Browsing by Author "Chou, Chien-Pin"

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An Algorithm and FORTRAN Program for Automatic Computation of the Zhang-Zhang Polynomial of Benzenoids
(2012)
Chou, Chien-Pin
;
Witek, Henryk A.
;
應用化學系
;
應用化學系分子科學碩博班
;
Department of Applied Chemistry
"An automatic computer code is developed to calculate the Zhang-Zhang (ZZ) polynomial (aka Clar covering polynomial) for benzenoid systems. The code can be routinely applied to dense pericondensed benzenoids containing up to 500 carbon atoms. For catacondensed and quasi-linear pericondensed benzenoid systems, the limiting number of atoms is much larger and may exceed 10000. A parallel implementation of the code is also presented, which allows one to surpass these limits with a large number of CPUs. The developed program is applied for finding the ZZ polynomials of various classes of benzenoid systems; general techniques and algorithms applicable in this context are reviewed and discussed. A survey of new results obtained in that way is presented in a sequel to this paper [C.-P. Chou, Y. Li, and H.A. Witek, MATCH Commun. Math. Comput. Chem., submitted]."
Automatized Parameterization of DFTB Using Particle Swarm Optimization
(2016-01)
Chou, Chien-Pin
;
Nishimura, Yoshifumi
;
Fan, Chin-Chai
;
Mazur, Grzegorz
;
Irle, Stephan
We present a novel density-functional tight-binding (DFTB) parametrization toolkit developed to optimize the parameters of various DFTB models in a fully automatized fashion. The main features of the algorithm, based on the particle swarm optimization technique, are discussed, and a number of initial pilot applications of the developed methodology to molecular and solid systems are presented.
Automatized Parameterization of DFTB Using Particle Swarm Optimization
(2016-01-01)
Chou, Chien-Pin
;
Nishimura, Yoshifumi
;
Fan, Chin-Chai
;
Mazur, Grzegorz
;
Irle, Stephan
We present a novel density-functional tight-binding (DFTB) parametrization toolkit developed to optimize the parameters of various DFTB models in a fully automatized fashion. The main features of the algorithm, based on the particle swarm optimization technique, are discussed, and a number of initial pilot applications of the developed methodology to molecular and solid systems are presented.
Automatized Parameterization of the Density-functional Tight-binding Method. II. Two-center Integrals
(2016-01-01)
Witek, Henryk A.
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Chou, Chien-Pin
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Mazur, Grzegorz
;
Nishimura, Yoshifumi
;
Irle, Stephan
We present an efficient numerical integration scheme (TWOCENT) to be used in the context of automatized parameterization of the density-functional tight-binding (DFTB) method. The accuracy of the integration process is assessed and its range of applicability is discussed. The functionality of the developed code is tested by reproducing the electronic portion of the existing mio parameter sets and by reproducing a series of reference DFT band structures of elemental solids.
Automatized Parameterization of the Density-functional Tight-binding Method. II. Two-center Integrals
(2016-01)
Witek, Henryk A.
;
Chou, Chien-Pin
;
Mazur, Grzegorz
;
Nishimura, Yoshifumi
;
Irle, Stephan
We present an efficient numerical integration scheme (TWOCENT) to be used in the context of automatized parameterization of the density-functional tight-binding (DFTB) method. The accuracy of the integration process is assessed and its range of applicability is discussed. The functionality of the developed code is tested by reproducing the electronic portion of the existing mio parameter sets and by reproducing a series of reference DFT band structures of elemental solids.
Automatized Parametrization of SCC-DFTB Repulsive Potentials: Application to Hydrocarbons
(2009-10-29)
Gaus, Michael
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Chou, Chien-Pin
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Witek, Henryk
;
Elstner, Marcus
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應用化學系
In this work, we derive and test a new automatized strategy to construct repulsive potentials for the self-consistent charge density functional tight-binding (SCC-DFTB) method. This approach allows one to explore the parameter space in a systematic fashion in order to find optimal solutions. We find that due to the limited flexibility of the SCC-DFTB electronic part, not all properties can be optimized simultaneously. For example, the optimization of heats of formation is in conflict with the optimization of vibrational frequencies. Therefore, a special parametrization, for vibrational frequencies is derived. It is shown that the performance of SCC-DFTB can be significantly improved using a more elaborate fitting strategy. A new fit for C and H is presented, which results in an average error of 2.6 kcal/mol for heats of formations for a large set of hydrocarbons, indicating that the performance of SCC-DFTB can be systematically improved also for other elements.
Closed-Form Formulas for the Zhang-Zhang Polynomials of Benzenoid Structures: Chevrons and Generalized Chevrons
(2014)
Chou, Chien-Pin
;
Witek, Henryk A.
;
應用化學系
;
應用化學系分子科學碩博班
;
Department of Applied Chemistry
Closed-form, general formulas for the Zhang-Zhang (ZZ) polynomials for two important classes of benzenoid structures, chevrons Ch(k, m, n) and generalized chevrons Ch(k, m, n(1), n(2)), are formally derived. The derivations rely on a new and important theorem, which states that the ZZ polynomial of two fused parallelograms can be represented as the product of the ZZ polynomials of the two separated fragments. This theoretical result seems to play an important role in the theory of pericondensed benzenoids and may prove useful for the process of discovering closed-form formulas of Zhang-Zhang polynomials of for a wide class of benzenoid structures.
Closed-form formulas for the Zhang-Zhang polynomials of benzenoid structures: Prolate rectangles and their generalizations
(2016-01-10)
Chou, Chien-Pin
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Kang, Jin-Su
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Witek, Henryk A.
;
應用化學系
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應用化學系分子科學碩博班
We show that the Zhang-Zhang (ZZ) polynomial of a benzenoid obtained by fusing a parallelogram M(m, n) with an arbitrary benzenoid structure ABC can be simply computed as a product of the ZZ polynomials of both fragments. It seems possible to extend this important result also to cases where both fused structures are arbitrary Kekulean benzenoids. Formal proofs of explicit forms of the ZZ polynomials for prolate rectangles Pr(m, n) and generalized prolate rectangles Pr ([m(1), m(2), ..., m(n)], n) follow as a straightforward application of the general theory, giving ZZ (Pr (m, n), x) = (1 + (1 x) . m)(n) and ZZ(Pr([m(1), m(2), ..., m(n)), n), x) = Pi(n)(k=1)(1 + (1 + x) . m(k)). (C) 2015 Elsevier B.V. All rights reserved.
Comment on "Zhang-Zhang polynomials of cyclo-polyphenacenes" by Q. Guo, H. Deng, and D. Chen
(2012-05-01)
Chou, Chien-Pin
;
Witek, Henryk A.
;
應用化學系
;
應用化學系分子科學碩博班
;
Department of Applied Chemistry
Explicit formulas for computing the Zhang-Zhang polynomial of cyclo-polyphenacenes, presented by Guo et al. (J. Math. Chem. 46:347, 2009) are found to be erroneous. In the present comment, a corrected version of Theorem 4.2 is given. The new formulation has been extensively tested by comparison with the Zhang-Zhang polynomials computed by brute force using a new, completely automatized computer code.
Determination of Zhang-Zhang Polynomials for Various Classes of Benzenoid Systems: Non-Heuristic Approach
(2014)
Chou, Chien-Pin
;
Witek, Henryk A.
;
應用化學系
;
應用化學系分子科學碩博班
;
Department of Applied Chemistry
We employ a graphical proof-oriented tool, ZZDecomposer, to discover formal derivations of Zhang-Zhang (ZZ) polynomials for various families and subfamilies of benzenoid structures including tripods, zigzag-edge coronoids fused with a starphene, oblate rectangles Or(m, 2), hexagons 0 (2,2, n), 0 (2,3, n), and 0(33, n), and multiple zigzag chains Z(4, n), Z(5, n), Z(6, n), Z (7, n), Z (8, n), and Z(9, n). Current derivations are based on formal graph decompositions of the analyzed structures. The decompositions provide appropriate recurrence formulas, which are subsequently solved, yielding closed-form expressions for the ZZ polynomials. We hope that in addition to many new basic facts about ZZ polynomials of some important classes of benzenoids, the current study will provide the researchers who are interested in mathematical graph theory with a practical guide to the ZZDecomposer functionality and will enable and facilitate their research.
Quantum chemical investigation of epoxide and ether groups in graphene oxide and their vibrational spectra
(2013)
Page, Alister J.
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Chou, Chien-Pin
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Pham, Buu Q.
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Witek, Henryk A.
;
Irle, Stephan
We present a detailed analysis of the factors influencing the formation of epoxide and ether groups in graphene nanoflakes using conventional density functional theory (DFT), the density-functional tight-binding (DFTB) method, pi-Huckel theory, and graph theoretical invariants. The relative thermodynamic stability associated with the chemisorption of oxygen atoms at various positions on hexagonal graphene flakes (HGFs) of D-6h-symmetry is determined by two factors - viz. the disruption of the p-conjugation of the HGF and the geometrical deformation of the HGF structure. The thermodynamically most stable structure is achieved when the former factor is minimized, and the latter factor is simultaneously maximized. Infrared (IR) spectra computed using DFT and DFTB reveal a close correlation between the relative thermodynamic stabilities of the oxidized HGF structures and their IR spectral activities. The most stable oxidized structures exhibit significant IR activity between 600 and 1800 cm(-1), whereas less stable oxidized structures exhibit little to no activity in this region. In contrast, Raman spectra are found to be less informative in this respect.
Two Examples for the Application of the ZZDecomposer: Zigzag-Edge Coronoids and Fenestrenes
(2015-01-01)
Chou, Chien-Pin
;
Witek, Henryk A.
;
應用化學系
;
應用化學系分子科學碩博班
;
Department of Applied Chemistry
In our recent paper [MATCH Commun. Math. Comput. Chem. 71 (2013) 741-764] some formulas and figures were misprinted. In this paper, we correct these problems giving formal derivations of Zhang-Zhang (ZZ) polynomials for two classes of benzenoid systems, zigzag-edge coronoids and fenestrenes.
When finite becomes infinite: convergence properties of vibrational spectra of oligomer chains
(2018-10-01)
Chou, Chien-Pin
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Witek, Henryk
;
Irle, Stephan
;
交大名義發表
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應用化學系
We present a computational study of convergence properties of vibrational IR and Raman spectra for a series of increasingly long units of polyethylene, cis- and trans-polyacetylenes, and polyynes. Convergent behavior to the spectra of infinitely long polymers was observed in all cases when chains reached lengths of approximately 60 carbon atoms, both with respect to the positions of the bands and to their intensities. The vibrational spectra of longer chains are practically indistinguishable. The convergence rate depends on the degree of the conjugation in a studied system: Vibrational spectra for oligoethylenes converge noticeably faster than the spectra for the conjugated systems. The slowest convergence is observed for skeletal motions of the oligomer chains, which may require more than a hundred carbon atoms in the chain to show deviations smaller than 1cm(-1) to the corresponding solid-state calculations. The results suggest that the boundary between the properties of finite and infinite molecular systems fades away for a surprisingly small number of atoms.
Zhang-Zhang Polynomials of Regular 5-tier Benzenoid Strips
(2017-01-01)
Witek, Henryk A.
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Langner, Johanna
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Mos, Grzegorz
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Chou, Chien-Pin
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應用化學系
Formal derivations of closed-form expressions for Clar covering polynomials (aka Zhang Zhang polynomials or ZZ polynomials) of twelve classes of regular 5-tier benzenoid strips are presented. The derived formulas, together with the results reported previously in the literature, complete the full collection of ZZ polynomial formulas for the regular 5-tier benzenoid strips.
Zhang-Zhang Polynomials of Various Classes of Benzenoid Systems
(2012)
Chou, Chien-Pin
;
Li, Yenting
;
Witek, Henryk A.
;
應用化學系
;
應用化學系分子科學碩博班
"The Zhang-Zhang(ZZ) polynomials (aka Clar covering polynomial) for several subclasses of catacondensed and pericondensed benzenoid systems have been computed using an automatic computer code developed in our group and described in [C.-P. Chou and H.A. Witek, MATCH Commun. Math. Comput. Chem., submitted]. General closed-form expressions for several series of catacondensed benzenoids and for the prolate rectangular pericondensed benzenoids have been obtained. The presented results suggest that general closed-form expressions for the ZZ polynomials of many classes of pericondensed benzenoid systems can be discovered by analysis of structural similarities between the ZZ polynomials of their subclasses. Methods and techniques of finding such similarities are outlined."
ZZDecomposer: A Graphical Toolkit for Analyzing the Zhang-Zhang Polynomials of Benzenoid Structures
(2014)
Chou, Chien-Pin
;
Witek, Henryk A.
;
應用化學系
;
應用化學系分子科學碩博班
;
Department of Applied Chemistry
We report a specialized, proof-oriented, graphical computer environment (referred to as ZZDecomposer) capable of performing interactive decompositions of the Zhang-Zhang polynomials for arbitrary benzenoid structures and enabling one in this way to conduct formal proofs of the derived formulas. The functionality and capabilities of the presented program are illustrated on a series of carefully selected examples. The introduced tool, described in detail in the body of the current paper, is subsequently applied for performing formal proofs for some of the heuristically discovered formulas presented in our previous work.