Lucjan Piela

University of Warsaw, Warszawa, Masovian Voivodeship, Poland

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Publications (50)82.17 Total impact

  • Lucjan Piela
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    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 01/2012; 112(18). · 1.17 Impact Factor
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    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 06/2009; 18(S14):431 - 442. · 1.17 Impact Factor
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    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 06/2009; 18(S14):419 - 429. · 1.17 Impact Factor
  • Lucjan Piela
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    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;
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    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. · 9.81 Impact Factor
  • Lucjan Piela, Joseph Delhalle
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    ABSTRACT: A very efficient and exact method for calculating the long-range effects in polymers is reported. The method is based on the multipole expansion within the Fock operator, and exact summation up to infinity is carried out. Only a small number of one-electron integrals have to be considered, while in the traditional approach one has to compute a large number of two-electron integrals. Results on LiH model polymer have been obtained with a remarkable accuracy within a negligible computing time.
    International Journal of Quantum Chemistry 10/2004; 13(5):605 - 617. · 1.17 Impact Factor
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    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. · 1.17 Impact Factor
  • Leszek Z. Stolarczyk, Lucjan Piela
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    ABSTRACT: A method of direct calculation of lattice sums in three-dimensional crystals is reported. The method is based on annihilation of some lowest multipole moments of the unit cell by a redefinition of the unit cell content. As a result, properties of the infinite crystal can be calculated as usual by taking a finite cluster of unit cells, but surrounded by an additional surface layer of a charge density (e.g., a layer of point charges). This charge density distribution produces the electric field approximating that one of the rest of the infinite crystal. The method proposed is easily applicable in the SCFLCAO procedure as well as in any method using a cluster representation for an infinite crystal. The validity of the infinite crystal model for a finite crystal is also discussed.
    International Journal of Quantum Chemistry 10/2004; 22(5):911 - 927. · 1.17 Impact Factor
  • Leszek Z. Stolarczyk, Lucjan Piela
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    ABSTRACT: The physical interpretation of intermolecular interactions is usually based on the well-known multipole expansion of the inverse of the interparticle distance. The interaction energy is then interpreted as a sum of terms arising from the interaction of various multipole moments of both systems. It is supposed that the interaction energy calculated via the truncated multipole expansion generally depends on the choice of local coordinate systems through the coordinate dependence of the multipole moments. In this paper we prove that each term of the multipole expansion given in the form ∑k = 1Ck/Rk is invariant with respect to identical translations and arbitrary rotations of the local coordinate systems. The invariant form of the convergence criterion of the multipole expansion is given and discussed.
    International Journal of Quantum Chemistry 10/2004; 15(6):701 - 711. · 1.17 Impact Factor
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    ABSTRACT: This paper analyzes the use of electric-field-variant (EFV) atomic orbitals in calculations of molecular polarizabilities using the finite field approximation. It is shown that, in the absence of an external electric field, the optimal positions of the orbital centers which minimize the total energy are already shifted with respect to the atomic sites and that these optimal positions constitute a better starting point to compute molecular polarizabilities by the finite field method. The technique is applied to the hydrogen molecule and to the alkane series CnH2n+2, n = 1, 2, 3, 4, 5, 6 in the framework of a floating spherical gaussian orbital-EFV basis.
    International Journal of Quantum Chemistry 10/2004; 34(S22):665 - 678. · 1.17 Impact Factor
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    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. · 1.17 Impact Factor
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    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. · 1.17 Impact Factor
  • Maciej Bagińki, Lucjan Piela
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    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. · 3.84 Impact Factor
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    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. · 3.84 Impact Factor
  • Edyta Małolepsza, Lucjan Piela
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    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). · 2.77 Impact Factor
  • Edyta Małolepsza, Lucjan Piela
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    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.
    01/2003;
  • Jaroslaw Pillardy, Lucjan Piela
    The Journal of Physical Chemistry. 04/2002; 99(31).
  • Journal of The American Chemical Society - J AM CHEM SOC. 04/2002; 109(15).
  • The Journal of Physical Chemistry. 04/2002; 96(11).
  • The Journal of Physical Chemistry. 04/2002; 96(11).