Irkutsk State University

Alexander B. Trofimov

trofimovAlexander Trofimov

D. Sc., Leading Researcher
Laboratory of Quantum Chemistry (LQC), 
Irkutsk State University (ISU)
Karl Marx Street, 1
Irkutsk, 664003, Russia
Phone:         +7 (3952) 33-21-76
FAX:           +7 (3952) 24-22-05

Curriculum Vitae

Education and Professional Experience

1984-1989       Education at the Chemistry Department of the Irkutsk State University (ISU).
1989-1990       Junior Researcher at the Laboratory of Quantum Chemistry (LQC) / ISU.
1990-1993       Ph. D. fellow at the ISU Chemistry Department (advisor Prof. N. M. Vitkovskaya).
1991-1993       Ph. D. fellow at the Theoretical Chemistry (TC) group of the Physical Chemistry Institute of the Heidelberg University (TC / PCI / Universität Heidelberg, Germany) with Prof. Dr. J. Schirmer.
1993-1995       Researcher at the LQC / ISU.
1995-1998       Leading Researcher at the LQC / ISU.
1997-1998       Alexander von Humboldt postdoctoral research fellow at the TC / PCI / Universität Heidelberg, Germany.
1998-2001       D. Sc. fellow at the ISU Chemistry Department.
2001-               Leading Researcher at the LQC / ISU.

Academic Degrees and Titles

1989    The Honor Diploma from the ISU (M. Sc. equivalent).
            Diploma work "Quantum Chemical Studies of the Stereochemical Aspects of the Direct Carbon-Carbon Spin-Spin Coupling Constants" (advisors Prof. L. B. Krivdin and Prof. N. M. Vitkovskaya).
1994    Ph. D. (Physical Chemistry).
            Thesis "A Method for Calculation of the Electron Excitation Spectra Based on the Polarization Propagator Theory" (advisors Prof. Dr. J. Schirmer and Prof. N. M. Vitkovskaya).
1999    Academic title "Senior Researcher"
            (Quantum Chemistry and Mathematical Modeling).
2006    D. Sc. (Physical Chemistry).
            Thesis "Developments and Applications of the Quantum-Chemical Green's Function Methods".

Research interests

The main research interests of our group comprise the development and implementation of electronic structure methods based on the Green's function (or propagator) theories, as well as application of such methods to various problems of quantum chemistry and molecular spectroscopy. More specifically, our research pertain to the so called algebraic diagrammatic construction (ADC) approximation schemes and the methods originating from the more general intermediate state representation (ISR) concept. We work in the close collaboration with Prof. Dr. J. Schirmer (TC / PCI / Universität Heidelberg, Germany) who is the author of the ADC and ISR theories.
Currently we carry out our research in the following fields:
  1. Development of the non-Dyson ADC approximations for electron propagator
  2. Development of the polarization propagator ADC approximation schemes
  3. Development of the extended ADC / ISR approximation schemes
  4. Theoretical studies of the valence-shell photoelectron spectra
  5. Theoretical studies of the core-level electron excitation and ionization spectra
  6. Investigation of vibronic and nonadiabatic effects in the excitation and ionization spectra


The Green's function (propagator) formalism can be considered as an alternative to the more ordinary wave function approach [T1-T4]. Initially it has been developed for description of many-body systems in context of the quantum field theory. In general, the Green's function (GF) methods set out from the idea that for the evaluation of the main characteristics of a many-body system one does not need to describe all particles of the system but rather requires an information about the behavior of one or two typical particles belonging to the system. The corresponding theoretical quantities are the one-particle and the two-particle Green's functions, respectively. As far as the electronic structure of atoms and molecules is concerned the one-particle Green's function contains the information about the energies and probabilities of an electron detachment/attachment processes. The two particle GF allows one to characterize the excitation processes which do not change the number of electrons in the system. It should be noted that in the GF methods the transition energies and the transition probabilities are determined directly what eliminates errors due to inconsistent treatment of the initial and final states.
The GF methods have played in quantum chemistry for a long time relatively minor role, since the higher-level approximation schemes required for adequate description of atomic and molecular electronic structure were not readily available. The situation has markedly changed when Schirmer introduced theoretical approach referred to as algebraic diagrammatic construction (ADC) [A1], which opens highly systematic way for formulation of the ADC(n) approximation schemes for arbitrary Green's functions (where the accuracy level is specified in terms of the order-parameter n of the many-body perturbation theory) [A1-A3]. The original ADC approach can be viewed as a specific reformulation of the perturbative diagrammatic expansions for the Green's functions in terms of the Feynman-Goldstone diagrams. The more recent work of Schirmer et al. has demonstrated that the ADC schemes can also be obtained within the framework of a more general concept of intermediate state representation (ISR) which uses the traditional for quantum chemistry language of wave functions [A5-A6]. The latter development not only integrates the ADC methods into quantum chemistry but also allows for formulation of the so called "extended" ADC / ISR approximation schemes which are suitable for investigation of individual states.

The main research fields

1. Development of the non-Dyson ADC approximations for electron propagator
Earlier we have formulated the so-called non-Dyson ADC approximation for electron propagator (one-particle Green's function) [6, 31]. The explicit non-Dyson ADC equations through third order were derived. The main advantage of the non-Dyson ADC(3) method (nD-ADC(3)) is that this scheme treats the electron ionization and electron attachment separately from each other what considerably reduces the computational costs compared to the usual Dyson expansion ADC(3) method. The most promising application field of the nD-ADC(3) method is the theoretical investigation of the molecular valence shell photoelectron spectra. The mean error of the nD-ADC(3) vertical ionization energies with respect to the experimental data (for the main photoelectron lines) is about 0.2 eV. At present we are perusing the development of a highly efficient computer code that exploits all numerical advantages of the nD-ADC(3) method. The new code should enable theoretical studies of larger organic and bioorganic molecules.
2. Development of the polarization propagator ADC approximation schemes
The ADC approximation schemes for polarization propagator (particle-hole Green's function) allow one to compute the spectra of electron excitations. In our previous work the ADC(3) approximation scheme for polarization propagator was derived and implemented [7, 18]. The mean error of the ADC(3) vertical excitation energies with respect to the experimental data is about 0.2 eV. The most obvious application field of the ADC(3) method is the theoretical studies of photoabsorption spectra and other photophysical and photochemical processes where various valence shell singlet and triplet electron excitations take place. The more simple ADC(2) approximation scheme has proved to be useful tool for studies of the core-level excitations [1, 2]. The ADC(2) method in combination with the so-called core-valence separation approximation allows one to reproduce qualitatively reliably the X-ray photoabsorption spectra [34, 36]. At present the work is carried out to implement the ADC(3) scheme for dipole transition moment calculation and to improve the performance of the existing ADC codes for polarization propagator.
3. Development of the extended ADC / ISR approximation schemes
The intermediate state representation of the one-particle operators is an important generalization of the ADC approach. The ISR and ADC schemes for polarization and electron propagators allow one to formulate computational methods for nearly any type of electronic properties [23, 30, 33]. Within the framework of the ADC / ISR approach it is possible for example to evaluate the one-particle properties of a system in the excited and ionized states, energies and probabilities of transitions between various excited and ionized states, linear and non-linear response properties in the electronic ground state. The second-order ADC / ISR scheme which we have implemented demonstrates good accuracy of results for excited-state dipole transition moments [23] and ground-state dipole polarizabilities [33]. At present we extend the method for treatment of further linear and non-linear ground-state properties and also implement schemes for calculations of one-electronic properties in ionized states.
4. Theoretical studies of the valence-shell photoelectron spectra
Theoretical studies of the molecular valence shell photoelectron spectra is one of the major application fields of the one-particle Green's function theory. Our work in this field is carried out in collaboration with the experimental group of Dr. D. M. P. Holland (Daresbury Laboratory, Daresbury, Warrington, UK). Among the systems which we currently investigate prevail biologically relevant molecules such as DNA bases [20, 32]. The theoretical studies in this field allow not only to reliably interpreted the observed spectra but also lead to better understanding of the electronic structure of the considered biomolecules and of the processes that take place in living nature under the influence of electromagnetic radiation. Most of the calculations are performed using the ADC(3) and OVGF (outer valence Green's function) approximation schemes for the one-particle Green's function.
5. Theoretical studies of the core-level electron excitation and ionization spectra
Theoretical studies of core excitations and ionization using ADC schemes allow for reliable interpretation of the results of the X-ray photoelectron spectroscopy (XPS) and the near edge X-ray absorption fine structure (NEXAFS) experiments. We carry out this work in collaboration with the group of Prof. K. C. Prince (Synchrotron Trieste, Trieste, Italy). Here our research are also focused at theoretical and experimental study of nucleobases (thymine, cytosine, guanine, adenine, uracil and its derivatives) [36].
6. Investigation of vibronic and nonadiabatic effects in the excitation and ionization spectra
In the interpretation of the excitation and ionization spectra of polyatomic molecules one often encounters a situation where even very accurate electronic structure calculations cannot correctly describe the observed spectra. In most cases this can be attributed to the presence of vibronic effects which mix the closely lying electronic states through vibrational excitations. The vibronic phenomena go beyond the scope of the adiabatic approximation and their investigation is a complicated task requiring special theoretical techniques. One of the most practical approaches here [T5] is based on the concept of vibronic model Hamiltonians formulated within the basis of diabatic electronic states. Once the appropriate vibronic Hamiltonian is defined and set up through a set of electronic structure calculations, the resulting vibronic spectrum can easily be calculated. The latter step is usually accomplished using Lanczos algorithm or a more general multiconfigurational time-dependent Hartree (MCTDH) approach [T6]. In the latter case the wave packet time evolution is studied and the vibronic spectrum is obtained through Fourier transformation of the resulting autocorrelation function. Although the theory of nonadiabatic effect is not our major specialty, we always pay special attention at typical signatures of vibronic effect in the spectra that we analyze and study more carefully those situations which lead to violations of the adiabatic approximation [5, 19, 25, 26].
The above research were supported at various times by grants from:
Selected Publications of A.B. Trofimov
(the key papers are available for downloading as PDF files)
1.    J. Schirmer, A. B. Trofimov, K. J. Randall, J. Feldhaus, A. M. Bradshaw, Y. Ma, C. T. Chen, F. Sette, K-shell excitation of the water, ammonia, and methane molecules using high-resolution photoabsorption spectroscopy // Phys. Rev. A.– 1993.– Vol. 47, No. 2.– P. 1136-1147.
2.    A. B. Trofimov, J. Schirmer, An efficient polarization propagator approach to valence electron excitation spectra // J. Phys. B: At. Mol. Opt. Phys.– 1995.– Vol. 28, No. 12.– P. 2299-2324.
3.    A. B. Trofimov, J. Schirmer, Polarization propagator study of electronic spectra of the key heterocyclic molecules. I. Pyrrole // Chem. Phys.– 1997.– Vol. 214, No. 2-3.– P. 153-170.
4.    A. B. Trofimov, J. Schirmer, Polarization propagator study of electronic spectra of the key heterocyclic molecules. II. Furan // Chem. Phys.– 1997.– Vol. 224, No. 2-3.– P. 175-190.
5.    A. B. Trofimov, H. Köppel, J. Schirmer, Vibronic structure of the valence p-photoelecton bands in furan, pyrrole, and thiophene // J. Chem. Phys.– 1998.– Vol. 109, No. 3.– P. 1025-1040.
6.    J. Schirmer, A. B. Trofimov, G. Stelter, A non-Dyson third-order approximation scheme for the electron propagator // J. Chem. Phys.– 1998.– Vol. 109, No. 12.– P. 4734-4744.
7.    A. B. Trofimov, G. Stelter, J. Schirmer, A consistent third-order propagator method for electronic excitation // J. Chem. Phys.– 1999.– Vol. 111, No. 22.– P. 9982-9999.
8.    W. N. Pang, J. F. Gao, C. J. Ruan, R. C. Shang, A. B. Trofimov, M. S. Deleuze, Valence electron momentum spectroscopy of n-butane // J. Chem. Phys.– 2000.– Vol. 112, No. 18.– P. 8043-8052.
9.    D. M. P. Holland, D. A. Shaw, L. Karlsson, L. G. Shpinkova, L. Cooper, A. B. Trofimov, J. Schirmer, An experimental and theoretical investigation of the valence shell photoelectron spectrum of cyanogen chloride // Molecular Physics.– 2000.– Vol. 98, No. 23.– P. 1939-1947.
10. A. B. Trofimov, E. V. Gromov, T. E. Moskovskaya, J. Schirmer, Theoretical evidence for a bound doubly-excited 1B2(C1s,n®p*2) state in H2CO below the C1s ionization threshold // J. Chem. Phys.– 2000.– Vol. 113, No. 16.– P. 6716-6723.
11. A. B. Trofimov, J. Schirmer, D. M. P. Holland, L. Karlsson, R. Maripuu, K. Siegbahn, A. W. Potts, An experimental and theoretical investigation of the valence shell photoelectron spectra of thiophene, 2-chlorothiophene and 3-chlorothiophene // Chem. Phys.– 2001.– Vol. 263, No. 1.– P. 167-193.
12. A. W. Potts, A. B. Trofimov, J. Schirmer, D. M. P. Holland, L. Karlsson, An experimental and theoretical investigation of the valence shell photoelectron spectra of 2-bromothiophene and 3-bromothiophene // Chem. Phys.– 2001.– Vol. 271, No. 3.– P. 337-356.
13. M. S. Deleuze, A. B. Trofimov, L. S. Cederbaum, Valence one-electron and shake-up ionization bands of polycyclic aromatic hydrocarbons. I. Benzene, naphthalene, anthracene, naphthacene, and pentacene // J. Chem. Phys.– 2001.– Vol. 115, No. 13.– P. 5859-5882.
14. M. G. Giuffreda, M. S. Deleuze, J.-P. François, A. B. Trofimov, Polarization propagator study of the valence electron excitation of linear carbon clusters C3, C5 and C7 // Int. J. Quantum Chem.– 2001.– Vol. 85, No. 4-5.– P. 475-491.
15. A. B. Trofimov, T. E. Moskovskaya, E. V. Gromov, H. Köppel, J. Schirmer, Theoretical study of K-shell excitations in formaldehyde // Phys. Rev. A.– 2001.– Vol. 64, No. 2.– P. 022504–1-022504–15.
16. D. M. P. Holland, A. W. Potts, L. Karlsson, A. B. Trofimov, J. Schirmer, The influence of shape resonance phenomena on the valence shell photoionization dynamics of silicon tetrafluoride // J. Phys. B: At. Mol. Opt. Phys.– 2002.– Vol. 35, No. 7.– P. 1741-1757.
17. A. B. Trofimov, J. Schirmer, D. M. P. Holland, A. W. Potts, L. Karlsson, R. Maripuu, K. Siegbahn, The influence of electron correlation and relativistic effects on the valence shell photoelectron spectrum of iodothiophene // J. Phys. B: At. Mol. Opt. Phys.– 2002.– Vol. 35, No. 24.– P. 5051-5079.
18. A. B. Trofimov, G. Stelter, J. Schirmer, Electron excitation energies using a consistent third-order propagator approach: Comparison with full configuration interaction and coupled cluster results // J. Chem. Phys.– 2002.– Vol. 117, No. 14.– P. 6402-6410.
19. E. V. Gromov, A. B. Trofimov, N. M. Vitkovskaya, J. Schirmer, H. Köppel, Theoretical study of the low-lying excited singlet states of furan // J. Chem. Phys.– 2003.– Vol. 119, No. 2.– P. 737-753.
20. A. W. Potts, D. M. P. Holland, A. B. Trofimov, J. Schirmer, L. Karlsson, K. Siegbahn, An experimental and theoretical study of the valence shell photoelectron spectra of purine and pyrimidine molecules // J. Phys. B: At. Mol. Opt. Phys.– 2003.– Vol. 36, No. 14.– P. 3129-3141.
21. A. B. Trofimov, E. V. Gromov, H. Köppel, J. Schirmer, K. C. Prince, R. Richter, M. De Simone, M. Coreno, A theoretical study of the 1B1(O1s®p*) and 1A1(O1s®3s) excited states of formaldehyde // J. Phys. B: At. Mol. Opt. Phys.– 2003.– Vol. 36, No. 18.– P. 3805-3816.
22. M. Pernpointner, A. B. Trofimov, The one-particle Green's function method in the Dirac-Hartree-Fock framework. I. Second-order valence ionization energies of Ne through Xe // J. Chem. Phys.– 2004.– Vol. 120, No. 9.– P. 4098-4106.
23. J. Schirmer, A. B. Trofimov, Intermediate state representation approach to physical properties of electronically excited molecules // J. Chem. Phys.– 2004.– Vol. 120, No. 24.– P. 11449-11464.
24. D. M. P. Holland, I. Powis, L. Karlsson, A. B. Trofimov, J. Schirmer, W. von Niessen, A study of the photoionisation dynamics of the cyanogen halides // Chem. Phys.– 2004.– Vol. 297, No. 1-3.– P. 55-73.
25. E. V. Gromov, A. B. Trofimov, N. M. Vitkovskaya, H. Köppel, J. Schirmer, H.-D. Meyer, L. S. Cederbaum, Theoretical study of excitations in furan: Spectra and molecular dynamics // J. Chem. Phys.– 2004.– Vol. 121, No. 10.– P. 4585-4598.
26. H. Köppel, E. V. Gromov, A. B. Trofimov, Multi-mode-multi-state quantum dynamics of key five-membered heterocycles: spectroscopy and ultrafast internal conversion // Chem. Phys.– 2004.– Vol. 304, No. 1-2.– P. 35-49.
27. A. B. Trofimov, V. G. Zakrzewski, O. Dolgunicheva, J. V. Ortiz, V. F. Sidorkin, E. F. Belogolova, M. Belogolov, V. A. Pestunovich, Silicon-nitrogen bonding in silatranes: assignment of photoelectron spectra // J. Am. Chem. Soc.– 2005.– Vol. 127, No. 3.– P. 986-995.
28. D. M. P. Holland, A. W. Potts, A. B. Trofimov, J. Breidbach, J. Schirmer, R. Feifel, T. Richter, K. Godehusen, M. Martins, A. Tutay, M. Yalcinkaya, M. Al-Hada, S. Eriksson, L. Karlsson, An experimental and theoretical study of the valence shell photoelctron spectrum of tetrafluoromethane // Chem. Phys.– 2005.– Vol. 308, No. 1-2.– P. 43-57.
29. I. Powis, J. D. Thrower, A. B. Trofimov, T. E. Moskovskaya, J. Schirmer, A. W. Potts, D. M. P. Holland, F. Bruhn, L. Karlsson, An experimental and theoretical study of the photoelectron spectrum of hydrogen selenide // Chem. Phys.– 2005.– Vol. 315, No. 1-2.– P. 121-132.
30. K. Gokhberg, A. B. Trofimov, T. Sommerfeld, L. S. Cederbaum, Ionization of metal atoms following valence-excitation of neighbouring molecules // Europhysics Lett. – 2005.– Vol. 72, No. 2.– P. 228-234.
31. A. B. Trofimov, J. Schirmer, Molecular ionization energies and ground- and ionic-state properties using a non-Dyson electron propagator approach // J. Chem. Phys.– 2005.– Vol. 123, No. 14.– P. 144115–1-144115–15.
32. A. B. Trofimov, J. Schirmer, V. B. Kobychev, A. W. Potts, D. M. P. Holland, L.Karlsson, Photoelectron spectra of the nucleobases cytosine, thymine and adenine // J. Phys. B: At. Mol. Opt. Phys.– 2006.– Vol. 39, No. 2.– P. 305-326.
33. A. B. Trofimov, I. L. Krivdina, J. Weller, J. Schirmer, Algebraic-diagram­matic construction propagator approach to molecular response properties // Chem. Phys.– 2006.– Vol. 329, No. 1-3.– P. 1-10.
34. I. Bâldea, B. Schimmelpfennig, M. Plaschke, J. Rothe, J. Schirmer, A.B. Trofimov, Th. Fanghänel, C 1s near edge X-ray absorption fine structure (NEXAFS) of substituted benzoic acids - A theoretical and experimental study // Journal of Electron Spectroscopy and Related Phenomena.– 2007.– Vol. 154, Iss. 3.– P. 109-118.
35. I. Powis, I. L. Zaytseva, A. B. Trofimov, J. Schirmer, D. M. P. Holland, A. W. Potts, L. Karlsson, A study of the valence shell electronic structure and photoionization dynamics of selenophene // J. Phys. B: At. Mol. Opt. Phys.– 2007.– Vol. 40.– P. 2019-2041.
36. O. Plekan, V. Feyer, R. Richter, M. Coreno, M. de Simone, K. C. Prince, A. B. Trofimov, E. V. Gromov, I. L. Zaytseva, J. Schirmer, A theoretical and experimental study of the near edge X-ray absorption fine structure (NEXAFS) and X-ray photoelectron spectra (XPS) of nucleobases: Thymine and adenine // Chem. Phys.– 2008.– Vol. 347.– P. 360-375.
Abstract of the D. Sc. Dissertation: A. B. Trofimov "Developments and Applications of the Quantum-Chemical Green's Function Methods", Irkutsk, 2006 (in Russian).


· Prof. Dr. J. Schirmer, Institute for Physical Chemistry of Heidelberg University, Germany.
· Dr. D.M.P. Holland, Daresbury Laboratory, Daresbury, Warrington, UK
· Prof. K. C. Prince, Synchrotron Trieste, Trieste, Italy

Recommended Literature

Textbooks and Review Articles

T1. A. L. Fetter and J. D. Walecka, Quantum Theory of Many-Particle Systems (McGraw-Hill, New York, 1971).
T2. A. A. Abrikosov, L. P. Gorkov, and I. E. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics (Prentice-Hall, Englewood Cliffs, 1963).
T3. R. D. Mattuck, A Guide to Feynman Diagrams in the Many-Body Problem (McGraw-Hill, London, 1967).
T4. Cederbaum L. S., Domke W. Theoretical aspects of ionization potentials and photoelectron spectroscopy: A Green's function approach // Adv. Chem. Phys.– 1977.– Vol. 36.– P. 205-344.
T5. Köppel H., Domcke W., Cederbaum L. S. Multimode molecular dynamics beyond the Born-Oppenheimer approximation // Adv. Chem. Phys.– 1984.– Vol. 57.– P. 59-246..
T6. The multiconfiguration time-dependent Hartree (MCTDH) method: a highly efficient algorithm for propagating wavepackets / M. H. Beck, A. Jäckle, G. A. Worth, H.–D. Meyer // Phys. Rep.– 2000.– Vol. 324.– P. 1-105.

Original Articles

A1. Schirmer J. Beyond the random-phase approximation: a new approximation scheme for the polarization propagator // Phys. Rev. A.– 1982.– Vol. 26.– P. 2395-2416.
A2. Schirmer J., Cederbaum L. S., Walter O. New approach to the one-particle Green's function for finite Fermi systems // Phys. Rev. A.– 1983.– Vol. 28.– P. 1237-1259.
A3. Schirmer J., Barth A. Higher-order approximations for the particle-particle propagator // Z. Phys. A.– 1984.– Vol. 317.– P. 267-279.
A4. Schirmer J. Closed-form intermediate representations of many-body propagators and resolvent matrices // Phys. Rev. A.– 1991.– Vol. 43.– P. 4647-4659.
A5. Mertins F., Schirmer J. Algebraic propagator approaches and intermediate-state representations. I. The biorthogonal and unitary coupled-cluster methods // Phys. Rev. A.– 1996.– Vol. 53.– P. 2140-2152.
A6. Mertins F., Schirmer J., Tarantelli A. Algebraic propagator approaches and intermediate-state representations. II. The equation-of-motion methods for N, N±1, N±2 electrons // Phys. Rev. A.– 1996.– Vol. 53.– P. 2153-2168.