Lucjan Piela

University of Warsaw, Warszawa, Masovian Voivodeship, Poland

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Publications (45)133.95 Total impact

  • Lucjan Piela
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    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
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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 09/2012; 112(18). DOI:10.1002/qua.24264 · 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;
  • Donald G. Truhlar · Lucjan Piela
    Physics Today 07/2008; 61(7). DOI:10.1063/1.2963024 · 5.89 Impact Factor
  • Source
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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. DOI:10.1073/pnas.0409389102 · 9.81 Impact Factor
  • Bogumił Jeziorski · Marek Bulski · Lucjan Piela
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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. DOI:10.1002/qua.560100208 · 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. DOI:10.1002/qua.560190304 · 1.17 Impact Factor
  • Maciej Bagińki · Lucjan Piela · Jeffrey Skolnick
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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. DOI:10.1002/jcc.540140411 · 3.60 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. DOI:10.1002/jcc.540140412 · 3.60 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). DOI:10.1021/jp034423+ · 2.78 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.
    Collection of Czechoslovak Chemical Communications 01/2003; DOI:10.1135/cccc20032344 · 1.14 Impact Factor
  • Marek Orzechowski · Piotr Cieplak · Lucjan Piela
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    ABSTRACT: The coiled-coil stability and rigidity may be of importance for molecular electronics (electronically bistable molecules). The coiled-coil binding free energy has been calculated using molecular dynamics (MD). The energy has been computed as a difference of the appropriate free energies; derived for the coiled-coil and isolated alpha-helices separately. All MD simulations have been performed using an explicit model of the solvent, whereas the continuum solvent approach has been applied to analyze the MD trajectories. The computed stability of the coiled-coil is of the order of -87 kcal/mol, i.e., about -1.2 kcal/mol per amino acid residue, and arises mainly from the electrostatic interactions and hydrophobic effect. The entropy term has been roughly estimated to be of the order of -22 kcal/mol. This assures that coiled-coil polypeptides may be used as a stable molecular scaffolding.
    Journal of Computational Chemistry 01/2002; 23(1):106-10. DOI:10.1002/jcc.10020 · 3.60 Impact Factor
  • Lucjan Piela
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    ABSTRACT: Deformation of the target function in global optimization has been a novel possibility for the last decade. The techniques based on the deformation turned out to be related to a variety of fundamental laws: diffusion equation, time-dependent Schrödinger equations, Smoluchowski dynamics, Bloch equation of canonical ensemble evolution with temperature and Gibbs free-energy principle. The progress indicator of global optimization in those methods takes different physical meanings: time, imaginary time or the inverse absolute temperature. Despite of the fact that the phenomena described are different, the resulting global optimization procedures have a remarkable similarity. In the case of the Gaussian ansatz for the wave function or density distribution, the underlying differential equations of motion for the Gaussian position and width are of the same kind for all the phenomena. The original potential energy function is smoothed by a convolution with a Gaussian distribution, its center denoting the current position in space during the minimization. The Gaussian position moves according to the negative gradient of the smoothed potential energy function. The Gaussian width is position dependent through the curvature of the smoothed potential energy function, and evolves according to the following rule. For sufficiently positive curvatures (close to minima of the smoothed potential) the width decreases, thus leading to a smoothed potential approaching the original potential energy function, while for negative curvatures (close to maxima) the width increases leading eventually to disappearance of humps of the original potential energy function. This allows for crossing barriers separating the energy basins. Some methods result in an additional term, which increases the width, when the potential becomes flat. This may be described as a feature allowing hunting for distant minima. Some deformation methods that are of nonconvolutional character are also discussed.
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    ABSTRACT: Two newly synthesised 21-amino acid peptides substituted with ferrocene groups preserve the helical structure of the peptide and behave as multi-centre donor systems with six electroactive reversible redox centres per molecule. The formal potential of the hexaferrocene compound is slightly less positive than that of its single centre analogue.
    Chemical Physics Letters 12/2001; 350(5-6):447-452. DOI:10.1016/S0009-2614(01)01325-2 · 1.99 Impact Factor
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    ABSTRACT: Two newly synthesised 21 - amino acid peptides based on L-leucine and L-lysine substituted with ferrocene groups preserve the helical structure of the peptide and behave as multi-centre donor systems with six electroactive reversible redox centres per molecule. The formal potential of the hexaferrocene compound is slightly less positive than that of its single centre analogue. CT interactions of the ferrocene peptides with chloranil are not confirmed by UV-vis spectra.
    Materials Science and Engineering C 12/2001; 18(1):121-124. DOI:10.1016/S0928-4931(01)00379-4 · 3.09 Impact Factor
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    ABSTRACT: A series of electron donors [neutral Ni(II) and Cu(II) complexes of tetraazatetraenemacrocyclic ligands] differing in metal ion, size of the macrocyclic ligand, and the length of the aliphatic bridges linking the macrocyclic units in dimeric species were synthesized and their redox, structural and spectroscopic properties were studied. The x-ray results for the donors under study show a nearly planar geometry of the monomeric tetraazamacrocyclic complexes and interesting 'organic-zeolite-like' structures of the dimers. The dimeric Ni complexes have flexible cavities between the two single ligands linked with aliphatic chains suitable for accommodating some small-sized guests. For the dimeric compounds the metal oxidation [M(II)/M(III)] takes place independently on each centre except one binuclear Ni complex, where the cooperativity of the metal centres was observed. Methyl substituents give rise to irreversibility of the oxidation process of the complexes studied. In the absence of these substituents neither reorganization nor ligand addition/elimination kinetics affect the electrode process. A common scale for the donors under study and some important acceptor compounds (p-benzoquinone, chloranil, tetracyanoethylene and tetracyanoquinodimethane, etc.) was proposed on the basis of their cyclic voltammetric behaviour in the same physicochemical conditions.
    Journal of Physical Organic Chemistry 02/2001; 14(2). DOI:10.1002/1099-1395(200102)14:2<63::AID-POC328>3.0.CO;2-W · 1.38 Impact Factor
  • Anna Jagielska · Lucjan Piela
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    ABSTRACT: Semiempirical theories predict that some donor–acceptor molecules may exhibit long-lived electronic metastable states. The states result from a cooperative effect of successive electron transfers from several donor to acceptor moieties of the molecule. Calculations within the Møller–Plesset second-order perturbation theory following the unrestricted Hartree–Fock, projected unrestricted Hartree–Fock, and complete active space self-consistent field procedures confirm the effect for the first time at the ab initio level. An equidistant linear chain (DA)n, where the donor (D) and acceptor (A) subunits are the lithium and fluorine atoms, respectively, has been chosen as a model for a molecule with fixed in space D and A substituents. The nearest-neighbor LiF distance is set to be sufficiently large to assure the isolated DA pair has lower energy in the neutral DA state than in the ionic D+A− one, i.e., a single electron transfer to occur requires energy. In the (DA)n system, a single electron transfer from D to the nearest A requires a comparable amount of energy (ΔEn1). It is shown, however, that, due to the cooperative nature of the excitations, the excited state corresponding to m such electron transfers (m>ncrit) may have an excitation energy ΔEnm lower than ΔEn1. Due to this a multiply excited state may be close in energy scale to the nonexcited one, both states separated by energy barrier related to ncrit. The effect has been checked against perturbations that mimic dimerization of the chain and a lateral extension of the D+ and A− charge distribution. It turned out that the cooperative effect is likely to survive these perturbations. © 2000 American Institute of Physics.
    The Journal of Chemical Physics 02/2000; 112(6):2579-2585. DOI:10.1063/1.480831 · 3.12 Impact Factor
  • Anna Jagielska · Robert Moszyński · Lucjan Piela
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    ABSTRACT: Some structural and energetical properties of the borazane molecule have been calculated by the Møller–Plesset perturbation theory accurate to the second, third, and fourth orders (MP2, MP3, MP4), the coupled cluster [CCSD(T)] approach, and the symmetry-adapted perturbation theory (SAPT). The geometry has been fully optimized at the MP2 level. The theoretical values for bond distances, bond angles, rotational barrier, dipole moment, vibrational frequencies, and the nuclear quadrupole coupling constants agree well with the experimental data. The dissociation energy, the BN bond distance, and the vibrational frequencies obtained indicate that borazane is to a considerable extent a floppy system, which has to be classified as a strong van der Waals complex rather than a molecule similar (isoelectronic) to ethane. The best estimate for the complex formation enthalpy corrected for the basis set superposition error is equal to 25.7±2 kcal/mol. As revealed by the SAPT analysis the main binding contributions are the induction and electrostatic effects. The dipole moment of the complex increases very strongly [from 1.53 to 5.30 D at the CCSD(T) level] upon the interaction due mainly to the umbrella structural polarization of the BH3 molecule and to the polarization of the electron cloud. © 1999 American Institute of Physics.
    The Journal of Chemical Physics 01/1999; 110(2):947-954. DOI:10.1063/1.478139 · 3.12 Impact Factor
  • Anna Jagielska · Robert Moszynski · Lucjan Piela
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    ABSTRACT: The structure, binding energies, harmonic vibrational frequencies, and nuclear quadrupole coupling constants of the cyanodihydroborate and boron tricyanide (known compounds, but no structural experimental data available) complexes with ammonia were calculated using the Møller–Plesset perturbation theory through the fourth order and by the coupled-cluster method including single, double, and approximate triple excitations. The origins of the bonding in these complexes were investigated by symmetry-adapted perturbation theory. The computed complex dissociation energies corrected for the basis-set superposition error are large: 27 and 36 kcal/mol, respectively. A peculiar change of the character of the HOMO orbital is taking place when the molecules approach each other. In both complexes, a large (umbrellalike) structural change of the boron moiety occurs due to the interaction with the virtually unchanged ammonia molecule and the accompanying large change of the dipole moment is taking place. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 75: 177–185, 1999
    International Journal of Quantum Chemistry 01/1999; 75(3):177-185. DOI:10.1002/(SICI)1097-461X(1999)75:33.0.CO;2-G · 1.17 Impact Factor
  • Jarosław Pillardy · Lucjan Piela
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    ABSTRACT: Spatial averaging of the potential energy function facilitates the search for the most stable configuration of a molecular system. Recently some global optimization methods of this kind have been designed in the literature that rely on physical phenomena such as diffusion, wave function evolution in quantum mechanics, Smoluchowski dynamics, evolution in temperature of canonical ensembles, etc. In the present article we highlight the fact that all these methods, when applied to the Gaussian distributions of an ensemble, represent special cases of a set of differential equations involving the spatially averaged potential energy. Their structure suggests that the nature's strategy to cope with the global optimization is robust and differs only in the details in particular applications. The strategy consists of going downhill of the averaged potential energy, removing the barriers, and hunting for low energy regions by a selective increasing of the spatial averaging. In this study we explore the deformation of the potential rather than its averaging. The deformation comes from scaling of atomic distances and reduces the barriers even more effectively than the Gaussian averaging. The position and widths of the Gaussian distribution evolve similarly to the Gaussian density annealing (GDA), but we allow elliptical instead of spherical Gaussians as well as branching of the single trajectory of the system into multiple ones. When the temperature reaches 0 K, one has a number of independent Gaussian distributions, each corresponding to a structure and (usually low) energy of the system. The multiple elliptic-Gaussian distance scaling method has been applied to clusters of argon atoms (N=5,…,31), a system serving usually as a benchmark domain. The method found the global minima for all but three clusters (of very low energy). The procedure is 20 or more times less expensive than the GDA one. © 1997 John Wiley & Sons, Inc. J Comput Chem18: 2040–2049, 1997
    Journal of Computational Chemistry 12/1998; 18(16):2040 - 2049. DOI:10.1002/(SICI)1096-987X(199712)18:16<2040::AID-JCC8>3.0.CO;2-L · 3.60 Impact Factor

Publication Stats

1k Citations
133.95 Total Impact Points


  • 1986–2014
    • University of Warsaw
      • Faculty of Chemistry
      Warszawa, Masovian Voivodeship, Poland
  • 1998
    • University of Namur
      Namen, Walloon, Belgium
  • 1987–1993
    • Cornell University
      • Department of Chemistry and Chemical Biology
      Итак, New York, United States