Lucjan Piela

University of Warsaw, Warszawa, Masovian Voivodeship, Poland

Are you Lucjan Piela?

Claim your profile

Publications (68)166.78 Total impact

  • Lucjan Piela
    [Show abstract] [Hide abstract]
    ABSTRACT: Electrons are believed to avoid one another in space (correlation) due to the Coulomb repulsion and/or the Pauli exclusion principle. It is shown, using examples of two-electron systems, that indeed the mean electron-electron distance increases in case of the ground electronic state as compared to the independent electron model. It is demonstrated however that there exist excited states, often of low energy, in which the electrons, while having a lot of free physical space (with nuclei being absent), choose to be close to each other in their motion ("anticorrelation"), as if they mutually attracted one another. The source of this effect, quantummechanical in nature, is the orthogonality of the eigenfunctions, that forces the electronic wave functions to differ widely, even at the price of short electron-electron distances. There are also excited states with a mixed behaviour, with complex and often intriguing correlation-anticorrelation patterns.
    Science China-Chemistry 10/2014; 57(10):1383-1392. DOI:10.1007/s11426-014-5157-0 · 1.52 Impact Factor
  • Lucjan Piela
    [Show abstract] [Hide abstract]
    ABSTRACT: The intermolecular interaction is ubiquitous and influences the results of virtually every chemical or physical experiment. There are some important questions left in the theory of intermolecular interaction. One of such questions is: what kind of objects do interact. In the article, we recall a kind of unusual symmetry requirement in a physical theory related to this question. Also, we introduce a gradation of such choices of the interacting subsystems leading eventually to the concept of the most natural choice. Electrostatics plays a special role in the intermolecular interaction. We discuss why electrostatics remains important even if other interactions are strong. Next, the electrostatic interactions are shown to be important in the three‐dimensional (3D) structure of proteins occurring in Nature. Predicting the molecule's lowest‐energy conformation or configuration represents a formidable task. There were many attempts to solve this problem for protein molecules, for which it is believed their native conformation corresponds to the lowest free energy. The challenge to find this conformation from a given sequence of amino acids (AAs) is known as a “second genetic code.” In fact all of these attempts are based on some smoothing of the energy landscape. In the article, some of these smoothing techniques are described, which finally turned out to be highly successful in finding native structures of globular proteins. When discussing the contributions to the conformational energy the importance of the electrostatic interactions has been stressed. In particular, it turned out that the dipole moments of the NH and of the CO bonds in proteins functioning in nature are oriented to good accuracy along the local intramolecular electric field. Thanks to an enormous effort of the protein folding community it is possible to predict the native 3D structure of globular proteins. It is also possible to design such AA sequences, which fold to the desired protein 3D structure. A certain reliable theoretical technique of protein folding has been used to study a possibility of conformational autocatalysis. It turned out that such an effect has been predicted for a small protein of 32 AAs, with carefully designed AA sequence. This may be seen as a model of the prion disease propagation. © 2012 Wiley Periodicals, Inc.
    International Journal of Quantum Chemistry 09/2012; 112(18). DOI:10.1002/qua.24264 · 1.17 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: We present π-electrons RHF-SCF and CI calculations of the evolution of the first singlet excited state transition energy as a function of chain length, in polyene oligomers ranging from C2H4 up to C42H44. The results indicate that in small oligomers, the excitation is delocalized over the whole molecule. Localization phenomena are present in the larger chains (larger than ∼ C14H16) thereby explaining the failure of the RHF-SCF technique to properly describe the first singlet excited state energies in the extended oligomers. Consequences in the use of so-called OAO techniques are pointed out.
    01/2010; 92(1). DOI:10.1002/bscb.19830920101
  • [Show abstract] [Hide abstract]
    ABSTRACT: Detailed numerical studies of the three related methods—restricted Hartree-Fock (RHF), alternant molecular orbital (AMO) with one and several coupling parameters, and unrestricted Hartree-Fock (UHF)—have been made for a linear chain of hydrogen atoms with uniform distances. The long-range electrostatic interactions have been properly included.
    International Journal of Quantum Chemistry 03/2009; 18(S14):419 - 429. DOI:10.1002/qua.560180843 · 1.17 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: A technique based on the multipole expansion is used to calculate accurately and for a negligible computing effort the long-range contributions in helical systems. The only quantities to be evaluated are the multipole moments of the charge distribution in the reduced unit cell. The method is applied to the 2*3/1 isotactic polypropylene helix.
    International Journal of Quantum Chemistry 03/2009; 18(S14). DOI:10.1002/qua.560180842 · 1.17 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: Fourier representation for long-range electrostatic contributions in model polymers is not uniformly efficient at all possible charge interdistances. Here we suggest replacing the Fourier formulas when they are no longer satisfactory by a Laplace transform-based procedure.
    International Journal of Quantum Chemistry 03/2009; 18(S14):431 - 442. DOI:10.1002/qua.560180844 · 1.17 Impact Factor
  • Lucjan Piela
    [Show abstract] [Hide abstract]
    ABSTRACT: There are plenty of possible structures (isomers) for a given number of atoms; their number quickly becoming astronomical for larger molecules. Usually only some of these structures (low-energy ones) play a role in experiments. However, in the theoretical description of the system in principle, all these structures have to be taken into account, a very costly adventure. Therefore, one of the challenges of chemistry (as well as of physics, biology, etc.) is the multiple minima problem, that is, how to identify the low-energy structures without calculating all possible configurations of atoms. The protein folding is given as an example of overcoming the multiple minima problem.
    03/2009: pages 137-148;
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Theoretical investigations of polymer electronic properties have mainly been based on nearly 1D model polymers even though some properties, including structure, can differ significantly in the crystal field created by the surrounding chains. Due to 3D lattice summations, consistent evaluation of the long-range Coulombic interactions in model polymer crystals is far more difficult compared to 1 D cases where procedures based on mathematical transformations (Fourier, Laplace, . . .) can be applied rather easily. Use of a logical extension of Evjen's method as indicated by Harris [ 11 looks very attractive in this context. The procedure is based upon the fact that the same charge distribution can be described by different repeating units. Choices can be made such that the leading moments of the charge distribution in each unit are annihilated, and the corresponding terms in a multipole expansion of the Coulombic interactions are thereby equal to zero. Prior to any attempt at its use for model polymer crystals we have studied the mechanism of this procedure on an infinite 1 D array of LiH molecules so as to identify computational aspects. Results are as follows: (i) infinite summation is avoided and the computational labour for long-range corrections amount to few additional nuclear attraction integrals. (ii) the procedure is of general applicability for polymer crystals (3D) but in the case of nearly 1D polymers it is restricted to systems having cylindrical symmetry.
    International Journal of Quantum Chemistry 03/2009; 15(S15):217. DOI:10.1002/qua.560200823 · 1.17 Impact Factor
  • Donald G. Truhlar, Lucjan Piela
    Physics Today 07/2008; 61(7). DOI:10.1063/1.2963024 · 5.89 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: There is a hypothesis that dangerous diseases such as bovine spongiform encephalopathy, Creutzfeldt-Jakob, Alzheimer's, fatal familial insomnia, and several others are induced by propagation of wrong or misfolded conformations of some vital proteins. If for some reason the misfolded conformations were acquired by many such protein molecules it might lead to a "conformational" disease of the organism. Here, a theoretical model of the molecular mechanism of such a conformational disease is proposed, in which a metastable (or misfolded) form of a protein induces a similar misfolding of another protein molecule (conformational autocatalysis). First, a number of amino acid sequences composed of 32 aa have been designed that fold rapidly into a well defined native-like alpha-helical conformation. From a large number of such sequences a subset of 14 had a specific feature of their energy landscape, a well defined local energy minimum (higher than the global minimum for the alpha-helical fold) corresponding to beta-type structure. Only one of these 14 sequences exhibited a strong autocatalytic tendency to form a beta-sheet dimer capable of further propagation of protofibril-like structure. Simulations were done by using a reduced, although of high resolution, protein model and the replica exchange Monte Carlo sampling procedure.
    Proceedings of the National Academy of Sciences 06/2005; 102(22):7835-40. DOI:10.1073/pnas.0409389102 · 9.81 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: Assuming a determinantal form for the wave-functions of free molecules, explicit formula for the first-order interaction energy of many closed-shell molecules has been derived. Provided that the determinants describing the free molecules are constructed from the Hartree-Fock orbitals, the two-, three-, and four-body effects predicted by the first-order perturbation theory are closely related to those which one obtains in the framework of the Löwdin LCAO MO-type approach. The results are illustrated by numerical calculations for the system of three ground-state helium atoms.
    International Journal of Quantum Chemistry 10/2004; 10(2):281 - 297. DOI:10.1002/qua.560100208 · 1.17 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: In the case of conjugated polyenic chains (polyacetylene), the relationships between the long- (or short-) range nature of the restricted Hartree–Fock exchange interaction, the role of correlation effects, and the size of energy gaps are illustrated.
    International Journal of Quantum Chemistry 10/2004; 23(3):1065 - 1072. DOI:10.1002/qua.560230330 · 1.17 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: Computation of exchange-polarization and electrostatic-polarization interaction energies between ions is the most expensive step in ab initio investigations of the properties of perfect and imperfect ionic crystals. In the present paper approximate formulas are proposed for these quantities. They save about 95% of the computation time and give these values with an error less than 0.2 kcal mol−1 as compared to ab initio results. The formulas for the exchange- and electrostatic-polarization energies involve the generalized overlap integral between the one-determinantal wave functions of the deformed ions. The approximations are tested in the calculations of the interactions of deformed ions in LiF and NaF crystals.
    International Journal of Quantum Chemistry 10/2004; 19(3):401 - 411. DOI:10.1002/qua.560190304 · 1.17 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: One of the features of the polypeptide backbone is that it represents a flexible chain that contains almost rigid CONH peptide bonds. One may try to substitute one or more such bonds by another relatively rigid unit to maintain the overall conformational properties of the backbone and at the same time modify some other properties of the molecule (“pseudopeptide”), such as the ability to form hydrogen bonds. By a detailed conformational analysis, it is shown that the carboncarbon double bond is quite isosteric with the peptide bond and for this reason suitable for such a substitution. This is accomplished by applying molecular mechanics in calculation of the ϕ, ψ maps for pseudopeptide analogs of the N-acetyl-Ala-NHMe molecule. © 1993 John Wiley & Sons, Inc.
    Journal of Computational Chemistry 09/2004; 14(4):471 - 477. DOI:10.1002/jcc.540140411 · 3.60 Impact Factor
  • Maciej Bagińki, Lucjan Piela
    [Show abstract] [Hide abstract]
    ABSTRACT: The conformational analysis for a molecule is often performed by assuming that the total conformational energy is a function of two dihedral angles. The resulting conformational energy map is sometimes not easy to interpret because what counts is not energy differences but rather the probability distribution map at a given temperature. In the present article, an algorithm to calculate such a map is given. An example concerning N-substituted amino sugars shows how the conformational probability map may be interpreted. In addition, a similarity index is proposed to get a measure of similarity of the conformational properties of two molecules. The index is based upon the analysis of the conformational probability maps for both molecules. © 1993 John Wiley & Sons, Inc.
    Journal of Computational Chemistry 09/2004; 14(4):478 - 483. DOI:10.1002/jcc.540140412 · 3.60 Impact Factor
  • Edyta Małolepsza, Lucjan Piela
    [Show abstract] [Hide abstract]
    ABSTRACT: A hardness of molecular surface (investigated by using the helium atom probe) is proposed as its descriptor. As an example, a homological series of the first-row hydrides has been studied. The molecular surface (“molecular shape”) is defined as an isosurface of the valence repulsion energy that is related to the Pauli exclusion principle. Interestingly, the amplitude of the surface−heavy atom distance is almost the same for all of the molecules, except the methane molecule, for which it is larger by about 33%. The Pauli hardness of a point on the isosurface is defined as the first derivative of the valence repulsion energy in the direction normal to the isosurface. Higher-order derivatives correspond to the nonlinear effects (hyperhardnesses). It turned out that the molecular surfaces of these molecules are convex and the Pauli hardness of a molecule varies within about 20% as a function of position on the molecular surface. The quantity also changes by about 30% among the molecules of the series. The molecule with the greatest Pauli hardness in the series is hydrogen fluoride, and the maximum Pauli hardness increases almost linearly with the atomic number of the heavy atom in the homological series studied. The minimum Pauli hardness behaves in a different way:  it is the largest for the hydrogen fluoride and then decreases for the water and ammonia, while the methane molecule represents a remarkable exception showing considerable increase of this quantity. As a result, the methane molecule exhibits the smallest, while the ammonia molecule the largest, hardness anisotropy among the first-row hydrides.
    The Journal of Physical Chemistry A 06/2003; 107(27). DOI:10.1021/jp034423+ · 2.78 Impact Factor
  • Edyta Małolepsza, Lucjan Piela
    [Show abstract] [Hide abstract]
    ABSTRACT: A molecular surface defined as an isosurface of the valence repulsion energy may be hard or soft with respect to probe penetration. As a probe, the helium atom has been chosen. In addition, the Pauli exclusion principle makes the electronic structure change when the probe pushes the molecule (at a fixed positions of its nuclei). This results in a HOMO-LUMO gap dependence on the probe site on the isosurface. A smaller gap at a given probe position reflects a larger reactivity of the site with respect to the ionic dissociation.
    Collection of Czechoslovak Chemical Communications 01/2003; DOI:10.1135/cccc20032344 · 1.14 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: A self-consistent multitorsional field (SCMTF) method of global optimization of the conformational energy of an oligopeptide is proposed. The method is based on the idea that the maximum of the square of the ground-state wave function is very often close to the global minimum of the potential energy and may be relatively unaffected by the complexity of the potential, e.g., its many minima. Using a mean field approximation, a set of coupled Schrodinger equations for the motion of the nuclei is solved iteratively in a dihedral-angle space, each equation depending on a single dihedral angle. To obtain the effective potential energy, and therefore the Hamiltonian, for the particular dihedral angle, a Monte Carlo averaging is carried out over all other dihedral angles. Thus, the wave function and therefore the probability distribution of a particular dihedral angle depends on the mean field of the rest of the molecule. The method was found to converge rapidly when applied to searches for the global minimum of the potential energy of terminally-blocked alanine. In the case of the pentapeptide Met-enkephalin, convergence was slightly slower, but it also led to the global minimum. Because the number of evaluations of the potential energy increases approximately linearly with the number of dihedral angles (not counting the cost to compute the potential energy), the method is expected to be applicable to larger molecules.
    The Journal of Physical Chemistry 04/2002; 96(11). DOI:10.1021/j100190a096 · 2.78 Impact Factor
  • The Journal of Physical Chemistry 04/2002; 94(15). DOI:10.1021/j100378a020 · 2.78 Impact Factor
  • The Journal of Physical Chemistry 04/2002; 93(8). DOI:10.1021/j100345a090 · 2.78 Impact Factor

Publication Stats

1k Citations
166.78 Total Impact Points

Institutions

  • 1969–2014
    • University of Warsaw
      • Faculty of Chemistry
      Warszawa, Masovian Voivodeship, Poland
  • 1987–2002
    • Cornell University
      • Department of Chemistry and Chemical Biology
      Итак, New York, United States
  • 1998
    • University of Namur
      Namen, Walloon, Belgium
  • 1981
    • Université Paris-Sud 11
      Orsay, Île-de-France, France