Dr. habil. Phys. Thesis (Collection of Works)
University of Latvia, 1998
SUMMARY
The habilitation work is made at the Department of Theoretical Physics and at the
Institute of Chemical Physics of the University of Latvia in 1973 - 1998.
The Thesis is composed of 26 works, 3 of them being deposited monographs
(NN 15 to 17), one review article (N 24), and 22 original papers published in Latvian and foreign scientific journals and collected works.
The works 1 to 6 are dedicated to Asymptotically Precise Density Functional and
Density Matrix Functional theories, 7 to 14 - to development of concepts and techniques in the Group Function theory, and 15 to 26 - to development and applications of the Method of Pseudopotentials and the Effective Potential Method.
The results of this work were presented as 24 talks or posters at Latvian or international conferences and published in the Abstracts of the conferences, as well as at 14 seminars as invited talks.
KONFERENCES * CONFERENCES * KOHФEPEHЦИИ
1. B. P. Zapol, G. Barinovs. Self-consistent equations for nonorthogonal electron group functions. Poster presentation at "QTS 97: Symposium on Quantum Theory and
Simulation of Bulk, Surface and Interface Phenomena". June 15 - 18, 1997 North
Carolina.
2. B. P. Zapol, G. Barinovs. From nonorthogonal electron group functions to generalized pseudopotencials. Talk presentation at "International Conference or
Computational Physics (PC'97)", 25-28 August 1997, Santa-Cruz, California.
3. B. P. Zapol, Properties of the Radon Transform of p-Electron Density, Symposium on Density Functional Theory and Applications (A Satellite Symposium of the 9th
International Congress of Quantum Chemistry), June 3-7, 1997, Duke University
Durham, North Carolina, USA.
4. G. Barinovs, B. Zapol, Electron Group Functions Theory Equations For Internally
Correlated And Mutually Nonorthogonal Groups, 6th Trieste Conference on Quarks and Leptons "Masses and Mixings"(ICTP, Trieste, Italy, 7-11 October, 1996).
5. B.P.Zapol, On pseudopotentials between internally correlated systems. 3rd Int. Conf.
On Computer Simulation of Radiation Effects in Solids (COSIRES'96), 2226 July,
Guildford, UK, 1996.
6. B.P.Zapol, Pseudopotentials for internally correlated systems: consistent approach.
1996 Fall Meeting of the Materials Research Society, 2-6 December 1996, Boston,
USA.

7. B.P.Zapol, G. Barinovs, R. Bukbards. Self-consistent equations and gauge transformations of electron group functions. CCP1/CCP5 Workshop 'Modeling of localised states in Condensed Matters', 14-16 June 1995, Keele, UK.
8. G. Barinovs, B. P. Zapol. Electron group functions theory equations. EXCAM workshop, Paris, France, 26-28 September 1996.
9. B. P. Zapol. From density to wave functions: a formal procedure. 6th International
Conference on the Application of the Density Functional Theory in Chemistry and
Physics, 1995 (DFT 95), Paris, France, August 29 - September 1, 1995.
10.B.P.Zapol. Integral-Geometrical Consideration of Density Matrices. DFT
Symposium, Cracow, 1994.
11.B.P.Zapol, V.E.Puchin. A transformation of electron group functions. In: Fourth
European Conference on Atomic and Molecular Physics. Riga, Latvia, 6-10 April
1992. Book of Abstracts, Part II, Riga, 1992. P.300.
12.L.N.Kantorovich, B.P.Zapol. The diagram technique for the non-orthogonal electron group functions. In: Conference on Quantum Chemistry of Solids,
November 26-30, 1990, Riga. Abstracts. Riga, University of Latvia, 1990. P.44-45.
13.V.E.Puchin, B.P.Zapol. A technique for non-empirical calculations of point defects in ionic crystals. In: Seventh Soviet Conference on Radiational Physics andChemistry of Non-organic Materials. Riga, October 11-13, 1989. Abstracts, Part 1.
Riga, 1989. P.76.
14.L.N.Kantorovich, B.P.Zapol. Diagram technique for non-orthogonal geminals in the theory of semiconductors. In: 14-th Soviet (Pekar) Seminar on the Theory of
Semiconductors, Donetsk, October 3-5, 1989. Abstract. Donetsk, Institute of Technic,
Academy of Sciences of Ucrainian SSR, 1989. P.61s
15.V.E.Puchin, L.N Kantorovich, B.P.Zapol. A code for non-empirical calculations of electronic structure of defects in ionic crystals. Presented at 27th session of the Soviet
Permanent Seminar on Computer modelling of radiative and other defects in crystals, held at K.D. Ushinsky Odessa State Institute of Pedagogy, Odessa, May
1988.
16.B.P.Zapol. Recurrence formulae for evaluation of three-centre integrals with a pseudopotential in Cartesian Gaussian basis. In: 2-nd Soviet Conference on Quantum
Chemistry of Solids. Abstracts. Riga, 1985. P.32.
17.B.P.Zapol, N.A.Kulagin. Hamiltonian for an impurity ion in the "free-ion approximation". In: 4-th Soviet Conference on the Theory of Atoms and Atomic
Spectra. Voronezh, June 3-6, 1980. Abstracts. Voronezh, 1980. P. 34-35.
18.Bystrov V.S., Zapol B.P., Kiselev V.F., Kozlov V.V. Computer minimization of functions of many arguments. In: Sc. Techn. Conf. "Young scientists-mechanics in favour of national economy". Abstracts. Riga, 1979. P.124.

l9.B.P.Zapol. Oscillator strengths for electric quadrupole transitions in alkali atoms and ions isoelectronic with lithium. In: 6-th Int. Conf. on Atomic Physics, Riga, August
17-22, 1978. Abstracts. Riga, 1978. P. 223-224.
20.V.S.Bystrov, B.P.Zapol, Yu.V.Shvilikh. Application of the Effective Potential
Method to calculations of atoms with two valent electrons. In: Soviet Conf. on
Modern Theory of Atoms and Atomic Spectra, Leningrad, February 1-4, 1977.
Abstracts. Leningrad, 1977. P. 178-179.
21.B.P.Zapol. Calculations of argentum atom by the Effective Potential Method. In:
Theory of Atoms and Atomic Spectra, Soviet Seminar. Tashkent, October 8-10, 1974.
Abstracts. "Fan" Publishers, Tashkent, 1974. P.36.
22.B.P.Zapol. Investigation of electron scattering on Na using the Effective Potential
Method. Ibid. P.36.
23.B.P.Zapol, R.M.Gataullin. Electron and positron in the Effective Potential field of helium atom. Ibid. P. 18.
24.B.P.Zapol, I.M.Taksar. Evaluation of wave functions and transition oscillator strengths for the external electron in boron atom by the Effective Potential Method.
In: Theory of Atoms and Atomic Spectra. Soviet Seminar. Riga, November 14-16,
1973. Riga, Latvian State Unbiversity, 1973. P.35.
UZAICINĀTAS LEKCIJAS * INVITED TALKS * ПPИГJIAШEHHbIE JIEKЦИИ
1. Group-functions method for many-electron systems. Seminar Talk at the Theoretical and Computational Physics Group, University of Keele, Keele, GB, 26 February 1996.
2. Electron localisation and electron correlation: are they compatible? Seminar Talk at the University College of London, London, GB, Spring 1996.
3. An Asymptotically Precise Density Functional Theory, Colloquium of the Centre for
Interdisciplinary Studies in Chemical Physics, 9 December 1996, University of
Western Ontario, London, Canada.
4. Electron Correlation and Pseudopotentials, Colloquium of the Centre for
Interdisciplinary Studies in Chemical Physics, 10 December 1996, University of
Wectern Ontario. London. Canada.
5. Electron Correlation and Pseudopotentials, Colloquium of the Winnipeg Institute for
Theoretical Physics, 13 December 1996, University of Manitoba, Winnipeg, Canada.
6. Generalization of the Concept of Pseudopotentials for the Case of Internally
Correlated Systems, Colloquium of the Society of Physics Students and the
Department of Physics, 17 December 1996, Michigan Technological University,
Houghton, Michigan, USA.

7. Density Functional Theory: achievements and problems, Seminar at the Department of Physics, 19 December 1996, Michigan Technological University, Houghton,
Michigan, USA.
8. Gauge transformations of group functions, Seminar at Kvantkemi Group, Uppsala
University, Sweden, February 1995.
9. Seminar of the Institute of Atomic Physics and Spectroscopy, Department of Physics,
University of Latvia, Riga (Latvia) (3 talks).
10. Seminar of the Department of Inorganic, Metalorganic and Analytic Chemistry,
University of Padua, Padua (Italy), 1994.
11. Theoretical chemistry group seminar, Department of Inorganic, Physical and
Materials Chemistry, University of Torino, Torino (Italy), 1993 .
12. Seminar of the Condensed Matter Group, International Centre for Theoretical
Physics, Trieste (Italy), 1992 .
13. Seminar of St-Petersburg Department of the Institute of Mathematics, Russian
Academy of Sciences, St-Petersburg (Russia), 1991.
14. Seminar of the Institute of Chemical Physics, University of Latvia, Riga, 1990 –
1997.
SATURS * CONTENTS * СОДЕРЖАРИЕ
1. B.P.Zapol. Integral-geometrical consideration of density matrices. Int. J. Quant.
Chem., 56, 535-545 (1995).
2. B.P.Zapol, Properties of the Radon Transform of electron density. Latv. J. Phys.
Tech. Sci. N. 5, 30-43 (1996).
3. B.P.Zapol, Application of the Radon Transform to problems of the Density
Functional Theory. Latv. J. Phys. Tech. Sci. N. 6, 46-56 (1996).
4. B.P.Zapol, P.B.Zapol. Generalized discrete Radon transform in a hypercube. In:
Radioelektronika i elektrosvyaz, Riga Techn. Univ., Riga, 1990, p.66-73 (Voprosy elektrodinamiki i teorii cepej, N17; in Russian).
5. B.P.Zapol. New expressions for the overlap integral of two linear harmonic oscillator wavefunctions. - Chem. Phys. Letters, 1982, 93, N 6, 549 - 552.
6. B.P.Zapol. On the evaluation of Franck-Condon factor in the harmonic approximation. -LPSR ZA Vēstis,. fiz. tehn. zin. sēr. 1982, N 3, 41 - 45 (in Russian).
7. B.P.Zapol, V.E.Puchin. Localization of electron group functions. Int. J. Quant.
Chem., 1992, 41, 581-590.

8. B.P.Zapol. Gauge Transformations of Electron Group Functions. J.: Chem. Phys.,
1996, 104 (23), 9461-9466.
9. L.N.Kantorovich, B.P.Zapol. A diagram technique for non-orthogonal electron group functions. I. Right coset decomposition of symmetric group. J. Chem. Phys., 1992, 96,
8420-8426.
10. L.N.Kantorovich, B.P.Zapol. Diagram technique for non-orthogonal electron group functions. II. Reduced density matrices and total energy. J. Chem. Phys.,
1992, 96, 8427-8438.
11. B.P.Zapol, L.N.Kantorovich. An operator technique for calculations using nonorthogonal electron group functions. Latv. J. Phys. Tech. Sci. 1993, N 5, p.l8-.
12. G. Barinovs, B. P. Zapol,, Total energy and self-consistent equations in the nonorthogonal group function method. Latv. J. Phys. Tech. Sci. N. 5, 44-52 (1996).
13. B. P. Zapol,, G. Barinovs, Many-Electron Pseudopotentials in the Group Functions
Theory. Latv.. J. Phys. Tech. Sci. N. 2 (1998, accepted).
14. V.E.Puchin, B.P.Zapol. On the possibility of localizing of electron group functions using the notion of antisymmetrical orthogonality. Preprint IC/90/381, International
Centre for Theoretical Physics, Miramare-Trieste, 1990, 15 p.
15. V.S.Blohin, B.P.Zapol, A.V.Lyubimov. Tables of optical electron energies, coefficients of analytical wavefunctions and oscillator strengths of dipole transitions for lithium atom and ions of its isoelectronic series (Z= 3 - 10). Latvian State
University, Riga, 1975. Dep. VINITI, N 2200-75, July 21, 1975. P.64, Tables 36,
Ref. 32 (in Russian).
16. V.S.Bystrov, B.P.Zapol, A.V.Lyubimov. Tables of optical electron energies, coefficients of analytical wavefunctions and oscillator strengths of dipole transitions for sodium and rubidium atoms. Polytechnical Institute of Riga, Riga, 1997.Dep. VINITI,
N2099-77. P.34, Tables 16, Ref.46 (inRussian).
17.3.B.P.Zapol, A.A.Karklinsh. Tables of r degree mean values for the external electron in alkali atoms, boron atom and ions of lithium isoelectronic series. Riga,
Latvian State University, 1979. Dep. VINITI, N 3529-79, Oct. 9, 1979. P.34, Tables
19, Ref.9 (in Russian).
18. I.M.Taksar, B.P.Zapol, R.M.Gataullin. Calculations of the external electron shells of atoms and ions in the effective field of nucleus and core. In: Theory of atoms and atomic spectra Materials of Soviet Seminar on the Theory of Atoms and
Atomic Spectra, Riga, November 14-16, 1973, vol. 2. Riga, Latvian State
University, 1974. pp. 97- 103.
19. B.P.Zapol, B.H.Levush, I.M.Taksar. The Effective Potential Method for computation of quantum systems. IV. Evaluation of wavefunctions and transition oscillator strengths for the external electron of boron atom. LPSR ZA Vēstis,. fiz. tehn. zin. sēr.
1973, N 5, 28 - 38 (in Russian).

20. B.P.Zapol. Evaluation of matrix elements of a pseudopotential in the Cartesian
Gaussian basis. Ibid., 1986, N 4, 3 - 9 (in Russian).
21. B.P.Zapol. Recurrence formulae for angular parts of matrix elements of a pseudopotential in the Cartesian Gaussian basis. Ibid., 1986, N 5, 111 - 114 (in
Russian).
22. V.E.Puchin, L.N Kantorovich, B.P.Zapol. A code for non-empirical calculations of electronic structure of defects in ionic crystals. In: Computer simulation of structural defects in crystals. Leningrad, A.Ya.Ioffe Institute of Physics and Technics,
Academy of Sciences of USSR, 1988. P.124 (in Russian).
23. B.P.Zapol, V.E.Puchin., E.N.Heifets, I.O.Zaks. Code for computing matrix elements of semilocal pseudopotential in Gaussian basis. Zh. Struct. Khim., 1989, 30,
No 4, 135-136 (in Russian).
24. B.P.Zapol. On the methods of evaluation of internal fields in ferroelectrics. In:
DiJrfused phase transitions, Riga, Latvian State University, 1978, p.119 - 138 (in
Russian).
25.. V.A.Kruglevsky, B.P.Zapol. Matrix elements of symmetric operators for evaluation of ion - ion interactions in ferroelectrics. - In: Phase transitions. Collected papers.
Riga, Latvian State University, 1983, p.165- 173.
B.P.Zapol, N.A.Kulagin. Exchange potential for an impurity ion in ferroelectrics.
Ibid., p.174-191.