qs_core_hamiltonian Module Reference

Calculation of the core Hamiltonian integral matrix <a|H|b> over Cartesian Gaussian-type functions. More...

Functions/Subroutines
subroutine, public	build_core_hamiltonian_matrix (qs_env, calculate_forces)
	Cosntruction of the QS Core Hamiltonian Matrix. More...
subroutine, public	dump_info_core_hamiltonian (qs_env, calculate_forces)
	Possibly prints matrices after the construction of the Core Hamiltonian Matrix. More...
subroutine, public	qs_matrix_h_allocate_imag_from_real (qs_env)
	(Re-)allocates matrix_h_im from matrix_h More...

Detailed Description

Calculation of the core Hamiltonian integral matrix <a|H|b> over Cartesian Gaussian-type functions.

<a|H|b> = <a|T|b> + <a|V|b>

Kinetic energy:

<a|T|b> = <a|-nabla**2/2|b> _______________/ | kinetic

Nuclear potential energy:

a) Allelectron calculation:

                erfc(r)

<a|V|b> = -Z*<a|------—|b> r

1 - erf(r) = -Z*<a|---------—|b> r

1 erf(r) = -Z*(<a|—|b> - <a|-----—|b>) r r

1 = -Z*(<a|—|b> - N*<ab||c>) r

-Z = <a|—|b> + Z*N*<ab||c> r _______/ _____/ | | nuclear coulomb

b) Pseudopotential calculation (Goedecker, Teter and Hutter; GTH):

<a|V|b> = <a|(V(local) + V(non-local))|b>

    = <a|(V(local)|b> + <a|V(non-local))|b>

<a|V(local)|b> = <a|-Z(eff)*erf(SQRT(2)*alpha*r)/r + (C1 + C2*(alpha*r)**2 + C3*(alpha*r)**4 + C4*(alpha*r)**6)*exp(-(alpha*r)**2/2))|b>

<a|V(non-local)|b> = <a|p(l,i)>h(i,j)<p(l,j)|b>

Literature

S. Goedecker, M. Teter and J. Hutter, Phys. Rev. B 54, 1703 (1996) C. Hartwigsen, S. Goedecker and J. Hutter, Phys. Rev. B 58, 3641 (1998) M. Krack and M. Parrinello, Phys. Chem. Chem. Phys. 2, 2105 (2000) S. Obara and A. Saika, J. Chem. Phys. 84, 3963 (1986)

History

• Joost VandeVondele (April 2003) : added LSD forces
• Non-redundant calculation of the non-local part of the GTH PP (22.05.2003,MK)
• New parallelization scheme (27.06.2003,MK)
• OpenMP version (07.12.2003,JGH)
• Binary search loop for VPPNL operators (09.01.2004,JGH,MK)
• Refactoring of pseudopotential and nuclear attraction integrals (25.02.2009,JGH)
• General refactoring (01.10.2010,JGH)
• Refactoring related to the new kinetic energy and overlap routines (07.2014,JGH)
• k-point functionality (07.2015,JGH)

Author

Matthias Krack (14.09.2000,21.03.02)

Function/Subroutine Documentation

build_core_hamiltonian_matrix()

subroutine, public qs_core_hamiltonian::build_core_hamiltonian_matrix	(	type(qs_environment_type), pointer	qs_env,
		logical, intent(in)	calculate_forces
	)

Cosntruction of the QS Core Hamiltonian Matrix.

Parameters

qs_env	...
calculate_forces	...

Author

Creation (11.03.2002,MK) Non-redundant calculation of the non-local part of the GTH PP (22.05.2003,MK) New parallelization scheme (27.06.2003,MK)

Definition at line 156 of file qs_core_hamiltonian.F.

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dump_info_core_hamiltonian()

subroutine, public qs_core_hamiltonian::dump_info_core_hamiltonian	(	type(qs_environment_type), pointer	qs_env,
		logical, intent(in)	calculate_forces
	)

Possibly prints matrices after the construction of the Core Hamiltonian Matrix.

Parameters

qs_env	...
calculate_forces	...

Definition at line 563 of file qs_core_hamiltonian.F.

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qs_matrix_h_allocate_imag_from_real()

subroutine, public qs_core_hamiltonian::qs_matrix_h_allocate_imag_from_real

(

type(qs_environment_type)

qs_env

)

(Re-)allocates matrix_h_im from matrix_h

Parameters

qs_env

...

Definition at line 746 of file qs_core_hamiltonian.F.

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