvector, CheMPS2::Hamiltonian *Ham, double *RePartsGF, double *ImPartsGF, double **TwoRDMreal=NULL, double **TwoRDMimag=NULL, double **TwoRDMrem=NULL) const
	Calculate the removal Green's function: GF[i+numLeft*j] = <GSvector| a^+_{orbsLeft[i], spin} [ alpha + beta * Ham + I*eta ]^{-1} a_{orbsRight[j], spin} |GSvector> More...
void	DensityResponseGF (const double omega, const double eta, const unsigned int orb_alpha, const unsigned int orb_beta, const double GSenergy, double *GSvector, double *RePartGF, double *ImPartGF) const
	Calculate the density response Green's function (= forward - backward propagating part) More...
void	DensityResponseGF_forward (const double omega, const double eta, const unsigned int orb_alpha, const unsigned int orb_beta, const double GSenergy, double *GSvector, double *RePartGF, double *ImPartGF, double *TwoRDMreal=NULL, double *TwoRDMimag=NULL, double *TwoRDMdens=NULL) const
	Calculate the forward propagating part of the density response Green's function: <GSvector| ( n_alpha - <GSvector| n_alpha |GSvector> ) [ omega - Ham + GSenergy + I*eta ]^{-1} ( n_beta - <GSvector| n_beta |GSvector> ) |GSvector> More...
void	DensityResponseGF_backward (const double omega, const double eta, const unsigned int orb_alpha, const unsigned int orb_beta, const double GSenergy, double *GSvector, double *RePartGF, double *ImPartGF, double *TwoRDMreal=NULL, double *TwoRDMimag=NULL, double *TwoRDMdens=NULL) const
	Calculate the backward propagating part of the density response Green's function: <GSvector| ( n_beta - <GSvector| n_beta |GSvector> ) [ omega + Ham - GSenergy + I*eta ]^{-1} ( n_alpha - <GSvector| n_alpha |GSvector> ) |GSvector> More...
void	CGSolveSystem (const double alpha, const double beta, const double eta, double *RHS, double *RealSol, double *ImagSol, const bool checkError=true) const
	Calculate the solution of the equation ( alpha + beta * Hamiltonian + I * eta ) Solution = RHS with conjugate gradient. More...
double	getFCIcoeff (int *bits_up, int *bits_down, double *vector) const
	Function which returns a FCI coefficient. More...

Static Public Member Functions
static void	FillRandom (const unsigned int vecLength, double *vec)
	Fill a vector with random numbers in the interval [-1,1[; used when output for GSDavidson is desired but no specific input can be given. More...
static void	ClearVector (const unsigned int vecLength, double *vec)
	Set the entries of a vector to zero. More...

Protected Member Functions
void	DiagHam (double *diag) const
	Function which returns the diagonal elements of the FCI Hamiltonian (without Econstant!!) = Slater determinant energies. More...
void	DiagHamSquared (double *output) const
	Function which returns the diagonal elements of the FCI Hamiltonian squared (without Econstant!!) More...
void	matvec (double *input, double *output) const
	Function which performs the Hamiltonian times Vector product (without Econstant!!) making use of the (ij|kl) = (ji|kl) = (ij|lk) = (ji|lk) symmetry of the electron repulsion integrals. More...
double	GetMatrixElement (int *bits_bra_up, int *bits_bra_down, int *bits_ket_up, int *bits_ket_down, int *work) const
	Sandwich the Hamiltonian between two Slater determinants (return a specific element) (without Econstant!!) More...
void	getBitsOfCounter (const int irrep_center, const unsigned int counter, int *bits_up, int *bits_down) const
	Find the bit representation of a global counter corresponding to " E_ij | FCI vector > " ; where irrep_center = I_i x I_j. More...
int	getUpIrrepOfCounter (const int irrep_center, const unsigned int counter) const
	Find the irrep of the up Slater determinant of a global counter corresponding to " E_ij | FCI vector > " ; where irrep_center = I_i x I_j. More...
void	ActWithSecondQuantizedOperator (const char whichOperator, const bool isUp, const unsigned int orbIndex, double *thisVector, const FCI *otherFCI, double *otherVector) const
	Set thisVector to a creator/annihilator acting on otherVector. More...
void	ActWithNumberOperator (const unsigned int orbIndex, double *resultVector, double *sourceVector) const
	Set resultVector to the number operator of a specific site acting on sourceVector. More...
void	CGCoreSolver (const double alpha, const double beta, const double eta, double *precon, double *Sol, double *RESID, double *PVEC, double *OxPVEC, double *temp, double *temp2) const
	Calculate the solution of the system Operator |Sol> = |RESID> with Operator = precon * [ ( alpha + beta * H )^2 + eta^2 ] * precon. More...
void	CGAlphaPlusBetaHAM (const double alpha, const double beta, double *in, double *out) const
	Calculate out = (alpha + beta * Hamiltonian) * in (Econstant is taken into account!!) More...
void	CGoperator (const double alpha, const double beta, const double eta, double *in, double *temp, double *out) const
	Calculate out = [(alpha + beta * Hamiltonian)^2 + eta^2] * in (Econstant is taken into account!!) More...
void	CGdiagonal (const double alpha, const double beta, const double eta, double *diagonal, double *workspace) const
	Calculate (without approximation) diagonal = diag[ (alpha + beta * Hamiltonian)^2 + eta^2 ] (Econstant is taken into account!!) More...
void	apply_excitation (double *orig_vector, double *result_vector, const int crea, const int anni, const int orig_target_irrep) const
	Apply E_{crea,anni} to |orig_vector> and store the result in |result_vector> More...

Static Protected Member Functions
static void	str2bits (const unsigned int Lvalue, const unsigned int bitstring, int *bits)
	Convertor between two representations of a same spin-projection Slater determinant. More...
static unsigned int	bits2str (const unsigned int Lvalue, int *bits)
	Convertor between two representations of a same spin-projection Slater determinant. More...
static double	FCIddot (const unsigned int vecLength, double *vec1, double *vec2)
	Take the inproduct of two vectors. More...
static void	FCIdcopy (const unsigned int vecLength, double *origin, double *target)
	Copy a vector. More...
static double	FCIfrobeniusnorm (const unsigned int vecLength, double *vec)
	Calculate the 2-norm of a vector. More...
static void	FCIdaxpy (const unsigned int vecLength, const double alpha, double *vec_x, double *vec_y)
	Do lapack's daxpy vec_y += alpha * vec_x. More...
static void	FCIdscal (const unsigned int vecLength, const double alpha, double *vec)
	Do lapack's dscal vec *= alpha. More...

Detailed Description

FCI class.

Author

Sebastian Wouters sebas.nosp@m.tian.nosp@m.woute.nosp@m.rs@g.nosp@m.mail..nosp@m.com

Date

November 6, 2014

The FCI class performs the full configuration interaction ground state calculation in a given particle number, irrep, and spin projection sector of a given Hamiltonian. It also contains the functionality to calculate Green's functions.

Definition at line 32 of file FCI.h.

Constructor & Destructor Documentation

CheMPS2::FCI::FCI	(	CheMPS2::Hamiltonian *	Ham,
		const unsigned int	Nel_up,
		const unsigned int	Nel_down,
		const int	TargetIrrep,
		const double	maxMemWorkMB = 100.0,
		const int	FCIverbose = 2
	)

Constructor.

Parameters

Ham	The Hamiltonian matrix elements
Nel_up	The number of up (alpha) electrons
Nel_down	The number of down (beta) electrons
TargetIrrep	The targeted point group irrep
maxMemWorkMB	Maximum workspace size in MB to be used for matrix vector product (this does not include the FCI vectors as stored for example in GSDavidson!!)
FCIverbose	The FCI verbose level: 0 print nothing, 1 print start and solution, 2 print everything

Definition at line 37 of file FCI.cpp.

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Member Function Documentation

void CheMPS2::FCI::ActWithNumberOperator ( const unsigned int  orbIndex, double *  resultVector, double *  sourceVector  ) const

protected

Set resultVector to the number operator of a specific site acting on sourceVector.

Parameters

orbIndex	Orbital index of the number operator
resultVector	Vector with length getVecLength(0) where the result of the operation should be stored
sourceVector	Vector with length getVecLength(0) on which the number operator acts

Definition at line 1957 of file FCI.cpp.

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void CheMPS2::FCI::ActWithSecondQuantizedOperator ( const char  whichOperator, const bool  isUp, const unsigned int  orbIndex, double *  thisVector, const FCI *  otherFCI, double *  otherVector  ) const

protected

Set thisVector to a creator/annihilator acting on otherVector.

Parameters

whichOperator	With which operator should be acted on the other FCI state: C means creator and A means annihilator
isUp	Boolean which denotes if the operator corresponds to an up (alpha) or down (beta) electron
orbIndex	Orbital index on which the operator acts
thisVector	Vector with length getVecLength(0) where the result of the operation should be stored
otherFCI	FCI instance which corresponds to the FCI vector otherVector on which is acted
otherVector	Vector with length otherFCI->getVecLength(0) which contains the FCI vector on which is acted

Definition at line 1975 of file FCI.cpp.

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void CheMPS2::FCI::apply_excitation ( double *  orig_vector, double *  result_vector, const int  crea, const int  anni, const int  orig_target_irrep  ) const

protected

Apply E_{crea,anni} to |orig_vector> and store the result in |result_vector>

Parameters

orig_vector	The original vector
result_vector	The result vector
crea	The orbital index of the creator
anni	The orbital index of the annihilator
orig_target_irrep	The irrep of the orig_vector

Definition at line 772 of file FCI.cpp.

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unsigned int CheMPS2::FCI::bits2str ( const unsigned int  Lvalue, int *  bits  )

staticprotected

Convertor between two representations of a same spin-projection Slater determinant.

Parameters

Lvalue	The number of orbitals
bits	Array with the Lvalue bits which should be combined to a single integer

Returns

The single integer which represents the bits in bits

Definition at line 397 of file FCI.cpp.

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double CheMPS2::FCI::CalcSpinSquared

(

double *

vector

)

const

Measure S(S+1) (spin squared)

Parameters

vector

The FCI vector of length getVecLength(0)

Returns

Measured value of S(S+1)

Definition at line 1405 of file FCI.cpp.

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void CheMPS2::FCI::CGAlphaPlusBetaHAM ( const double  alpha, const double  beta, double *  in, double *  out  ) const

protected

Calculate out = (alpha + beta * Hamiltonian) * in (Econstant is taken into account!!)

Parameters

alpha	The parameter alpha of the operator
beta	The parameter beta of the operator
in	On entry the vector of size getVecLength(0) on which the operator should be applied; unchanged on exit
out	Array of size getVecLength(0), which contains on exit (alpha + beta * Hamiltonian) * in

Definition at line 2142 of file FCI.cpp.

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void CheMPS2::FCI::CGCoreSolver ( const double  alpha, const double  beta, const double  eta, double *  precon, double *  Sol, double *  RESID, double *  PVEC, double *  OxPVEC, double *  temp, double *  temp2  ) const

protected

Calculate the solution of the system Operator |Sol> = |RESID> with Operator = precon * [ ( alpha + beta * H )^2 + eta^2 ] * precon.

Parameters

alpha	The parameter alpha of the operator
beta	The parameter beta of the operator
eta	The parameter eta of the operator
precon	The diagonal preconditioner
Sol	On entry this array of size getVecLength(0) contains the initial guess; on exit the solution is stored here
RESID	On entry the RHS of the equation is stored in this array of size getVecLength(0), on exit it is overwritten
PVEC	Workspace of size getVecLength(0)
OxPVEC	Workspace of size getVecLength(0)
temp	Workspace of size getVecLength(0)
temp2	Workspace of size getVecLength(0)

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void CheMPS2::FCI::CGdiagonal ( const double  alpha, const double  beta, const double  eta, double *  diagonal, double *  workspace  ) const

protected

Calculate (without approximation) diagonal = diag[ (alpha + beta * Hamiltonian)^2 + eta^2 ] (Econstant is taken into account!!)

Parameters

alpha	The parameter alpha of the operator
beta	The parameter beta of the operator
eta	The parameter eta of the operator
diagonal	Array of size getVecLength(0), which contains on exit diag[ (alpha + beta * Hamiltonian)^2 + eta^2 ]
workspace	Workspace of size getVecLength(0)

Definition at line 2162 of file FCI.cpp.

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void CheMPS2::FCI::CGoperator ( const double  alpha, const double  beta, const double  eta, double *  in, double *  temp, double *  out  ) const

protected

Calculate out = [(alpha + beta * Hamiltonian)^2 + eta^2] * in (Econstant is taken into account!!)

Parameters

alpha	The parameter alpha of the operator
beta	The parameter beta of the operator
eta	The parameter eta of the operator
in	On entry the vector of size getVecLength(0) on which the operator should be applied; unchanged on exit
out	Array of size getVecLength(0), which contains on exit [(alpha + beta * Hamiltonian)^2 + eta^2] * in
temp	Workspace of size getVecLength(0)

Definition at line 2153 of file FCI.cpp.

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void CheMPS2::FCI::CGSolveSystem	(	const double	alpha,
		const double	beta,
		const double	eta,
		double *	RHS,
		double *	RealSol,
		double *	ImagSol,
		const bool	checkError = true
	)		const

Calculate the solution of the equation ( alpha + beta * Hamiltonian + I * eta ) Solution = RHS with conjugate gradient.

Parameters

alpha	The real part of the scalar in the operator
beta	The real-valued prefactor of the Hamiltonian in the operator
eta	The imaginary part of the scalar in the operator
RHS	The real-valued right-hand side of the equation with length getVecLength(0)
RealSol	On exit this array of length getVecLength(0) contains the real part of the solution
ImagSol	On exit this array of length getVecLength(0) contains the imaginary part of the solution
checkError	If true, the RMS error without preconditioner will be calculated and printed after convergence

Definition at line 2066 of file FCI.cpp.

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void CheMPS2::FCI::ClearVector ( const unsigned int  vecLength, double *  vec  )

static

Set the entries of a vector to zero.

Parameters

vecLength	The vector length
vec	The vector which has to be set to zero

Definition at line 1908 of file FCI.cpp.

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void CheMPS2::FCI::DensityResponseGF	(	const double	omega,
		const double	eta,
		const unsigned int	orb_alpha,
		const unsigned int	orb_beta,
		const double	GSenergy,
		double *	GSvector,
		double *	RePartGF,
		double *	ImPartGF
	)		const

Calculate the density response Green's function (= forward - backward propagating part)

Parameters

omega	The frequency value
eta	The regularization parameter (... + I*eta in the denominator)
orb_alpha	The first orbital index
orb_beta	The second orbital index
GSenergy	The ground state energy returned by GSDavidson
GSvector	The ground state vector as calculated by GSDavidson
RePartGF	On exit RePartGF[0] contains the real part of the density response Green's function
ImPartGF	On exit ImPartGF[0] contains the imaginary part of the density response Green's function

Definition at line 2398 of file FCI.cpp.

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void CheMPS2::FCI::DensityResponseGF_backward	(	const double	omega,
		const double	eta,
		const unsigned int	orb_alpha,
		const unsigned int	orb_beta,
		const double	GSenergy,
		double *	GSvector,
		double *	RePartGF,
		double *	ImPartGF,
		double *	TwoRDMreal = NULL,
		double *	TwoRDMimag = NULL,
		double *	TwoRDMdens = NULL
	)		const

Calculate the backward propagating part of the density response Green's function: <GSvector| ( n_beta - <GSvector| n_beta |GSvector> ) [ omega + Ham - GSenergy + I*eta ]^{-1} ( n_alpha - <GSvector| n_alpha |GSvector> ) |GSvector>

Parameters

omega	The frequency value
eta	The regularization parameter
orb_alpha	The first orbital index
orb_beta	The second orbital index
GSenergy	The ground state energy returned by GSDavidson
GSvector	The ground state vector as calculated by GSDavidson
RePartGF	On exit RePartGF[0] contains the real part of the backward propagating part of the density response Green's function
ImPartGF	On exit ImPartGF[0] contains the imaginary part of the backward propagating part of the density response Green's function
TwoRDMreal	If not NULL, on exit the 2-RDM of Re{ [ omega + Ham - GSenergy + I*eta ]^{-1} ( n_alpha - <GSvector| n_alpha |GSvector> ) |GSvector> }
TwoRDMimag	If not NULL, on exit the 2-RDM of Im{ [ omega + Ham - GSenergy + I*eta ]^{-1} ( n_alpha - <GSvector| n_alpha |GSvector> ) |GSvector> }
TwoRDMdens	If not NULL, on exit the 2-RDM of ( n_alpha - <GSvector| n_alpha |GSvector> ) |GSvector>

Definition at line 2458 of file FCI.cpp.

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void CheMPS2::FCI::DensityResponseGF_forward	(	const double	omega,
		const double	eta,
		const unsigned int	orb_alpha,
		const unsigned int	orb_beta,
		const double	GSenergy,
		double *	GSvector,
		double *	RePartGF,
		double *	ImPartGF,
		double *	TwoRDMreal = NULL,
		double *	TwoRDMimag = NULL,
		double *	TwoRDMdens = NULL
	)		const

Calculate the forward propagating part of the density response Green's function: <GSvector| ( n_alpha - <GSvector| n_alpha |GSvector> ) [ omega - Ham + GSenergy + I*eta ]^{-1} ( n_beta - <GSvector| n_beta |GSvector> ) |GSvector>

Parameters

omega	The frequency value
eta	The regularization parameter
orb_alpha	The first orbital index
orb_beta	The second orbital index
GSenergy	The ground state energy returned by GSDavidson
GSvector	The ground state vector as calculated by GSDavidson
RePartGF	On exit RePartGF[0] contains the real part of the forward propagating part of the density response Green's function
ImPartGF	On exit ImPartGF[0] contains the imaginary part of the forward propagating part of the density response Green's function
TwoRDMreal	If not NULL, on exit the 2-RDM of Re{ [ omega - Ham + GSenergy + I*eta ]^{-1} ( n_beta - <GSvector| n_beta |GSvector> ) |GSvector> }
TwoRDMimag	If not NULL, on exit the 2-RDM of Im{ [ omega - Ham + GSenergy + I*eta ]^{-1} ( n_beta - <GSvector| n_beta |GSvector> ) |GSvector> }
TwoRDMdens	If not NULL, on exit the 2-RDM of ( n_beta - <GSvector| n_beta |GSvector> ) |GSvector>

Definition at line 2422 of file FCI.cpp.

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void CheMPS2::FCI::Diag4RDM	(	double *	vector,
		double *	three_rdm,
		const unsigned int	orbz,
		double *	output
	)		const

Construct part of the 4-RDM: output(i,j,k,p,q,r) = Gamma^4(i,j,k,z,p,q,r,z)

Parameters

vector	The FCI vector of length getVecLength(0)
three_rdm	The spin-summed 3-RDM as calculated by Fill3RDM
orbz	The orbital z which is fixed in Gamma^4(i,j,k,z,p,q,r,z)
output	To store part of the 4-RDM output(i,j,k,p,q,r) = output[ i + L * ( j + L * ( k + L * ( p + L * ( q + L * r ) ) ) ) ]; needs to be of size getL()^6; point group symmetry shows in elements being zero; has 12-fold permutation symmetry just like 3-RDM

Definition at line 1176 of file FCI.cpp.

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void CheMPS2::FCI::DiagHam ( double *  diag ) const

protected

Function which returns the diagonal elements of the FCI Hamiltonian (without Econstant!!) = Slater determinant energies.

Parameters

diag	Vector with getVecLength(0) variables which contains on exit the diagonal elements of the FCI Hamiltonian

Definition at line 1467 of file FCI.cpp.

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void CheMPS2::FCI::DiagHamSquared ( double *  output ) const

protected

Function which returns the diagonal elements of the FCI Hamiltonian squared (without Econstant!!)

Parameters

output

Vector with getVecLength(0) variables which contains on exit the diagonal elements of the FCI Hamiltonian squared

Definition at line 1504 of file FCI.cpp.

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void CheMPS2::FCI::FCIdaxpy ( const unsigned int  vecLength, const double  alpha, double *  vec_x, double *  vec_y  )

staticprotected

Do lapack's daxpy vec_y += alpha * vec_x.

Parameters

vecLength	The vector length
alpha	The scalar factor
vec_x	The vector which has to be added to vec_y in rescaled form
vec_y	The target vector

Definition at line 1890 of file FCI.cpp.

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void CheMPS2::FCI::FCIdcopy ( const unsigned int  vecLength, double *  origin, double *  target  )

staticprotected

Copy a vector.

Parameters

vecLength	The vector length
origin	Vector to be copied
target	Where to copy the vector to

Definition at line 1868 of file FCI.cpp.

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double CheMPS2::FCI::FCIddot ( const unsigned int  vecLength, double *  vec1, double *  vec2  )

staticprotected

Take the inproduct of two vectors.

Parameters

vecLength	The vector length
vec1	The first vector
vec2	The second vector

Returns

The inproduct < vec1 | vec2 >

Definition at line 1876 of file FCI.cpp.

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void CheMPS2::FCI::FCIdscal ( const unsigned int  vecLength, const double  alpha, double *  vec  )

staticprotected

Do lapack's dscal vec *= alpha.

Parameters

vecLength	The vector length
alpha	The scalar factor
vec	The vector which has to be rescaled

Definition at line 1899 of file FCI.cpp.

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double CheMPS2::FCI::FCIfrobeniusnorm ( const unsigned int  vecLength, double *  vec  )

staticprotected

Calculate the 2-norm of a vector.

Parameters

vecLength	The vector length
vec	The vector

Returns

The 2-norm of vec

Definition at line 1884 of file FCI.cpp.

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double CheMPS2::FCI::Fill2RDM	(	double *	vector,
		double *	TwoRDM
	)		const

Construct the (spin-summed) 2-RDM of a FCI vector: Gamma^2(i,j,k,l) = sum_sigma,tau < a^+_i,sigma a^+_j,tau a_l,tau a_k,sigma > = TwoRDM[ i + L * ( j + L * ( k + L * l ) ) ].

Parameters

vector	The FCI vector of length getVecLength(0)
TwoRDM	To store the 2-RDM; needs to be of size getL()^4; point group symmetry shows in 2-RDM elements being zero

Returns

The energy of the given FCI vector, calculated by contraction of the 2-RDM with Gmat and ERI

Definition at line 805 of file FCI.cpp.

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void CheMPS2::FCI::Fill3RDM	(	double *	vector,
		double *	ThreeRDM
	)		const

Construct the (spin-summed) 3-RDM of a FCI vector: Gamma^3(i,j,k,l,m,n) = sum_sigma,tau,s < a^+_{i,sigma} a^+_{j,tau} a^+_{k,s} a_{n,s} a_{m,tau} a_{l,sigma} > = ThreeRDM[ i + L * ( j + L * ( k + L * ( l + L * ( m + L * n ) ) ) ) ].

Parameters

vector	The FCI vector of length getVecLength(0)
ThreeRDM	To store the 3-RDM; needs to be of size getL()^6; point group symmetry shows in 3-RDM elements being zero

Definition at line 1168 of file FCI.cpp.

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void CheMPS2::FCI::Fill4RDM	(	double *	vector,
		double *	FourRDM
	)		const

Construct the (spin-summed) 4-RDM of a FCI vector: Gamma^4(i,j,k,l,p,q,r,t) = sum_sigma,tau,s,z < a^+_{i,sigma} a^+_{j,tau} a^+_{k,s} a^+_{l,z} a_{t,z} a_{r,s} a_{q,tau} a_{p,sigma} > = FourRDM[ i + L * ( j + L * ( k + L * ( l + L * ( p + L * ( q + L * ( r + L * t ) ) ) ) ) ) ].

Parameters

vector	The FCI vector of length getVecLength(0)
FourRDM	To store the 4-RDM; needs to be of size getL()^8; point group symmetry shows in 4-RDM elements being zero

Definition at line 896 of file FCI.cpp.

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void CheMPS2::FCI::FillRandom ( const unsigned int  vecLength, double *  vec  )

static

Fill a vector with random numbers in the interval [-1,1[; used when output for GSDavidson is desired but no specific input can be given.

Parameters

vecLength	The length of the vector; when used for GSDavidson it should be getVecLength(0)
vec	The vector to fill with random numbers

Definition at line 1914 of file FCI.cpp.

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void CheMPS2::FCI::Fock4RDM	(	double *	vector,
		double *	ThreeRDM,
		double *	Fock,
		double *	output
	)		const

Construct the (spin-summed) contraction of the 4-RDM with the Fock operator: output(i,j,k,p,q,r) = sum_{l,t} Fock(l,t) * Gamma^4(i,j,k,l,p,q,r,t)

Parameters

vector	The FCI vector of length getVecLength(0)
ThreeRDM	The spin-summed 3-RDM as calculated by Fill3RDM
Fock	The symmetric Fock operator Fock(i,j) = Fock[ i + L * j ] = Fock[ j + L * i ]
output	To store the contraction output(i,j,k,p,q,r) = output[ i + L * ( j + L * ( k + L * ( p + L * ( q + L * r ) ) ) ) ]; needs to be of size getL()^6; point group symmetry shows in elements being zero; has 12-fold permutation symmetry just like 3-RDM

Definition at line 1160 of file FCI.cpp.

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void CheMPS2::FCI::getBitsOfCounter ( const int  irrep_center, const unsigned int  counter, int *  bits_up, int *  bits_down  ) const

protected

Find the bit representation of a global counter corresponding to " E_ij | FCI vector > " ; where irrep_center = I_i x I_j.

Parameters

irrep_center	The single electron excitation irrep I_i x I_j
counter	The given global counter corresponding to " E_ij | FCI vector > "
bits_up	Array of length L to store the bit representation of the up (alpha) electrons in
bits_down	Array of length L to store the bit representation of the down (beta) electrons in

Definition at line 417 of file FCI.cpp.

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double CheMPS2::FCI::getEconst ( ) const

inline

Function which returns the nuclear repulsion energy.

Returns

The nuclear repulsion energy

Definition at line 92 of file FCI.h.

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double CheMPS2::FCI::getERI ( const int  orb1, const int  orb2, const int  orb3, const int  orb4  ) const

inline

Function which returns the electron repulsion integral (in chemists notation: integral dr1 dr2 orb1(r1) * orb2(r1) * orb3(r2) * orb4(r2) / |r1-r2|)

Parameters

orb1	First orbital index (electron at position r1)
orb2	Second orbital index (electron at position r1)
orb3	Third orbital index (electron at position r2)
orb4	Fourth orbital index (electron at position r2)

Returns

The desired electron repulsion integral

Definition at line 82 of file FCI.h.

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double CheMPS2::FCI::getFCIcoeff	(	int *	bits_up,
		int *	bits_down,
		double *	vector
	)		const

Function which returns a FCI coefficient.

Parameters

bits_up	The bit string representation of the up or alpha electron Slater determinant
bits_down	The bit string representation of the down or beta electron Slater determinant
vector	The FCI vector with getVecLength(0) variables from which a coefficient is desired

Returns

The corresponding FCI coefficient; 0.0 if bits_up and bits_down do not form a valid FCI determinant

Definition at line 435 of file FCI.cpp.

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double CheMPS2::FCI::getGmat ( const int  orb1, const int  orb2  ) const

inline

Function which returns the AUGMENTED one-body matrix elements ( G_{ij} = T_{ij} - 0.5 * sum_k ERI_{ikkj} ; see Chem. Phys. Lett. 111 (4-5), 315-321 (1984) )

Parameters

orb1	First orbital index
orb2	Second orbital index

Returns

The desired AUGMENTED one-body matrix element

Definition at line 88 of file FCI.h.

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unsigned int CheMPS2::FCI::getL ( ) const

inline

Getter for the number of orbitals.

Returns

The number of orbitals

Definition at line 52 of file FCI.h.

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double CheMPS2::FCI::GetMatrixElement ( int *  bits_bra_up, int *  bits_bra_down, int *  bits_ket_up, int *  bits_ket_down, int *  work  ) const

protected

Sandwich the Hamiltonian between two Slater determinants (return a specific element) (without Econstant!!)

Parameters

bits_bra_up	Bit representation of the <bra| Slater determinant of the up (alpha) electrons (length L)
bits_bra_down	Bit representation of the <bra| Slater determinant of the down (beta) electrons (length L)
bits_ket_up	Bit representation of the |ket> Slater determinant of the up (alpha) electrons (length L)
bits_ket_down	Bit representation of the |ket> Slater determinant of the down (beta) electrons (length L)
work	Work array of length 8

Returns

The FCI Hamiltonian element which connects the given two Slater determinants

Definition at line 1722 of file FCI.cpp.

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unsigned int CheMPS2::FCI::getNel_down ( ) const

inline

Getter for the number of down or beta electrons.

Returns

The number of down or beta electrons

Definition at line 60 of file FCI.h.

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unsigned int CheMPS2::FCI::getNel_up ( ) const

inline

Getter for the number of up or alpha electrons.

Returns

The number of up or alpha electrons

Definition at line 56 of file FCI.h.

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int CheMPS2::FCI::getOrb2Irrep ( const int  orb ) const

inline

Get an orbital irrep.

Parameters

orb	The orbital index

Returns

The irrep of orbital orb

Definition at line 74 of file FCI.h.

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int CheMPS2::FCI::getTargetIrrep ( ) const

inline

Get the target irrep.

Returns

The target irrep

Definition at line 69 of file FCI.h.

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int CheMPS2::FCI::getUpIrrepOfCounter ( const int  irrep_center, const unsigned int  counter  ) const

protected

Find the irrep of the up Slater determinant of a global counter corresponding to " E_ij | FCI vector > " ; where irrep_center = I_i x I_j.

Parameters

irrep_center	The single electron excitation irrep I_i x I_j
counter	The given global counter corresponding to " E_ij | FCI vector > "

Returns

The corresponding irrep of the up Slater determinant

Definition at line 409 of file FCI.cpp.

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unsigned int CheMPS2::FCI::getVecLength ( const int  irrep_center ) const

inline

Getter for the number of variables in the vector " E_ij | FCI vector > " ; where irrep_center = I_i x I_j.

Parameters

irrep_center

The single electron excitation irrep I_i x I_j

Returns

The number of variables in the corresponding vector

Definition at line 65 of file FCI.h.

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void CheMPS2::FCI::GFmatrix_addition	(	const double	alpha,
		const double	beta,
		const double	eta,
		int *	orbsLeft,
		const unsigned int	numLeft,
		int *	orbsRight,
		const unsigned int	numRight,
		const bool	isUp,
		double *	GSvector,
		CheMPS2::Hamiltonian *	Ham,
		double *	RePartsGF,
		double *	ImPartsGF,
		double **	TwoRDMreal = NULL,
		double **	TwoRDMimag = NULL,
		double **	TwoRDMadd = NULL
	)		const

Calculate the addition Green's function: GF[i+numLeft*j] = <GSvector| a_{orbsLeft[i], spin} [ alpha + beta * Ham + I*eta ]^{-1} a^+_{orbsRight[j], spin} |GSvector>

Parameters

alpha	Constant parameter in the resolvent
beta	Prefector of the Hamiltonian in the resolvent
eta	The regularization parameter
orbsLeft	The left orbital indices
numLeft	The number of left orbital indices
orbsRight	The right orbital indices
numRight	The number of right orbital indices
isUp	If true, the spin projection value of the second quantized operators is up, otherwise it will be down
GSvector	The ground state vector as calculated by GSDavidson
Ham	The Hamiltonian, which contains the matrix elements
RePartsGF	On exit RePartsGF[i+numLeft*j] contains the real part of the addition Green's function
ImPartsGF	On exit ImPartsGF[i+numLeft*j] contains the imaginary part of the addition Green's function
TwoRDMreal	If not NULL, TwoRDMreal[j] contains on exit the 2-RDM of Re{ [ alpha + beta * Ham + I*eta ]^{-1} a^+_{orbsRight[j], spin} | GSvector > }
TwoRDMimag	If not NULL, TwoRDMimag[j] contains on exit the 2-RDM of Im{ [ alpha + beta * Ham + I*eta ]^{-1} a^+_{orbsRight[j], spin} | GSvector > }
TwoRDMadd	If not NULL, TwoRDMadd[j] contains on exit the 2-RDM of a^+_{orbsRight[j], spin} | GSvector >

Definition at line 2215 of file FCI.cpp.

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void CheMPS2::FCI::GFmatrix_removal	(	const double	alpha,
		const double	beta,
		const double	eta,
		int *	orbsLeft,
		const unsigned int	numLeft,
		int *	orbsRight,
		const unsigned int	numRight,
		const bool	isUp,
		double *	GSvector,
		CheMPS2::Hamiltonian *	Ham,
		double *	RePartsGF,
		double *	ImPartsGF,
		double **	TwoRDMreal = NULL,
		double **	TwoRDMimag = NULL,
		double **	TwoRDMrem = NULL
	)		const

Calculate the removal Green's function: GF[i+numLeft*j] = <GSvector| a^+_{orbsLeft[i], spin} [ alpha + beta * Ham + I*eta ]^{-1} a_{orbsRight[j], spin} |GSvector>

Parameters

alpha	Constant parameter in the resolvent
beta	Prefector of the Hamiltonian in the resolvent
eta	The regularization parameter
orbsLeft	The left orbital indices
numLeft	The number of left orbital indices
orbsRight	The right orbital indices
numRight	The number of right orbital indices
isUp	If true, the spin projection value of the second quantized operators is up, otherwise it will be down
GSvector	The ground state vector as calculated by GSDavidson
Ham	The Hamiltonian, which contains the matrix elements
RePartsGF	On exit RePartsGF[i+numLeft*j] contains the real part of the removal Green's function GF[i+numLeft*j]
ImPartsGF	On exit ImPartsGF[i+numLeft*j] contains the imaginary part of the removal Green's function GF[i+numLeft*j]
TwoRDMreal	If not NULL, TwoRDMreal[j] contains on exit the 2-RDM of Re{ [ alpha + beta * Ham + I*eta ]^{-1} a_{orbsRight[j], spin} | GSvector > }
TwoRDMimag	If not NULL, TwoRDMimag[j] contains on exit the 2-RDM of Im{ [ alpha + beta * Ham + I*eta ]^{-1} a_{orbsRight[j], spin} | GSvector > }
TwoRDMrem	If not NULL, TwoRDMrem[j] contains on exit the 2-RDM of a_{orbsRight[j], spin} | GSvector >

Definition at line 2306 of file FCI.cpp.

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double CheMPS2::FCI::GSDavidson	(	double *	inoutput = NULL,
		const int	DVDSN_NUM_VEC = CheMPS2::DAVIDSON_NUM_VEC
	)		const

Calculates the FCI ground state with Davidson's algorithm.

Parameters

inoutput	If inoutput!=NULL, vector with getVecLength(0) variables which contains the initial guess at the start, and on exit the solution of the FCI calculation
DVDSN_NUM_VEC	The maximum number of vectors to use in Davidson's algorithm; adjustable in case memory becomes an issue

Returns

The ground state energy

Definition at line 1920 of file FCI.cpp.

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unsigned int CheMPS2::FCI::LowestEnergyDeterminant

(

)

const

Return the global counter of the Slater determinant with the lowest energy.

Returns

The global counter of the Slater determinant with the lowest energy

Definition at line 1700 of file FCI.cpp.

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void CheMPS2::FCI::matvec ( double *  input, double *  output  ) const

protected

Function which performs the Hamiltonian times Vector product (without Econstant!!) making use of the (ij|kl) = (ji|kl) = (ij|lk) = (ji|lk) symmetry of the electron repulsion integrals.

Parameters

input	The vector of length getVecLength(0) on which the Hamiltonian should act
output	Vector of length getVecLength(0) which contains on exit the Hamiltonian times input

Definition at line 618 of file FCI.cpp.

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void CheMPS2::FCI::RetardedGF	(	const double	omega,
		const double	eta,
		const unsigned int	orb_alpha,
		const unsigned int	orb_beta,
		const bool	isUp,
		const double	GSenergy,
		double *	GSvector,
		CheMPS2::Hamiltonian *	Ham,
		double *	RePartGF,
		double *	ImPartGF
	)		const

Calculate the retarded Green's function (= addition + removal amplitude)

Parameters

omega	The frequency value
eta	The regularization parameter (... + I*eta in the denominator)
orb_alpha	The first orbital index
orb_beta	The second orbital index
isUp	If true, the spin projection value of the second quantized operators is up, otherwise it will be down
GSenergy	The ground state energy returned by GSDavidson
GSvector	The ground state vector as calculated by GSDavidson
Ham	The Hamiltonian, which contains the matrix elements
RePartGF	On exit RePartGF[0] contains the real part of the retarded Green's function
ImPartGF	On exit ImPartGF[0] contains the imaginary part of the retarded Green's function

Definition at line 2191 of file FCI.cpp.

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void CheMPS2::FCI::RetardedGF_addition	(	const double	omega,
		const double	eta,
		const unsigned int	orb_alpha,
		const unsigned int	orb_beta,
		const bool	isUp,
		const double	GSenergy,
		double *	GSvector,
		CheMPS2::Hamiltonian *	Ham,
		double *	RePartGF,
		double *	ImPartGF,
		double *	TwoRDMreal = NULL,
		double *	TwoRDMimag = NULL,
		double *	TwoRDMadd = NULL
	)		const

Calculate the addition part of the retarded Green's function: <GSvector| a_{alpha, spin(isUp)} [ omega - Ham + GSenergy + I*eta ]^{-1} a^+_{beta, spin(isUp)} |GSvector>

Parameters

omega	The frequency value
eta	The regularization parameter
orb_alpha	The first orbital index
orb_beta	The second orbital index
isUp	If true, the spin projection value of the second quantized operators is up, otherwise it will be down
GSenergy	The ground state energy returned by GSDavidson
GSvector	The ground state vector as calculated by GSDavidson
Ham	The Hamiltonian, which contains the matrix elements
RePartGF	On exit RePartGF[0] contains the real part of the addition part of the retarded Green's function
ImPartGF	On exit ImPartGF[0] contains the imaginary part of the addition part of the retarded Green's function
TwoRDMreal	If not NULL, on exit the 2-RDM of Re{ [ omega - Ham + GSenergy + I*eta ]^{-1} a^+_{beta, spin(isUp)} | GSvector > }
TwoRDMimag	If not NULL, on exit the 2-RDM of Im{ [ omega - Ham + GSenergy + I*eta ]^{-1} a^+_{beta, spin(isUp)} | GSvector > }
TwoRDMadd	If not NULL, on exit the 2-RDM of a^+_{beta, spin(isUp)} | GSvector >

Definition at line 2287 of file FCI.cpp.

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void CheMPS2::FCI::RetardedGF_removal	(	const double	omega,
		const double	eta,
		const unsigned int	orb_alpha,
		const unsigned int	orb_beta,
		const bool	isUp,
		const double	GSenergy,
		double *	GSvector,
		CheMPS2::Hamiltonian *	Ham,
		double *	RePartGF,
		double *	ImPartGF,
		double *	TwoRDMreal = NULL,
		double *	TwoRDMimag = NULL,
		double *	TwoRDMrem = NULL
	)		const

Calculate the removal part of the retarded Green's function: <GSvector| a^+_{beta, spin(isUp)} [ omega + Ham - GSenergy + I*eta ]^{-1} a_{alpha, spin(isUp)} |GSvector>

Parameters

omega	The frequency value
eta	The regularization parameter
orb_alpha	The first orbital index
orb_beta	The second orbital index
isUp	If true, the spin projection value of the second quantized operators is up, otherwise it will be down
GSenergy	The ground state energy returned by GSDavidson
GSvector	The ground state vector as calculated by GSDavidson
Ham	The Hamiltonian, which contains the matrix elements
RePartGF	On exit RePartGF[0] contains the real part of the removal part of the retarded Green's function
ImPartGF	On exit ImPartGF[0] contains the imaginary part of the removal part of the retarded Green's function
TwoRDMreal	If not NULL, on exit the 2-RDM of Re{ [ omega + Ham - GSenergy + I*eta ]^{-1} a_{alpha, spin(isUp)} | GSvector > }
TwoRDMimag	If not NULL, on exit the 2-RDM of Im{ [ omega + Ham - GSenergy + I*eta ]^{-1} a_{alpha, spin(isUp)} | GSvector > }
TwoRDMrem	If not NULL, on exit the 2-RDM of a_{alpha, spin(isUp)} | GSvector >

Definition at line 2378 of file FCI.cpp.

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void CheMPS2::FCI::str2bits ( const unsigned int  Lvalue, const unsigned int  bitstring, int *  bits  )

staticprotected

Convertor between two representations of a same spin-projection Slater determinant.

Parameters

Lvalue	The number of orbitals
bitstring	The input integer, whos bits are the occupation numbers of the orbitals
bits	Contains on exit the Lvalue bits of bitstring

Definition at line 391 of file FCI.cpp.

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---

The documentation for this class was generated from the following files:

• FCI.h
• FCI.cpp