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The '2D' papers
===============
Reviews:
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[97] L. Laaksonen, P. Pyykkö and D. Sundholm: Fully numerical Hartree-Fock
methods for molecules, Computer Phys. Reports 4, 313-344 (1986).
[112] P. Pyykkö: Fully numerical solution of Hartree-Fock and similar
equations for diatomic molecules, in "Recent Progress in Many-Body Theories",
Vol. 1, Ed. A.J. Kallio, E. Pajanne and R.F. Bishop, Plenum Press, New York,
(1988) pp. 349-355.
[113] P.Pyykkö: Fully numerical calculations for diatomic systems,
in Proc. NATO
ARW on "Numerical Determination of the Electronic Structure of Atoms,
Diatomic and Polyatomic Molecules", Versailles, April 17-22, 1988, Ed. M.
Defranceschi and J. Delhalle, Kluwer, Dordrecht (1989), 161- 175.
[122] L. Laaksonen, D. Sundholm and P. Pyykkö: Fully numerical Hartree-Fock
methods for molecules, in "Scientific Computing in Finland", ed. K. Kankaala
and R. Nieminen, CSC Res. Report R1/89, Espoo (1989) pp. 183-213.
[136] P. Pyykkö, D. Sundholm, L. Laaksonen and J. Olsen: Two fully numerical
methods in quantum chemistry, in "The CP 90 Europhysics Conference on
Computational Physics", ed. A. Tenner, World Scientific, Singapore (1991),
pp. 455-457.
E. A. McCullough, Jr.: Numerical Hartree-Fock methods for molecules, in
Encyclopedia of Computational Chemistry, ed. P. von Rague Schleyer et al.,
Wiley, Chichester and New York, Vol. 3, 1998, pp. 1941-1947.
Program:
--------
[DS] 56. J. Kobus, L. Laaksonen, D. Sundholm,
"A Numerical Hartree-Fock Program for
Diatomic Molecules", Computer Phys. Commun. 98 (1996) 346-358;
http://scaregrow.1g.fi/num2d.html
Some original papers:
---------------------
[77] L. Laaksonen, P. Pyykkö and D. Sundholm: Two-dimensional fully
numerical solutions of molecular Schrödinger equations. I. One-electron
molecules, Internat. J. Quantum Chem. 23, 309-317 (1983).
[78] L. Laaksonen, P. Pyykkö and D. Sundholm: Two-dimensional fully
numerical solutions of molecular Schrödinger
equations. II. Solution of the Poisson equation and results for singlet states
of H$_2$ and HeH$^+$, Internat. J. Quantum Chem. 23, 319-323 (1983).
[84] L. Laaksonen, P. Pyykkö and D. Sundholm: Two-dimensional fully numerical
solutions of molecular Hartree-Fock equations: LiH and BH, Chem. Phys. Lett.
96, 1-3 (1983).
[86] L. Laaksonen, D. Sundholm, P. Pyykkö, "Two-Dimensional Fully Numerical
MCSCF Calculations on H2 and LiH: The Dipole Moment of LiH", Chem. Phys.
Lett. 105 (1984) 573-575.
[88] D. Sundholm, P. Pyykkö, L. Laaksonen and A.J. Sadlej: Nuclear
quadrupole moment of lithium from combined fully numerical and discrete
basis-set calculations on LiH, Chem. Phys. Lett. 112, 1-9 (1984).
[89] L. Laaksonen, D. Sundholm and P. Pyykkö: Two-dimensional, fully
numerical molecular calculations. IV. Hartree-Fock-Slater results on
second-row diatomic molecules, Internat. J. Quantum Chem. 27, 601-612 (1985).
[90] D.Sundholm, P. Pyykkö and L. Laaksonen: Fully numerical HFS
calculations on Cr$_2$: basis-set truncation error on the bond length and
interaction of the semicore orbitals, Finnish Chem. Letters, 51-55 (1985).
[91] D. Sundholm, P. Pyykkö and L. Laaksonen: Two-dimensional, fully
numerical molecular calculations. VIII. Electric field gradients of
diatomic hydrides LiH - ClH at the HFS level, Mol. Phys. 55, 627-635 (1985).
[92] D. Sundholm, P. Pyykkö, L. Laaksonen and A.J. Sadlej: Nuclear
quadrupole moment of nitrogen from combined fully numerical and discrete
basis-set calculations on NO$^+$ and N$_2$, Chem. Phys. 101, 219-225 (1986).
[93] D. Sundholm, P. Pyykkö and L. Laaksonen: Two-dimensional, fully
numerical molecular calculations. 10. Hartree-Fock results for He$_2$,
Li$_2$, Be$_2$, HF, OH$^-$, N$_2$, CO, BF, NO$^+$ and CN$^-$,
Mol. Phys. 56, 1411-1418 (1985).
[98] D. Sundholm, P. Pyykkö and L. Laaksonen: Two-dimensional, fully
numerical solutions of second-order Dirac equations for diatomic molecules.
Part 3, Phys. Scripta 36, 400-402 (1987).
[99] P. Pyykkö, D. Sundholm and L. Laaksonen: Two-dimensional, fully
numerical molecular calculations. XI. Hartree-Fock results for BeH$^+$,
LiHe$^+$, CH$^+$, NeH$^+$, C$_2$, BeO, LiF, NaH, MgH$^+$, HeNe, LiNa and
F$_2$, Mol. Phys. 60, 597-604 (1987).
[104] P. Pyykkö, G.H.F. Diercksen, F. M\"{u}ller-Plathe and L. Laaksonen:
Fully numerical Hartree-Fock calculations on
the third-row diatomics AlF, SiO, PN, CS, BCl, SH$^-$ and P$_2$, Chem. Phys.
Lett. 134, 575-578 (1987).
[107} P. Pyykkö, G.H.F. Diercksen, F. M\"{u}ller-Plathe and L. Laaksonen:
Fully numerical Hartree-Fock calculations on
NaF, MgO, BeS and ArH$^+$. On the dipole moment of ArH$^+$, Chem. Phys.
Lett. 141, 535-539 (1987).
[108] G.H.F. Diercksen, A.J. Sadlej, D. Sundholm and P. Pyykkö: Towards an
accurate determination of the nuclear quadrupole moment of Li from molecular
data: LiF, Chem. Phys. Lett. 143, 163-168 (1988).
From the list of Dage Sundholm:
==============================
12. E.J. Baerends, P. Vernooijs, A. Rozendaal, P.M. Boerrigter,
M. Krijn, D. Feil, D. Sundholm, "Basis Set Effects on the Electron
Density and Spectroscopic Properties of CO", J. Mol. Struct. THEOCHEM
133 (1985) 147-159.
21. D. Sundholm, "Two-Dimensional Fully Numerical Solution of Molecular Dirac
Equations: Dirac-Slater Calculations on LiH, Li2, BH, and CH+", Chem. Phys.
Letters 149 (1988) 251-256.
22. D. Sundholm, J. Olsen, P.Å. Malmqvist, B.O. Roos, "Numerical MCSCF in One
and Two Dimensions", in "Numerical Determination of the Electronic Structure
of Atoms, Diatomic and Polyatomic Molecules", Proc. NATO Advanced Research
Workshop, Versailles 1988, Edited by M. Defranceschi and J. Delhalle.
Dordrecht: Reidel, (1989), pp. 329-334.
46. D. Sundholm, "Fully Numerical Solutions of Molecular Dirac Equations for
Highly Charged One-Electron Homonuclear Diatomic Molecules", Chem. Phys.
Letters 223 (1994) 469-473.
55. K. Nordlund, N. Runeberg, D. Sundholm: "Repulsive interatomic potentials
calculated using Hartree-Fock and density-functional theory methods",
Nucl. Instr. Meth. Phys. Res. B 132 (1997) 45-54.
F. A. Pahl, N. C. Handy: Plane waves and radial polynomials: a new mixed
basis, Mol. Phys. 100 (2002) 3199-3224.
[Contains a new F2 HF benchmark by D. S., ref. [20].]
Further original papers by J. Kobus and S. Wilson exist:
=========================================================
11. J.Kobus, Vectorizable algorithm for the (multicolour) successive
overrelaxation method, in Proceedings of the 4th International Conference
Physics Computing '92, eds. R.A. de Groot and J.Nadrchal (World Scientific,
Singapore, 1993)
12.J.Kobus, Finite-difference versus finite-element methods, Chem. Phys.
Lett. 202 7-12 (1993)
13.J.Kobus, Vectorizable algorithm for the (multicolour) successive
overrelaxation method, Comp. Phys. Commun. 78 247-255 (1994)
14.J. Kobus, D. Moncrieff and S. Wilson, A comparison of finite basis set
and finite difference methods for the ground state of the CS molecule, J.
Phys. B: Atom. Mol. Opt. Phys. 27 2867-2875 (1994)
15.J. Kobus, D. Moncrieff and S. Wilson, A comparison of finite difference
and finite basis set Hartree-Fock calculations for the ground state potential
energy curve of CO, J. Phys. B:Atom. Mol. Opt. Phys. 27 5139-5147 (1994)
16. D. Moncrieff, J. Kobus and S. Wilson; A universal basis set for high
precision electronic structure studies; J. Phys. B: Atom. Mol. Opt. Phys. 28
(1995) 4555-4557
17.J. Kobus, D. Moncrieff and S. Wilson; A comparison of finite basis set
and finite difference Hartree-Fock calculations for the BF, AlF and GaF
molecules; Mol. Phys. 86 (1995) 1315-1330
J. Kobus, D. Moncrieff and S. Wilson, Visualization of deficiencies
in approximate molecular wave functions: The orbital amplitude difference
function for the matrix Hartree-Fock description of the ground state
of the boron fluoride molecule, Mol. Phys. 92 (1997) 1015-1028.
J. Kobus: Diatomic molecules: Exact solutions of the HF equations,
Adv. Quantum Chem. 28 (1997) 1-14.
D. Moncrieff, J. Kobus, and S. Wilson, A comparison of finite basis
set and finite difference Hartree-Fock calculations for the InF and TlF
molecules, Mol. Phys. 93 (1998) 713-725.
J. Kobus, D. Moncrieff, and S. Wilson, A comparison of finite basis
set and finite difference Hartree-Fock calculations for the open-shell $\left(
X^2\sigma ^{+}\right)$ species BeF, BO, CN and N$_2^{+}$,
Mol. Phys. 96 (1999) 1559-1567.
J. Kobus, D. Moncrieff, and S. Wilson, A comparison of finite basis
set and finite difference Hartree-Fock calculations for the open-shell
(X${^2}\sigma^{+}$) species BeF, MgF, CaF and SrF,
Mol. Phys. 98 (2000) 401-407.
J. Kobus, D. Moncrieff and S. Wilson, Comparison of the electric moments
obtained from finite basis set and finite difference Hartree-Fock calculations
for diatomic molecules, Phys. Rev. A 62 (2000) 062503.
J. Kobus, H. M. Quiney, S. Wilson, A comparison of finite difference and
finite basis set Hartree-Fock calculations for the N2 molecule with finite
nuclei, J. Phys. B 34 (2001) 2045-2056.
J. Kobus, D. Moncrieff and S. Wilson, Comparison of the polarizabilities
and hyperpolarizabilities obtained from finite basis set and finite
difference Hartree-Fock calculations for diatomic molecules,
J. Phys. B 34 (2001) 5127-5143.
[H2, LiH, BH, FH]
J. Kobus, D. Moncrieff and S. Wilson, A comparison of finite basis set and
finite difference Hartree-Fock calculations for the open-shell (X 2\Sigma)
molecules BaF and YbF, Mol. Phys. 100 (2002) 499-508.
J. Styszynski, J. Kobus: Relativistic and correlation effects on
spectroscopic constants of hydrogen astatide molecule,
Chem. Phys. Lett. 369 (2003) 441-448.
J. Kobus, D. Moncrieff, S. Wilson: Comparison of the polarizabilities and
hyperpolarizabilities obtained from finite basis set and finite difference
Hartree-Fock calculations for diatomic molecules. II. Refinement of basis sets
and grids for hyperpolarizability calculations, J. Phys. B 37 (2004) 571-585.
J. Kobus, D. Moncrieff, S. Wilson: Comparison of the polarizabilities and
hyperpolarizabilities obtained from finite basis set and finite difference
Hartree-Fock calculations for diatomic molecules: III. The ground states
of N2, CO and BF, J. Phys. B 40 (2007) 877-896.
J. Kobus: Hartree-Fock limit values of multipole moments,
polarizabilities and hyperpolarizabilities for atoms
and diatomic molecules, Comp. Lett 3 (2-4) (2007) 71-113.
From the list of Stephen Wilson:
================================
B.H. Wells and S. Wilson:
On the accuracy of the algebraic approximation for diatomic molecules
J. Phys. B: At. Mol. Phys. 18 (1985) L731
B.H. Wells and S. Wilson:
Universal basis sets of elliptical functions. Applications to simple
diatomic molecules.
J. Phys. B: At. Mol. Phys. 19 (1985) 17
L. Laaksonen, I.P. Grant, S. Wilson: The Dirac equation in the algebraic
approximation VI. Molecular self-consistent field studies using basis
sets of Gaussian-type functions, Journal of Physics B: Atomic and
Molecular and Optical Physics, 21 (1988) 1969-1985
B.H. Wells and S. Wilson:
On the accuracy of the algebraic approximation in molecular electronic
structure calculations. I. Calculations for H$_2${}$^{+}$, HeH$^{2+}$, H$_2$
and HeH$^{+}$ using basis sets of atom centred Gaussian-type functions
J. Phys. B: At. Mol. Opt. Phys. 22 (1989) 1285.
J.W. Thompson and S. Wilson:
On the accuracy of the algebraic approximation in molecular electronic
structure calculations II. Comparison of diatomic molecule self-consistent
field calculations using basis sets of elliptical functions with fully
numerical Hartree-Fock studies.
J. Phys. B: At. Mol. Opt. Phys. 23 (1990) 2205.
D. Moncrieff, S. Wilson:
On the accuracy of the algebraic approximation in molecular electronic
structure calculations. III. Comparison of
matrix Hartree-Fock and numerical Hartree-Fock calculations for the
ground state of the nitrogen molecule, J. Phys. B 26 (1993) 1605-1616.
D. Moncrieff and S. Wilson:
Finite basis set versus finite difference and finite element methods
Chem. Phys. Letters 209 (1993) 423-426.
D. Moncrieff and S. Wilson:
Universal basis sets for high precision electronic structure studies
J. Phys. B: At. Mol. Opt. Phys. 27 (1994) 1
D. Moncrieff and S. Wilson:
Distributed Gaussian basis sets: Description of the Hartree-Fock ground
state energies of N$_2$, CO and BF using s- and p-type Gaussian functions
Mol. Phys. 85 (1995) 103
D. Moncrieff, S. Wilson: On the accuracy of the algebraic approximation in
molecular electronic structure calculations: V. Electron correlation in the
ground state of the nitrogen molecule, J. Phys. B: At. Mol. Opt. Phys.,
29 (1996) 2425-2451.
S. Wilson and D. Moncrieff:
Distributed Gaussian Basis Sets: Some Recent Results and Prospects
Adv. Quantum Chem. 28 (1997) 47-63.
D. Moncrieff and S. Wilson:
A universal basis set for high-precision molecular electronic structure
studies: correlation effects in the ground states of N$_2$,
CO, BF and NO$^+$, J. Phys. B: At. Mol. Opt. Phys. 31 (1998) 3819-3841.
D. Moncrieff and S. Wilson:
On the accuracy of the algebraic approximation in molecular electronic
structure calculations: VIII. Matrix Hartree-Fock and many-body perturbation
theory applied to a negative molecular ion,
J. Phys. B: At. Mol. Opt. Phys. 32 (1999) 2195-2202. [CN$^-$]
From the list of Leif Laaksonen :
=================================
(11.) L. Laaksonen and I.P. Grant: Two-dimensional fully numerical solutions
of molecular Dirac equations. One-electron molecules.
Chem. Phys. Lett. 109 (1984) 485.
(13.) L. Laaksonen and I.P. Grant: Two-dimensional fully numerical solutions
of molecular Dirac equations. Results for ground
singlet states of H2 and HeH+. Chem. Phys. Lett. 112 (1984) 157.
(25.) L. Laaksonen, F. Müller-Plathe and G.H.F Diercksen: On the Basis-Set
Truncation Error: Fully-numerical RHF Calculations on Open-Shell Hydrides.
J. Chem. Phys. 89 (1988) 4903.
(26.) F. Müller-Plathe, G.H. Diercksen and L. Laaksonen: Application of the
Two-dimensional Fully-Numerical RHF Method To Open-Shell Hydrides:
M. Defranceschi and J. Delhalle (eds). Numerical Determination of the
Electronic Structure of Atoms, Diatomic and Polyatomic molecules. (1989) 311.
(27.) F. Müller-Plathe and L. Laaksonen: Hartree-Fock-limit properties for
SiC, SiN, Si2, Si2*, and SiS. Chem. Phys. Lett. 160 (1989) 175.
From E.K.U. Gross:
=================
T. Grabo and E. K. U. Gross: The optimized effective potential method of
density functional theory: Applications to atomic and molecular systems,
Int. J. Quantum Chem. 64 (1997) 95-110.
T. Grabo, T. Greibich and E. K. U. Gross: Optimized effective potential
for atoms and molecules, Molecular Engineering 7 (1997) 27-50.
T. Grabo: Orbital Dependent Functionals in Density Functional Theory,
Ph. D. Thesis, Wuerzburg (1997), 91 p.
Others:
======
A. Halkier, W. Klopper, T. Helgaker, and P. Jorgensen, Basis-set
convergence of the molecular electronic dipole moment, J. Chem. Phys.
111 (1999) 4424-4430.
F. Jensen, The basis set convergence of the Hartree-Fock energy for
$H_2$, J. Chem. Phys. 110 (1999) 6601-5.
J. Styszy{\'n}ski, Relativistic core-valence correlation effects on
molecular properties of the hydrogen halide molecules, Chem. Phys. Lett.,
317 (2000) 351-359.
A. K. Roy, A. J. Thakkar, MacLaurin expansions of electron momentum
densities for 78 diatomic molecules: a numerical Hartree-Fock study,
Chem. Phys. Lett. 362 (2002) 428-434.
A. N. Artemyev, E. V. Ludena, V. V. Karasiev, A. J. Hern\'andez,
A finite B-spline basis set for accurate diatomic molecule calculations,
J. Comput. Chem. 25 (2004) 368-374.
[Both HF and MP2 energies for CO, LiH, BH, HF, H2, Li2, N2]
F. Jensen, On the accuracy of numerical Hartree-Fock energies,
Theor. Chem. Accounts 113 (2005) 187-190.
[42 diatomic species treated. Accuracy 1 micro-Hartree or better.]
A. Makmal, S. Kuemmel and L. Kronik, Fully numerical all-electron solutions
of the optimized effective potential equation for diatomic molecules,
J. Chem. Theory Comput. 5 (2009) 1731-1740.
L. Tao, C.W. McCurdy and T. N. Rescigno, Grid-based methods for diatomic
quantum scattering problems. II. Time-dependent treatment of single- and
two-photon ionization of H_2^+, Phys. Rev. A 80 (2009) 013402.
Very accurate finite-element calculations by the Kassel group:
=============================================================
O. Kullie and D. Kolb, High accuracy Dirac-finite-element (FEM)
calculations for H2(+) and Th2{179+}, Eur. Phys. J. D
17 (2001) 167-173.
O. Kullie and D. Kolb, Dirac finite element method calculations for
Th2{179+}, J. Phys. B 36 (2003) 4361-4366.
O. Kullie, D Kolb and A. Rutkowski, Two-spinor fully relativistic
finite-element (FEM) solution of the two-center Coulomb problem,
Chem. Phys. Lett. 383 (2003) 215-221.
H. Zhang, O. Kullie and D. Kolb, Minimax LCAO approach to the
relativistic two-centre Coulomb problem
and its finite element (FEM) spectrum, J. Phys. B 37 (2004) 905-916.
O Kullie, E Engel and D Kolb,
Accurate local density functional calculations with relativistic
two-spinor minimax and finite element method for the alkali dimers,
J. Phys. B 42 (2009) 095102.
Further related papers:
======================
I.-H. Lee, Y.-H. Kim and R. M. Martin: One-way multigrid method in
electronic-structure calculations, Phys. Rev. B 61 (2000) 4397-4400.
[Same approach was used in the '2D' package.]
F. A. Pahl and N. C. Handy: Mol. Phys. 100 (2002) 3199-3224.
[NO+, BF, CO, HF, H2, C2, N2, F2, HB. A new mixed basis,
strictly localized, plane waves and functions, femtometre accuracy.]
M. Heiskanen, T. Torsti, M. J. Puska, and R. M. Nieminen: Multigrid
method for electronic structure calculations, Phys. Rev. B 63 (2002)
245106, pp. 1-8.
[A '3D' code for Kohn-Sham orbitals using a special
set of points. Shares with the '2D' code the features of Rayleigh
quotient eigenvalues, point-relaxation wave-function solver, and Schmidt
orthogonalization.]
T. Torsti, M. Heiskanen, M. J. Puska and R. M. Nieminen: MIKA:
Multigrid-based program package for electronic structure calculations,
Int. J. Quantum Chem. 91 (2003) 171-176.
For current news on the MIKA code, see: http://www.csc.fi/physics/mika/
Y. V. Vanne and A. Saenz, Numerical treatment of diatomic two-electron
molecules using a B-spline based CI method, J. Phys. B 37 (2004) 4101-4118.
T. Ono and K. Hirose, Real-space electronic-structure calculations with a
time-saving double-grid technique, Phys. Rev. B 72 (2005) 085115.
T. Torsti, T. Eirola, J. Enkovaara, T. Hakala, P. Havu, V. Havu, T.
Höynälänmaa, J. Ignatius, M. Lyly, I. Makkonen, T. T. Rantala, J. Ruokolainen,
K. Ruotsalainen, E. Räsänen, H. Saarikoski and M. J. Puska:
Three real-space discretization techniques in electronic structure
calculations, arXiv:cond-mat/0601201 v2 24 Jan 2006.
S. Yamakawa and S. Hyodo, Gaussian finite-element mixed-basis method for
electronic structure calculation, Phys. Rev. B 71 (2005) 035113.
T. Shiozaki and S. Hirata, Grid-based numerical Hartree-Fock solution
of polyatomic molecules, Phys. Rev. A 76 (2007) 040503.
A. K. Roy, Pseudopotential density functional treatment of atoms and
molecules in cartesian coordinate grid, Chem. Phys. Lett. 461 (2008) 142-149.
I----------------------------------------------------------I
I Prof. Pekka Pyykkö I
I Department of Chemistry I
I University of Helsinki I
I P.O.B. 55 (A.I. Virtasen aukio 1) I
I FIN-00014 Helsinki I
I Finland I
I I
I Telephone: 358-9-191 50171 I
I Secretary: 358-9-191 50170 I
I FAX: 358-9-191 50169 I
I E-mail: Pekka.Pyykko@helsinki.fi I
I----------------------------------------------------------I
I Did you visit www.csc.fi/rtam/, I
I www.chem.helsinki.fi/~pyykko ? I
I----------------------------------------------------------I