<div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://files.passeidireto.com/dc6b95e1-a73f-459a-86cb-1624067fba8a/bg1.png"></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf2" class="pf w2 h2" data-page-no="2"><div class="pc pc2 w2 h2"><div class="t m0 x1 h3 y1 ff1 fs0 fc0 sc0 ls0 ws0">Computational C<span class="_0 blank"> </span>hemistry and Molecular Modeling</div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf3" class="pf w2 h2" data-page-no="3"><div class="pc pc3 w2 h2"><div class="t m0 x1 h3 y1 ff1 fs0 fc0 sc0 ls1 ws1">K. I. Ramachandran<span class="_1 blank"> </span>· G. Deepa ·<span class="_1 blank"> </span>K. Namboori</div><div class="t m0 x1 h4 y2 ff1 fs1 fc0 sc0 ls2 ws2">Computational Chemistry</div><div class="t m0 x1 h4 y3 ff1 fs1 fc0 sc0 ls2 ws3">and Molecular Modeling</div><div class="t m0 x1 h5 y4 ff1 fs2 fc0 sc0 ls3 ws4">Principles and<span class="_2 blank"> </span>Applications</div><div class="t m0 x1 h6 y5 ff2 fs3 fc0 sc0 ls4">123</div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf4" class="pf w2 h2" data-page-no="4"><div class="pc pc4 w2 h2"><div class="t m0 x2 h7 y6 ff1 fs4 fc0 sc0 ls7 ws6">Dr<span class="_3 blank"></span>. K. I. Ramachandran</div><div class="t m0 x2 h7 y7 ff1 fs4 fc0 sc0 ls8 ws7">Dr<span class="_3 blank"></span>. G. Deepa</div><div class="t m0 x2 h7 y8 ff1 fs4 fc0 sc0 ls9 ws8">K. Namboori</div><div class="t m0 x2 h7 y9 ff1 fs4 fc0 sc0 lsa ws9">Amrita Vishwa V<span class="_3 blank"></span>idyapeetham Uni<span class="_3 blank"></span>versit<span class="_0 blank"> </span>y</div><div class="t m0 x2 h7 ya ff1 fs4 fc0 sc0 lsb wsa">Computational<span class="_4 blank"> </span>Engineeri<span class="_0 blank"> </span>ng and Networking</div><div class="t m0 x2 h7 yb ff1 fs4 fc0 sc0 lsc wsb">641 10<span class="_3 blank"></span>5 Ettimadai</div><div class="t m0 x2 h7 yc ff1 fs4 fc0 sc0 ls5 wsc">Coimbatore</div><div class="t m0 x2 h7 yd ff1 fs4 fc0 sc0 lsd wsd">India</div><div class="t m0 x2 h7 ye ff1 fs4 fc0 sc0 lse wse">ki_ram@e<span class="_3 blank"></span>ttimadai.amrita.edu</div><div class="t m0 x2 h7 yf ff1 fs4 fc0 sc0 lsf wsf">os_de<span class="_3 blank"></span>epa@ettimadai.amrita<span class="_3 blank"></span>.edu</div><div class="t m0 x2 h7 y10 ff1 fs4 fc0 sc0 ls10 ws10">n_krishnan@ettimadai.amrita.edu</div><div class="t m0 x2 h7 y11 ff1 fs4 fc0 sc0 lsd ws11">ISBN<span class="_0 blank"> </span>-13 978-3-540-77302-<span class="_0 blank"> </span>3<span class="_5 blank"> </span>e-ISB<span class="_0 blank"> </span>N-13 978-3-540-<span class="_0 blank"> </span>77304-7</div><div class="t m0 x2 h7 y12 ff1 fs4 fc0 sc0 lsd ws12">DOI 10.1007/<span class="_0 blank"> </span>978-3-540-77304-7</div><div class="t m0 x2 h7 y13 ff1 fs4 fc0 sc0 ls11 ws13">© 2008<span class="_4 blank"> </span>Springer-<span class="_6 blank"></span>V<span class="_6 blank"></span>erlag Berl<span class="_0 blank"> </span>in Hei<span class="_0 blank"> </span>delberg</div><div class="t m0 x2 h7 y14 ff1 fs4 fc0 sc0 ls9 ws14">Library of Congr<span class="_0 blank"> </span>ess Control N<span class="_0 blank"> </span>umber: 2007941252</div><div class="t m0 x2 h8 y15 ff1 fs5 fc0 sc0 ls12 ws15">This work is subje<span class="_3 blank"></span>ct<span class="_7 blank"> </span>to copyri<span class="_3 blank"></span>ght.<span class="_7 blank"> </span>All rights are rese<span class="ls13 ws16">rved, whether<span class="_4 blank"> </span>the w<span class="_0 blank"> </span>hole or part o<span class="_0 blank"> </span>f the material<span class="_7 blank"> </span>is</span></div><div class="t m0 x2 h8 y16 ff1 fs5 fc0 sc0 lsd ws17">concerned, speci\ufb01cally the rights of<span class="_8 blank"> </span>translation, repr<span class="ls14 ws18">inting, reuse of<span class="_8 blank"> </span>illustrations, recitation,<span class="_9 blank"> </span>broadcasting,</span></div><div class="t m0 x2 h8 y17 ff1 fs5 fc0 sc0 ls15 ws19">reproduction<span class="_9 blank"> </span>on micro\ufb01lm or in any other<span class="_9 blank"> </span>w<span class="_3 blank"></span>ay<span class="_3 blank"></span>, and stor<span class="ls16 ws1a">age<span class="_9 blank"> </span>in data banks.<span class="_9 blank"> </span>Duplication<span class="_9 blank"> </span>of this publication</span></div><div class="t m0 x2 h8 y18 ff1 fs5 fc0 sc0 ls17 ws1b">or parts thereof<span class="_7 blank"> </span>is permitted<span class="_7 blank"> </span>only<span class="_4 blank"> </span><span class="ls18 ws1c">under the provisions<span class="_7 blank"> </span>of the German Copyright Law of September 9,</span></div><div class="t m0 x2 h8 y19 ff1 fs5 fc0 sc0 ls19 ws1d">1965, in<span class="_4 blank"> </span>its current<span class="_4 blank"> </span>version, and perm<span class="_0 blank"> </span>ission<span class="_4 blank"> </span>for use mu<span class="ls18 ws1e">s<span class="_0 blank"> </span>t always be obtained<span class="_7 blank"> </span>fro<span class="ls1a ws1f">m Springer<span class="_3 blank"></span>. 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It<span class="_4 blank"> </span>h<span class="_0 blank"> </span>as a<span class="_7 blank"> </span>wide</div><div class="t m0 x1 hb y29 ff1 fs7 fc0 sc0 ls35 ws35">range of<span class="_9 blank"> </span>applications in vari<span class="_3 blank"></span>ous disciplines of engineering sciences, such as<span class="_9 blank"> </span>materi-</div><div class="t m0 x1 hb y2a ff1 fs7 fc0 sc0 ls23 ws36">als science, chemical engin<span class="ls24 ws37">eering, biomedical<span class="_b blank"> </span>engineering, etc.<span class="_b blank"> </span>Knowledge of com-</span></div><div class="t m0 x1 hb y2b ff1 fs7 fc0 sc0 ls2b ws38">putational chemi<span class="_3 blank"></span>stry is<span class="_c blank"> </span>essent<span class="_3 blank"></span>ial to<span class="_c blank"> </span>understand the behavior<span class="_7 blank"> </span>of nanosystems; it is</div><div class="t m0 x1 hb y2c ff1 fs7 fc0 sc0 ls29 ws39">probably t<span class="_3 blank"></span>he easiest route or gate<span class="_3 blank"></span>way to t<span class="_3 blank"></span>he f<span class="ls23 ws3a">ast-growing discipline of nanosciences</span></div><div class="t m0 x1 hb y2d ff1 fs7 fc0 sc0 ls25 ws3b">and nanotechnology<span class="_3 blank"></span>,<span class="_8 blank"> </span>which co<span class="_3 blank"></span>vers man<span class="_3 blank"></span>y areas of research dealing wi<span class="_3 blank"></span>th objects that</div><div class="t m0 x1 hb y2e ff1 fs7 fc0 sc0 ls36 ws3c">are measured in<span class="_a blank"> </span>nanometers and which is<span class="_a blank"> </span>expected to rev<span class="_3 blank"></span>olutionize the industrial</div><div class="t m0 x1 hb y2f ff1 fs7 fc0 sc0 ls26 ws3d">sector in<span class="_9 blank"> </span>the<span class="_9 blank"> </span>coming decades.</div><div class="t m0 x4 hb y30 ff1 fs7 fc0 sc0 ls37 ws3e">Consideri<span class="_3 blank"></span>ng<span class="_4 blank"> </span>the importance<span class="_9 blank"> </span>of<span class="_4 blank"> </span>this<span class="_4 blank"> </span>discipli<span class="_3 blank"></span>ne,<span class="_4 blank"> </span>computational chemist<span class="_3 blank"></span>ry<span class="_4 blank"> </span>is<span class="_4 blank"> </span>being</div><div class="t m0 x1 hb y31 ff1 fs7 fc0 sc0 ls36 ws3f">taught presently as a<span class="_9 blank"> </span>course at the postgraduate and research lev<span class="_3 blank"></span>el in<span class="_9 blank"> </span>many uni<span class="_3 blank"></span>versi-</div><div class="t m0 x1 hb y32 ff1 fs7 fc0 sc0 ls38 ws40">ties. This<span class="_b blank"> </span>book is<span class="_9 blank"> </span>the result of<span class="_9 blank"> </span>the need<span class="_b blank"> </span>for<span class="_9 blank"> </span>a comprehensive<span class="_8 blank"> </span>te<span class="_3 blank"></span>xtbook on the<span class="_9 blank"> </span>subject<span class="_3 blank"></span>,</div><div class="t m0 x1 hb y33 ff1 fs7 fc0 sc0 ls27 ws41">which was felt by the authors while<span class="_b blank"> </span>teachin<span class="_0 blank"> </span><span class="ls2c ws42">g the course. It cov<span class="_3 blank"></span>ers all the aspects of</span></div><div class="t m0 x1 hb y34 ff1 fs7 fc0 sc0 ls39 ws43">computatio<span class="_0 blank"> </span>nal chemistr<span class="_0 blank"> </span>y required f<span class="_0 blank"> </span>or<span class="_9 blank"> </span>a<span class="_9 blank"> </span>cou<span class="_0 blank"> </span>rse, with<span class="_9 blank"> </span>suf\ufb01cient illustr<span class="_0 blank"> </span>ations, n<span class="_0 blank"> </span>umeri-</div><div class="t m0 x1 hb y35 ff1 fs7 fc0 sc0 ls28 ws44">cal examples, applications, and exercises. <span class="ls3a ws45">For a<span class="_9 blank"> </span>computational chemis<span class="_3 blank"></span>t,<span class="_9 blank"> </span>scientist<span class="_3 blank"></span>,<span class="_9 blank"> </span>or</span></div><div class="t m0 x1 hb y36 ff1 fs7 fc0 sc0 ls2b ws46">researcher<span class="_3 blank"></span>, thi<span class="_3 blank"></span>s<span class="_9 blank"> </span>book will be highly useful in understanding<span class="_8 blank"> </span>and mastering the art of</div><div class="t m0 x1 hb y37 ff1 fs7 fc0 sc0 ls3b ws47">chemical<span class="_a blank"> </span>computation<span class="_0 blank"> </span>. Familiarization<span class="_7 blank"> </span>with<span class="_c blank"> </span>common<span class="_a blank"> </span>and<span class="_a blank"> </span>commercial<span class="_a blank"> </span>software in</div><div class="t m0 x1 hb y38 ff1 fs7 fc0 sc0 ls29 ws48">molecular modeling is<span class="_4 blank"> </span>also incorporated. Moreover<span class="_3 blank"></span>, the application o<span class="_0 blank"> </span>f<span class="_9 blank"> </span>the<span class="_9 blank"> </span>concepts</div><div class="t m0 x1 hb y39 ff1 fs7 fc0 sc0 ls29 ws49">in<span class="_9 blank"> </span>related \ufb01elds<span class="_b blank"> </span>such<span class="_9 blank"> </span>as<span class="_9 blank"> </span>biomedical engineering, computational<span class="_8 blank"> </span>drug<span class="_9 blank"> </span>designing, etc.</div><div class="t m0 x1 hb y3a ff1 fs7 fc0 sc0 ls2a ws4a">has been added.</div><div class="t m0 x4 hb y3b ff1 fs7 fc0 sc0 ls2b ws4b">The book<span class="_4 blank"> </span>begins wi<span class="_3 blank"></span>th an introductory<span class="_4 blank"> </span>chapter on computat<span class="_3 blank"></span>ional c<span class="_3 blank"></span>hemistry and</div><div class="t m0 x1 hb y3c ff1 fs7 fc0 sc0 ls3c ws4c">molecular mo<span class="_0 blank"> </span>deling. In th<span class="_0 blank"> </span>is chap<span class="_0 blank"> </span>ter (Ch<span class="ls2c ws4d">ap.<span class="_d blank"> </span>1), we<span class="_d blank"> </span>emphasize the four computa-</span></div><div class="t m0 x1 hb y3d ff1 fs7 fc0 sc0 ls3d ws4e">tional<span class="_a blank"> </span>criteria<span class="_a blank"> </span>f<span class="_0 blank"> </span>or<span class="_a blank"> </span>modelin<span class="_0 blank"> </span>g any sy<span class="_0 blank"> </span>stem,<span class="_a blank"> </span>namely<span class="_a blank"> </span>stability<span class="_3 blank"></span>, sy<span class="_0 blank"> </span>mmetry<span class="_3 blank"></span>, qu<span class="_0 blank"> </span>antization,</div><div class="t m0 x1 hb y3e ff1 fs7 fc0 sc0 ls24 ws4f">and homogeneity<span class="_3 blank"></span>.<span class="_9 blank"> </span>In<span class="_a blank"> </span>Chap. 2, \u201cSymmetry and Point Groups\u201d, el<span class="_3 blank"></span>ements of molec-</div><div class="t m0 x1 hb y3f ff1 fs7 fc0 sc0 ls3e ws50">ular sym<span class="_0 blank"> </span>metry and<span class="_c blank"> </span>po<span class="_0 blank"> </span>int group ar<span class="_0 blank"> </span>e explained. A n<span class="_0 blank"> </span>umber of<span class="_c blank"> </span>illustrative examples</div><div class="t m0 x1 hb y40 ff1 fs7 fc0 sc0 ls2d ws51">and d<span class="_0 blank"> </span>iagrams are given. The transformation matrix for each<span class="_d blank"> </span>symmetry operation</div><div class="t m0 x1 hb y41 ff1 fs7 fc0 sc0 ls2b ws52">is included t<span class="_3 blank"></span>o<span class="_1 blank"> </span>provide<span class="_a blank"> </span>a computational kno<span class="_3 blank"></span>w-ho<span class="_3 blank"></span>w<span class="_3 blank"></span>.<span class="_a blank"> </span>In Chap. 3, the basic princi-</div><div class="t m0 x1 hb y42 ff1 fs7 fc0 sc0 ls2e ws53">ples of<span class="_7 blank"> </span>quantum mechanics are<span class="_7 blank"> </span>presente<span class="ls2f ws54">d to enhance<span class="_4 blank"> </span>the reader\u2019<span class="_3 blank"></span>s<span class="_4 blank"> </span>ability to under-</span></div><div class="t m0 x1 hb y43 ff1 fs7 fc0 sc0 ls30 ws55">stand the quantum mechanical modeling t<span class="_3 blank"></span>echniques. In Chaps. 4\u201310, computational</div><div class="t m0 x1 hb y44 ff1 fs7 fc0 sc0 ls31 ws56">techniques with<span class="_7 blank"> </span>different le<span class="_3 blank"></span>vels o<span class="_0 blank"> </span>f<span class="_4 blank"> </span>accura<span class="ls32 ws57">cy<span class="_9 blank"> </span>hav<span class="_3 blank"></span>e been arranged. The chapters als<span class="_3 blank"></span>o</span></div><div class="t m0 x5 hc y45 ff1 fs8 fc0 sc0 ls3f ws58">vii</div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf7" class="pf w2 h2" data-page-no="7"><div class="pc pc7 w2 h2"><div class="t m0 x2 hc y46 ff1 fs8 fc0 sc0 ls46 ws59">viii <span class="ls1c ws5a">Preface</span></div><div class="t m0 x2 hb y6 ff1 fs7 fc0 sc0 ls24 ws5b">cover H<span class="_3 blank"></span>uckel\u2019<span class="_3 blank"></span>s mol<span class="_3 blank"></span>ecular orbital theory<span class="_6 blank"></span>, Hartree-Fock<span class="_4 blank"> </span>(HF) approximation,<span class="_4 blank"> </span>semi-</div><div class="t m0 x2 hb y47 ff1 fs7 fc0 sc0 ls31 ws5c">empirical methods, ab<span class="_4 blank"> </span>initio<span class="_7 blank"> </span><span class="ls40 ws5d">techniques, density functi<span class="ls32 ws5e">onal theory<span class="_3 blank"></span>, reduced density</span></span></div><div class="t m0 x2 hb y48 ff1 fs7 fc0 sc0 ls29 ws5f">matrix, and molecular mechanics methods.</div><div class="t m0 x6 hb y49 ff1 fs7 fc0 sc0 ls29 ws60">T<span class="_6 blank"></span>opics such as the ov<span class="_3 blank"></span>erlap inte<span class="_3 blank"></span>gral, the Coul<span class="_3 blank"></span>omb inte<span class="_3 blank"></span>gral and the resonance<span class="_b blank"> </span>inte-</div><div class="t m0 x2 hb y4a ff1 fs7 fc0 sc0 ls41 ws61">gral, the secular matrix, and the solution t<span class="ls31 ws62">o the secular matrix have been included in</span></div><div class="t m0 x2 hb y4b ff1 fs7 fc0 sc0 ls42 ws63">Chap. 4 with speci\ufb01c applications<span class="_4 blank"> </span>such as <span class="ls43 ws64">aromaticity<span class="_3 blank"></span>, charge d<span class="_0 blank"> </span>ensity calcu<span class="_0 blank"> </span>lation,</span></div><div class="t m0 x2 hb y4c ff1 fs7 fc0 sc0 ls43 ws65">the<span class="_9 blank"> </span>stability an<span class="_0 blank"> </span>d delocalizatio<span class="_0 blank"> </span>n energy spectrum, the<span class="_9 blank"> </span>highest o<span class="_0 blank"> </span>ccupied molecu<span class="_0 blank"> </span>lar or-</div><div class="t m0 x2 hb y4d ff1 fs7 fc0 sc0 ls30 ws66">bital (HOMO), the lowe<span class="_3 blank"></span>st unoccupied molecular orbital (LU<span class="_3 blank"></span>MO), bond order, t<span class="_3 blank"></span>he</div><div class="t m0 x2 hb y4e ff1 fs7 fc0 sc0 ls40 ws67">free valence inde<span class="_3 blank"></span>x, the electrophilic and nucleophilic<span class="_b blank"> </span>substitution, etc. In the chap-</div><div class="t m0 x2 hb y4f ff1 fs7 fc0 sc0 ls47 ws68">ter on<span class="_7 blank"> </span>HF the<span class="_0 blank"> </span>ory (Chap. 5<span class="_0 blank"> </span>), the fo<span class="_0 blank"> </span>rmulation of the Fock matr<span class="_0 blank"> </span>ix has been<span class="_7 blank"> </span>inclu<span class="_0 blank"> </span>ded.</div><div class="t m0 x2 hb y50 ff1 fs7 fc0 sc0 ls34 ws69">Chapter 6<span class="_a blank"> </span>concerns different types of basis<span class="_a blank"> </span>sets.<span class="_c blank"> </span>This chapter covers in detail all</div><div class="t m0 x2 hb y51 ff1 fs7 fc0 sc0 ls35 ws6a">important<span class="_b blank"> </span>minimal basi<span class="_3 blank"></span>s sets and extended<span class="_b blank"> </span>basis s<span class="_3 blank"></span>ets such as GTOs<span class="_3 blank"></span>, STOs, doubl<span class="_3 blank"></span>e-</div><div class="t m0 x2 hb y52 ff1 fs7 fc0 sc0 ls48 ws6b">zeta, tr<span class="_0 blank"> </span>iple-zeta, quad<span class="_0 blank"> </span>ruple-zeta, split-valence, polarized, and diffuse. In<span class="_c blank"> </span>Chap.<span class="_c blank"> </span>7,</div><div class="t m0 x2 hb y53 ff1 fs7 fc0 sc0 ls3a ws6c">semi-empiri<span class="_3 blank"></span>cal methods are int<span class="_3 blank"></span>roduced; bes<span class="_3 blank"></span>ides givi<span class="_3 blank"></span>ng an overvie<span class="_3 blank"></span>w of<span class="_7 blank"> </span>the theory</div><div class="t m0 x2 hb y54 ff1 fs7 fc0 sc0 ls30 ws6d">and equations,<span class="_7 blank"> </span>a performance of the methods<span class="_4 blank"> </span>based on the neglect of di<span class="_3 blank"></span>fferential</div><div class="t m0 x2 hb y55 ff1 fs7 fc0 sc0 ls49 ws6e">overlap,<span class="_7 blank"> </span>with an emphasis on AM1, MNDO, and PM3 is e<span class="_3 blank"></span>xp<span class="_0 blank"> </span>lained. Chapter<span class="_7 blank"> </span>8 is</div><div class="t m0 x2 hb y56 ff1 fs7 fc0 sc0 ls40 ws6f">on ab initio methods, cov<span class="_3 blank"></span>ering areas such as the correlation<span class="_9 blank"> </span>technique, the Möller<span class="_3 blank"></span>-</div><div class="t m0 x2 hb y57 ff1 fs7 fc0 sc0 ls28 ws70">Plesset<span class="_b blank"> </span>perturbation<span class="_b blank"> </span>theory<span class="_3 blank"></span>, the<span class="_b blank"> </span>gener<span class="_0 blank"> </span><span class="ls31 ws71">alized valence bond (GVB) method, the multi-</span></div><div class="t m0 x2 hb y58 ff1 fs7 fc0 sc0 ls33 ws72">con\ufb01gurations s<span class="_3 blank"></span>elf<span class="_7 blank"> </span>consist<span class="_3 blank"></span>ent<span class="_4 blank"> </span>\ufb01eld<span class="_4 blank"> </span>(MCSCF<span class="ls24 ws73">) theory<span class="_3 blank"></span>, con\ufb01guration interact<span class="_3 blank"></span>ion (CI)</span></div><div class="t m0 x2 hb y59 ff1 fs7 fc0 sc0 ls24 ws74">and coupled cluster theory (CC<span class="_3 blank"></span>).</div><div class="t m0 x6 hb y5a ff1 fs7 fc0 sc0 ls34 ws75">Density funct<span class="_3 blank"></span>ional theory<span class="_9 blank"> </span>(DFT) seems<span class="_9 blank"> </span>to be an extremely<span class="_9 blank"> </span>successful approach</div><div class="t m0 x2 hb y5b ff1 fs7 fc0 sc0 ls30 ws76">for the descripti<span class="_3 blank"></span>on of the ground<span class="_b blank"> </span>stat<span class="_3 blank"></span>e<span class="_9 blank"> </span>p<span class="_0 blank"> </span>roperties<span class="_b blank"> </span>of metals<span class="_3 blank"></span>, semiconductors,<span class="_b blank"> </span>and in-</div><div class="t m0 x2 hb y5c ff1 fs7 fc0 sc0 ls2e ws77">sulators. The success of DFT<span class="_9 blank"> </span>not only encom<span class="ls23 ws3a">passes s<span class="_3 blank"></span>tandard bulk materials but also</span></div><div class="t m0 x2 hb y5d ff1 fs7 fc0 sc0 ls29 ws78">complex<span class="_4 blank"> </span>materials such as protei<span class="_3 blank"></span>ns and carbon nanotubes<span class="_3 blank"></span>. The chapter on dens<span class="_3 blank"></span>ity</div><div class="t m0 x2 hb y5e ff1 fs7 fc0 sc0 ls38 ws79">functional<span class="_b blank"> </span>theory (Chap.<span class="_b blank"> </span>9) covers<span class="_8 blank"> </span>the entire applications<span class="_b blank"> </span>of the theory<span class="_6 blank"></span>.</div><div class="t m0 x6 hb y5f ff1 fs7 fc0 sc0 ls4a ws7a">Chapter 10 explains reduced density matrix and its applicatio<span class="_0 blank"> </span>ns in molecular</div><div class="t m0 x2 hb y60 ff1 fs7 fc0 sc0 ls38 ws7b">modeling. W<span class="_3 blank"></span>hile<span class="_b blank"> </span>tradit<span class="_3 blank"></span>ional methods for computing t<span class="_3 blank"></span>he orbitals are scaling cubically</div><div class="t m0 x2 hb y61 ff1 fs7 fc0 sc0 ls3a ws7c">with respect to the number of el<span class="_3 blank"></span>ectrons, the computation<span class="_8 blank"> </span>of the density matri<span class="_3 blank"></span>x offers</div><div class="t m0 x2 hb y62 ff1 fs7 fc0 sc0 ls2a ws7d">the opportunity<span class="_b blank"> </span>to achie<span class="_3 blank"></span>ve<span class="_b blank"> </span>linear complexit<span class="_3 blank"></span>y<span class="_3 blank"></span>. W<span class="_6 blank"></span>e descri<span class="_3 blank"></span>be several<span class="_b blank"> </span>iterat<span class="_3 blank"></span>ion schemes</div><div class="t m0 x2 hb y63 ff1 fs7 fc0 sc0 ls30 ws7e">for the computation<span class="_8 blank"> </span>of the density mat<span class="_3 blank"></span>rix. W<span class="_6 blank"></span>e also brie\ufb02y present<span class="_8 blank"> </span>the concept of the</div><div class="t m0 x2 hb y64 ff1 fs7 fc0 sc0 ls36 ws7f">best <span class="ff3 ls44">n</span><span class="ls45 ws80">-term approximat<span class="_3 blank"></span>ion.</span></div><div class="t m0 x6 hb y65 ff1 fs7 fc0 sc0 ls48 ws81">Chapter 11 is on m<span class="_0 blank"> </span>olecular mechanics and modelin<span class="_0 blank"> </span>g, in which v<span class="_3 blank"></span>ariou<span class="_0 blank"> </span>s force</div><div class="t m0 x2 hb y66 ff1 fs7 fc0 sc0 ls38 ws82">\ufb01elds required<span class="_b blank"> </span>to express t<span class="_3 blank"></span>he total energy<span class="_b blank"> </span>term are introduced.<span class="_b blank"> </span>Computations<span class="_b blank"> </span>using</div><div class="t m0 x2 hb y67 ff1 fs7 fc0 sc0 ls41 ws83">common molecular mechanics force<span class="_9 blank"> </span>\ufb01elds<span class="_9 blank"> </span>are<span class="_9 blank"> </span>explained.</div><div class="t m0 x6 hb y68 ff1 fs7 fc0 sc0 ls45 ws84">Computati<span class="_3 blank"></span>ons of<span class="_d blank"> </span>molecular properties using the<span class="_d blank"> </span>common computational t<span class="_3 blank"></span>ech-</div><div class="t m0 x2 hb y69 ff1 fs7 fc0 sc0 ls3a ws85">niques are e<span class="_3 blank"></span>xplained in Chap. 12. In thi<span class="_3 blank"></span>s<span class="_c blank"> </span>chapter<span class="_3 blank"></span>, we ha<span class="_3 blank"></span>ve included a secti<span class="_3 blank"></span>on on</div><div class="t m0 x2 hb y6a ff1 fs7 fc0 sc0 ls3a ws86">a comparison of v<span class="_3 blank"></span>arious modeling techniques<span class="_3 blank"></span>. This helps the reader to choose the</div><div class="t m0 x2 hb y6b ff1 fs7 fc0 sc0 ls38 ws43">method for a particular computation.</div><div class="t m0 x6 hb y6c ff1 fs7 fc0 sc0 ls4a ws87">The need and the<span class="_b blank"> </span>possibility f<span class="_0 blank"> </span>or high perf<span class="_0 blank"> </span>ormance computing (HPC) in m<span class="_0 blank"> </span>olecular</div><div class="t m0 x2 hb y6d ff1 fs7 fc0 sc0 ls38 ws88">modeling is explained in Chap. 13. This chapter explains HPC as a<span class="_a blank"> </span>technique for</div><div class="t m0 x2 hb y6e ff1 fs7 fc0 sc0 ls29 ws89">providing the foundation to meet<span class="_9 blank"> </span>the<span class="_9 blank"> </span>data<span class="_9 blank"> </span>and<span class="_9 blank"> </span>computing demands of<span class="_9 blank"> </span>Research and</div><div class="t m0 x2 hb y6f ff1 fs7 fc0 sc0 ls29 ws8a">De<span class="_3 blank"></span>velopment<span class="_4 blank"> </span>(R&D) grids<span class="_3 blank"></span>. HPC helps in harnes<span class="_3 blank"></span>sing data and comput<span class="_3 blank"></span>er resources</div><div class="t m0 x2 hb y70 ff1 fs7 fc0 sc0 ls4b ws8b">in<span class="_7 blank"> </span>a<span class="_7 blank"> </span>m<span class="_0 blank"> </span>ulti-site,<span class="_7 blank"> </span>multi-o<span class="_0 blank"> </span>rganizational co<span class="_0 blank"> </span>ntext<span class="_4 blank"> </span>effecti<span class="_3 blank"></span>ve<span class="_7 blank"> </span>cluster<span class="_7 blank"> </span>ma<span class="_0 blank"> </span>nagemen<span class="_0 blank"> </span>t, mak<span class="_0 blank"> </span>ing</div><div class="t m0 x2 hb y71 ff1 fs7 fc0 sc0 ls38 ws43">use of<span class="_9 blank"> </span>maximum computing i<span class="_3 blank"></span>nv<span class="_3 blank"></span>estment for molecular modeli<span class="_3 blank"></span>ng.</div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf8" class="pf w2 h2" data-page-no="8"><div class="pc pc8 w2 h2"><div class="t m0 x1 hc y46 ff1 fs8 fc0 sc0 ls4e ws8c">Preface <span class="ls46">ix</span></div><div class="t m0 x4 hb y6 ff1 fs7 fc0 sc0 ls34 ws8d">Some typical projects<span class="_3 blank"></span>/res<span class="ls2f ws8e">earch topics on<span class="_1 blank"> </span>molecular modeling are included in</span></div><div class="t m0 x1 hb y47 ff1 fs7 fc0 sc0 ls4f ws8f">Chap. 14.<span class="_b blank"> </span>This chapter h<span class="_0 blank"> </span>elps the read<span class="_0 blank"> </span>er to familiarize himself with<span class="_b blank"> </span>the mod<span class="_0 blank"> </span>ern trends</div><div class="t m0 x1 hb y48 ff1 fs7 fc0 sc0 ls4c ws90">in research<span class="_b blank"> </span>connected with computati<span class="ls30 ws91">onal chemis<span class="_3 blank"></span>try<span class="_9 blank"> </span>and<span class="_9 blank"> </span>molecular modeling.</span></div><div class="t m0 x4 hb y49 ff1 fs7 fc0 sc0 ls29 ws92">Chapter<span class="_d blank"> </span>15 is on basic mathemati<span class="_3 blank"></span>cs and contains<span class="_c blank"> </span>an introduction<span class="_d blank"> </span>to compu-</div><div class="t m0 x1 hb y4a ff1 fs7 fc0 sc0 ls29 ws93">tational tools s<span class="_3 blank"></span>uch as Microsoft Excel, MA<span class="_e blank"></span>TLAB, etc. This helps e<span class="_3 blank"></span>ven a non-</div><div class="t m0 x1 hb y4b ff1 fs7 fc0 sc0 ls36 ws94">mathematics<span class="_7 blank"> </span>person to understand<span class="_7 blank"> </span>the mathematics us<span class="_3 blank"></span>ed in the text t<span class="_3 blank"></span>o appreciate</div><div class="t m0 x1 hb y4c ff1 fs7 fc0 sc0 ls3a ws95">the real art<span class="_a blank"> </span>of computing. S<span class="_3 blank"></span>uf\ufb01cient a<span class="_3 blank"></span>dditions ha<span class="_3 blank"></span>ve been included as an appendix</div><div class="t m0 x1 hb y4d ff1 fs7 fc0 sc0 ls40 ws96">to<span class="_9 blank"> </span>cover<span class="_8 blank"> </span>areas such<span class="_9 blank"> </span>as<span class="_9 blank"> </span>operators, HuckelMO hetero atom parameters, Microsoft Ex-</div><div class="t m0 x1 hb y4e ff1 fs7 fc0 sc0 ls34 ws97">cel<span class="_b blank"> </span>in<span class="_9 blank"> </span>the balancing of<span class="_b blank"> </span>chemical<span class="_b blank"> </span>equations, simultaneous spectros<span class="_3 blank"></span>copic analysis, the</div><div class="t m0 x1 hb y4f ff1 fs7 fc0 sc0 ls37 ws98">computation of bond enthalpy of hydrocarbons, graphi<span class="_3 blank"></span>ng chemical analysis data,</div><div class="t m0 x1 hb y50 ff1 fs7 fc0 sc0 ls39 ws99">titration data p<span class="_0 blank"> </span>lotting, the app<span class="_0 blank"> </span>lication of curve \ufb01tting in ch<span class="_0 blank"> </span>emistry<span class="_3 blank"></span>, the determina-</div><div class="t m0 x1 hb y51 ff1 fs7 fc0 sc0 ls4a ws5e">tion of solvation energy<span class="_3 blank"></span>,<span class="_b blank"> </span>and the determ<span class="_0 blank"> </span>ination of partial molar volume.</div><div class="t m0 x4 hb y52 ff1 fs7 fc0 sc0 ls24 ws73">An exclus<span class="_3 blank"></span>ive<span class="_b blank"> </span>URL (http://w<span class="_3 blank"></span>ww<span class="_3 blank"></span>.amrita.edu/cen/<span class="_3 blank"></span>ccmm)<span class="_b blank"> </span>for this book wi<span class="_3 blank"></span>th the re-</div><div class="t m0 x1 hb y53 ff1 fs7 fc0 sc0 ls34 ws9a">quired support materi<span class="_3 blank"></span>als has<span class="_b blank"> </span>been provided for readers which contains a chapterwise</div><div class="t m0 x1 hb y54 ff1 fs7 fc0 sc0 ls30 ws9b">Po<span class="_3 blank"></span>werPoint presentation, numeri<span class="_3 blank"></span>cal solutions to exercises<span class="_3 blank"></span>, the<span class="_4 blank"> </span>input/output \ufb01l<span class="_3 blank"></span>es<span class="_7 blank"> </span>of</div><div class="t m0 x1 hb y55 ff1 fs7 fc0 sc0 ls34 ws9c">computations<span class="_8 blank"> </span>done with software such as Gaussian, Spartan etc., HTML-bas<span class="_3 blank"></span>ed pro-</div><div class="t m0 x1 hb y56 ff1 fs7 fc0 sc0 ls4f ws9d">gramming environments<span class="_9 blank"> </span>for the de<span class="_0 blank"> </span>termination of eigenv<span class="_3 blank"></span>alues/eig<span class="_0 blank"> </span>en<span class="_3 blank"></span>vectors<span class="_b blank"> </span>o<span class="_0 blank"> </span>f sym-</div><div class="t m0 x1 hb y57 ff1 fs7 fc0 sc0 ls2f ws9e">metrical<span class="_b blank"> </span>matrices<span class="_9 blank"> </span>and<span class="_b blank"> </span>interconv<span class="_3 blank"></span>ersion of<span class="_b blank"> </span><span class="ls3e ws9f">u<span class="_0 blank"> </span>nits, an<span class="_0 blank"> </span>d the step<span class="_0 blank"> </span>-by-step imp<span class="_0 blank"> </span>lementation</span></div><div class="t m0 x1 hb y58 ff1 fs7 fc0 sc0 ls50 wsa0">of cluster comput<span class="_3 blank"></span>ing. A comprehensi<span class="_3 blank"></span>ve<span class="_8 blank"> </span>survey co<span class="_3 blank"></span>vering<span class="_b blank"> </span>the possible j<span class="_3 blank"></span>ournals, pub-</div><div class="t m0 x1 hb y59 ff1 fs7 fc0 sc0 ls35 wsa1">lications<span class="_3 blank"></span>,<span class="_a blank"> </span>software, and Internet support concerned wi<span class="_3 blank"></span>th<span class="_c blank"> </span>this discipline ha<span class="_3 blank"></span>ve been</div><div class="t m0 x1 hb y5a ff1 fs7 fc0 sc0 ls35 wsa2">included.</div><div class="t m0 x4 hb y5b ff1 fs7 fc0 sc0 ls24 wsa3">The uniqueness<span class="_8 blank"> </span>of<span class="_9 blank"> </span>this book can be summarized as follo<span class="_3 blank"></span>ws:</div><div class="t m0 x7 hb y72 ff1 fs7 fc0 sc0 ls38 ws43">1.<span class="_2 blank"> </span>It<span class="_9 blank"> </span>provides a comprehensi<span class="_3 blank"></span>ve<span class="_b blank"> </span>background<span class="_8 blank"> </span>theory for molecular modeling.</div><div class="t m0 x7 hb y73 ff1 fs7 fc0 sc0 ls3c wsa4">2.<span class="_f blank"> </span>It inclu<span class="_0 blank"> </span>des ap<span class="_0 blank"> </span>plications fr<span class="_0 blank"> </span>om all<span class="_4 blank"> </span>related areas.</div><div class="t m0 x7 hb y74 ff1 fs7 fc0 sc0 ls4d wsa5">3.<span class="_2 blank"> </span>It<span class="_9 blank"> </span>includes<span class="_9 blank"> </span>suf\ufb01cient numerical e<span class="_3 blank"></span>xamples and<span class="_9 blank"> </span>exercises.</div><div class="t m0 x7 hb y75 ff1 fs7 fc0 sc0 ls3c wsa6">4.<span class="_f blank"> </span>Numerou<span class="_0 blank"> </span>s explanatory<span class="_9 blank"> </span>illustrations/\ufb01gu<span class="_0 blank"> </span>res are<span class="_9 blank"> </span>in<span class="_0 blank"> </span>cluded.</div><div class="t m0 x7 hb y76 ff1 fs7 fc0 sc0 ls35 wsa7">5.<span class="_2 blank"> </span>A<span class="_c blank"> </span>separate chapter on basic mathematics and applicat<span class="_3 blank"></span>ion tools such as<span class="_c blank"> </span>MA<span class="_e blank"></span>T<span class="_6 blank"></span>-</div><div class="t m0 x8 hb y77 ff1 fs7 fc0 sc0 ls37 ws7d">LAB is included.</div><div class="t m0 x7 hb y78 ff1 fs7 fc0 sc0 ls37 wsa8">6.<span class="_2 blank"> </span>A<span class="_1 blank"> </span>chapter on<span class="_1 blank"> </span>high performance comput<span class="_3 blank"></span>ing is included with examples from</div><div class="t m0 x8 hb y79 ff1 fs7 fc0 sc0 ls2b wsa9">molecular modeli<span class="_3 blank"></span>ng.</div><div class="t m0 x7 hb y7a ff1 fs7 fc0 sc0 ls29 wsaa">7.<span class="_2 blank"> </span>A chapter on chemical<span class="_b blank"> </span>computation<span class="_b blank"> </span>using the reduced<span class="_b blank"> </span>densit<span class="_3 blank"></span>y matrix method is</div><div class="t m0 x8 hb y7b ff1 fs7 fc0 sc0 ls29 wsab">included.</div><div class="t m0 x7 hb y7c ff1 fs7 fc0 sc0 ls29 wsac">8.<span class="_2 blank"> </span>Sample projects<span class="_b blank"> </span>and research<span class="_b blank"> </span>topics from<span class="_b blank"> </span>the area<span class="_b blank"> </span>are included.</div><div class="t m0 x7 hb y7d ff1 fs7 fc0 sc0 ls29 wsaa">9.<span class="_2 blank"> </span>It includes an exclus<span class="_3 blank"></span>ive<span class="_b blank"> </span>web si<span class="_3 blank"></span>te with required s<span class="_3 blank"></span>upport materials<span class="_3 blank"></span>.</div><div class="t m0 x1 hb y69 ff1 fs7 fc0 sc0 ls41 wsad">W<span class="_3 blank"></span>ith the vast teaching e<span class="_3 blank"></span>xpertise of the authors, the arrangement<span class="_c blank"> </span>and designing</div><div class="t m0 x1 hb y6a ff1 fs7 fc0 sc0 ls32 wsae">of the topics in the book has<span class="_d blank"> </span>been made accord<span class="ls2f wsaf">ing to<span class="_d blank"> </span>the<span class="_d blank"> </span>requirements/interests</span></div><div class="t m0 x1 hb y6b ff1 fs7 fc0 sc0 ls41 wsb0">of<span class="_d blank"> </span>the<span class="_d blank"> </span>teaching/learning community<span class="_3 blank"></span>. W<span class="_6 blank"></span><span class="ls2e wsb1">e hope that the reader community appre-</span></div><div class="t m0 x1 hb y6c ff1 fs7 fc0 sc0 ls34 wsb2">ciates this. Comput<span class="_3 blank"></span>ational chemi<span class="_3 blank"></span>stry principles<span class="_7 blank"> </span>extended to molecula<span class="_3 blank"></span>r simulation</div><div class="t m0 x1 hb y6d ff1 fs7 fc0 sc0 ls45 wsb3">are not included<span class="_7 blank"> </span>in this book;<span class="_7 blank"> </span>we hope that a s<span class="_3 blank"></span>ister publication<span class="_7 blank"> </span>of this book co<span class="_3 blank"></span>v-</div><div class="t m0 x1 hb y6e ff1 fs7 fc0 sc0 ls3c wsb4">ering that aspect will<span class="_1 blank"> </span>be released in the near futur<span class="_0 blank"> </span>e. W<span class="_6 blank"></span>e have<span class="_c blank"> </span>tried to ma<span class="_0 blank"> </span>ke the</div><div class="t m0 x1 hb y6f ff1 fs7 fc0 sc0 ls28 wsb5">explanations<span class="_d blank"> </span>clear and complete to the satis<span class="_3 blank"></span>faction of the reader<span class="_3 blank"></span>.<span class="_1 blank"> </span>Ho<span class="_3 blank"></span>wev<span class="_3 blank"></span>er,<span class="_d blank"> </span>re-</div><div class="t m0 x1 hb y70 ff1 fs7 fc0 sc0 ls3a wsb6">garding an<span class="_3 blank"></span>y<span class="_a blank"> </span>queries, suggestions, c<span class="_3 blank"></span>orrections, modi\ufb01cations<span class="_4 blank"> </span>and<span class="_a blank"> </span>advice, the read-</div><div class="t m0 x1 hb y71 ff1 fs7 fc0 sc0 ls3a wsb7">ers are al<span class="_3 blank"></span>ways welcome<span class="_10 blank"> </span>to contact t<span class="_3 blank"></span>he authors at the foll<span class="_3 blank"></span>owing<span class="_d blank"> </span>email address:</div><div class="t m0 x1 hb y7e ff1 fs7 fc0 sc0 ls4d wsb8">n_krishnan@ettimadai.amrita.edu.</div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf9" class="pf w2 h2" data-page-no="9"><div class="pc pc9 w2 h2"><div class="t m0 x2 hc y46 ff1 fs8 fc0 sc0 ls51">x<span class="ls4e wsb9">Preface</span></div><div class="t m0 x6 hb y6 ff1 fs7 fc0 sc0 ls53 wsba">The authors<span class="_7 blank"> </span>would like t<span class="_3 blank"></span>o<span class="_c blank"> </span>take this opportunity<span class="_4 blank"> </span>to acknowledge<span class="_7 blank"> </span>the follo<span class="_3 blank"></span>wing</div><div class="t m0 x2 hb y47 ff1 fs7 fc0 sc0 ls37 wsbb">persons<span class="_4 blank"> </span>who spend their v<span class="_3 blank"></span>aluable<span class="_4 blank"> </span>time in dis<span class="_3 blank"></span>cussions wit<span class="_3 blank"></span>h the authors and<span class="_4 blank"> </span>helped</div><div class="t m0 x2 hb y48 ff1 fs7 fc0 sc0 ls37 wsbc">them to enri<span class="_3 blank"></span>ch this book<span class="_8 blank"> </span>with their sugges<span class="_3 blank"></span>tions<span class="_b blank"> </span>and comments:</div><div class="t m0 x9 hb y7f ff1 fs7 fc0 sc0 ls2f wsbd">1.<span class="_2 blank"> </span>Brahmachari Abhayamrita Chaitanya,<span class="_c blank"> </span><span class="ls22 wsbe">the Chief Operating Of\ufb01cer<span class="_a blank"> </span>of Amrita</span></div><div class="t m0 xa hb y80 ff1 fs7 fc0 sc0 ls3c ws47">University<span class="_6 blank"></span>, and Dr<span class="_3 blank"></span>. P<span class="_6 blank"></span>. V<span class="_e blank"></span>enk<span class="_0 blank"> </span>ata Rangan, the V<span class="_3 blank"></span>ice Chancello<span class="_0 blank"> </span>r of Amrita Univer<span class="_3 blank"></span>-</div><div class="t m0 xa hb y81 ff1 fs7 fc0 sc0 ls2b wsbf">sity<span class="_6 blank"></span>,<span class="_7 blank"> </span>for their<span class="_7 blank"> </span>unstinte<span class="_3 blank"></span>d support and<span class="_7 blank"> </span>constant encouragement<span class="_b blank"> </span>in<span class="_7 blank"> </span>all<span class="_7 blank"> </span>our endeav-</div><div class="t m0 xa hb y82 ff1 fs7 fc0 sc0 ls52 wsc0">ours.</div><div class="t m0 x9 hb y83 ff1 fs7 fc0 sc0 ls38 wsc1">2.<span class="_2 blank"> </span>Dr<span class="_3 blank"></span>. C. S. Shastry<span class="_3 blank"></span>, Profes<span class="_3 blank"></span>sor of the Department of Science,<span class="_a blank"> </span>for his insightful</div><div class="t m0 xa hb y84 ff1 fs7 fc0 sc0 ls29 wsa6">lectures on<span class="_9 blank"> </span>quantum mechanics.</div><div class="t m0 x9 hb y85 ff1 fs7 fc0 sc0 ls40 wsc2">3.<span class="_2 blank"> </span>Mr<span class="_3 blank"></span>. K. Narayanan K<span class="_3 blank"></span>utty of the Departm<span class="ls22 wsc3">ent of<span class="_7 blank"> </span>Science,<span class="_7 blank"> </span>for<span class="_7 blank"> </span>h<span class="_0 blank"> </span>is contribution to</span></div><div class="t m0 xa hb y86 ff1 fs7 fc0 sc0 ls30 wsc4">the chapter on<span class="_9 blank"> </span>quantum mechanics.</div><div class="t m0 x9 hb y87 ff1 fs7 fc0 sc0 ls38 wsc5">4.<span class="_2 blank"> </span>Mr<span class="_3 blank"></span>.<span class="_7 blank"> </span>G. Narayanan Nair<span class="_7 blank"> </span>of<span class="_7 blank"> </span>the Systems Department, for his contributi<span class="_3 blank"></span>on to<span class="_7 blank"> </span>the</div><div class="t m0 xa hb y88 ff1 fs7 fc0 sc0 ls54 wsc6">s<span class="_11 blank"></span>e<span class="_11 blank"></span>c<span class="_11 blank"></span>t<span class="_11 blank"></span>i<span class="_11 blank"></span>o<span class="_12 blank"></span>no<span class="_11 blank"></span>nH<span class="_11 blank"></span>P<span class="_11 blank"></span>C<span class="_11 blank"></span>.</div><div class="t m0 x9 hb y89 ff1 fs7 fc0 sc0 ls34 wsc7">5.<span class="_2 blank"> </span>Mr<span class="_3 blank"></span>. M. Sree<span class="_3 blank"></span>vals<span class="_3 blank"></span>an, Mr<span class="_6 blank"></span>. P<span class="_6 blank"></span>. Gopakumar<span class="_9 blank"> </span>and Mr<span class="_3 blank"></span>. Ajai<span class="_4 blank"> </span>Narendran<span class="_4 blank"> </span>of the S<span class="_3 blank"></span>ystems</div><div class="t m0 xa hb y8a ff1 fs7 fc0 sc0 ls2b wsc8">Department,<span class="_8 blank"> </span>for<span class="_9 blank"> </span>their help in making the websi<span class="_3 blank"></span>te for the book.</div><div class="t m0 x9 hb y8b ff1 fs7 fc0 sc0 ls2b wsc9">6.<span class="_2 blank"> </span>Dr<span class="_3 blank"></span>. K. P<span class="_6 blank"></span>. Soman, Head of the Cent<span class="_3 blank"></span>re for Computational<span class="_9 blank"> </span>Engineering and Net-</div><div class="t m0 xa hb y8c ff1 fs7 fc0 sc0 ls33 wsca">working, for his<span class="_9 blank"> </span>continuous support and<span class="_9 blank"> </span>encouragement.</div><div class="t m0 x9 hb y8d ff1 fs7 fc0 sc0 ls37 wscb">7.<span class="_2 blank"> </span>Mr<span class="_3 blank"></span>. K. R. Sunderl<span class="_3 blank"></span>al and Mr<span class="_6 blank"></span>. V<span class="_e blank"></span>. S. B<span class="_3 blank"></span>inoy from<span class="_7 blank"> </span>the interact<span class="_3 blank"></span>ive<span class="_4 blank"> </span>media group<span class="_7 blank"> </span>of</div><div class="t m0 xa hb y8e ff1 fs7 fc0 sc0 ls24 wscc">\u2018<span class="_6 blank"></span>Amrita V<span class="_6 blank"></span>ishwa V<span class="_3 blank"></span>i<span class="_3 blank"></span>dyapeetham-Univ<span class="_3 blank"></span>ersity\u2019<span class="_9 blank"> </span>for drawing<span class="_4 blank"> </span>excellent<span class="_4 blank"> </span>diagrams in-</div><div class="t m0 xa hb y8f ff1 fs7 fc0 sc0 ls33 wscd">cluded in the book.</div><div class="t m0 x9 hb y90 ff1 fs7 fc0 sc0 ls29 wsce">8.<span class="_2 blank"> </span>All our colleagues, dear and near ones, friends<span class="_8 blank"> </span>and s<span class="_3 blank"></span>tudents for their cooperation</div><div class="t m0 xa hb y91 ff1 fs7 fc0 sc0 ls53 wscf">and support.</div><div class="t m0 x9 hb y72 ff1 fs7 fc0 sc0 ls38 wsd0">9.<span class="_2 blank"> </span>All<span class="_1 blank"> </span>the of\ufb01cia<span class="_3 blank"></span>ls of<span class="_1 blank"> </span>Springer-<span class="_3 blank"></span>V<span class="_6 blank"></span>erlag<span class="_d blank"> </span>Berlin Heidelber<span class="_3 blank"></span>g and le-tex publishi<span class="_3 blank"></span>ng</div><div class="t m0 xa hb y73 ff1 fs7 fc0 sc0 ls48 wsd1">services oHG, Leipzig fo<span class="_0 blank"> </span>r materializing this pr<span class="_0 blank"> </span>oject in a highly ap<span class="_0 blank"> </span>preciable man-</div><div class="t m0 xa hb y74 ff1 fs7 fc0 sc0 ls36 wsd2">ner<span class="_3 blank"></span>.</div><div class="t m0 x2 hb y61 ff1 fs7 fc0 sc0 ls36 ws80">Coimbatore, March 2008<span class="_13 blank"> </span>K. I.<span class="_9 blank"> </span>Ramachandran</div><div class="t m0 xb hb y92 ff1 fs7 fc0 sc0 ls36 wsd3">Gopakumar Deepa</div><div class="t m0 xb hb y64 ff1 fs7 fc0 sc0 ls37 wsd4">Krishnan Namboori P<span class="_e blank"></span>.K.</div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pfa" class="pf w2 h2" data-page-no="a"><div class="pc pca w2 h2"><div class="t m0 x1 ha y26 ff4 fs0 fc0 sc0 ls57">Contents</div><div class="t m0 x1 hb y23 ff4 fs7 fc0 sc0 ls58 wsd5">1<span class="_14 blank"> </span>Introduction <span class="ff1 ls55 wsd6">..... .... ..... ..... ..... ..... ..... ..... ..... ..... .<span class="_15 blank"> </span>1</span></div><div class="t m0 xc hb y27 ff1 fs7 fc0 sc0 ls59 wsd7">1.1<span class="_16 blank"> </span>A<span class="_9 blank"> </span>De\ufb01nitio<span class="_0 blank"> </span>n of<span class="_9 blank"> </span>Comp<span class="_0 blank"> </span>utational Ch<span class="_0 blank"> </span>emistry<span class="_10 blank"> </span><span class="ls55 wsd6">.......... ..... ..... .<span class="_15 blank"> </span>1</span></div><div class="t m0 xc hb y28 ff1 fs7 fc0 sc0 ls55 wsd6">1<span class="_12 blank"></span>.<span class="_12 blank"></span>2<span class="_17 blank"> </span>M<span class="_12 blank"></span>o<span class="_12 blank"></span>d<span class="_18 blank"></span>e<span class="_12 blank"></span>l<span class="_12 blank"></span>s<span class="_b blank"> </span>......... ..... ..... ..... ..... ..... ..... ..... ..... .<span class="_15 blank"> </span>2</div><div class="t m0 xc hb y29 ff1 fs7 fc0 sc0 ls55 wsd6">1<span class="_12 blank"></span>.<span class="_12 blank"></span>3<span class="_17 blank"> </span>A<span class="_12 blank"></span>p<span class="_12 blank"></span>p<span class="_18 blank"></span>r<span class="_12 blank"></span>o<span class="_12 blank"></span>x<span class="_18 blank"></span>i<span class="_12 blank"></span>m<span class="_12 blank"></span>a<span class="_12 blank"></span>t<span class="_18 blank"></span>i<span class="_12 blank"></span>o<span class="_12 blank"></span>n<span class="_12 blank"></span>s<span class="_0 blank"> </span>...................... ..... ..... ..... ..... .<span class="_15 blank"> </span>3</div><div class="t m0 xc hb y2a ff1 fs7 fc0 sc0 ls3c wsd8">1.4<span class="_16 blank"> </span>Reality <span class="ls55 wsd6">.............. ..... ..... ..... ..... ..... ..... ..... .<span class="_15 blank"> </span>4</span></div><div class="t m0 xc hb y2b ff1 fs7 fc0 sc0 ls38 wsd9">1.5<span class="_16 blank"> </span>Comput<span class="_3 blank"></span>ational<span class="_b blank"> </span>Chemistry<span class="_b blank"> </span>Methods <span class="ls55 wsd6">........... ..... ..... ..... .<span class="_15 blank"> </span>4</span></div><div class="t m0 xd hb y2c ff1 fs7 fc0 sc0 ls39 wsda">1.5.1<span class="_14 blank"> </span>Ab Initio Calcu<span class="_0 blank"> </span>lations<span class="_2 blank"> </span><span class="ls55 wsd6">.... ..... ..... ..... ..... ..... .<span class="_15 blank"> </span>5</span></div><div class="t m0 xd hb y2d ff1 fs7 fc0 sc0 ls55 wsd6">1<span class="_12 blank"></span>.<span class="_12 blank"></span>5<span class="_18 blank"></span>.<span class="_12 blank"></span>2<span class="_19 blank"> </span>S<span class="_12 blank"></span>e<span class="_12 blank"></span>m<span class="_12 blank"></span>i<span class="_12 blank"></span>e<span class="_18 blank"></span>m<span class="_12 blank"></span>p<span class="_12 blank"></span>i<span class="_18 blank"></span>r<span class="_12 blank"></span>i<span class="_12 blank"></span>c<span class="_12 blank"></span>a<span class="_18 blank"></span>lC<span class="_12 blank"></span>a<span class="_12 blank"></span>l<span class="_12 blank"></span>c<span class="_12 blank"></span>u<span class="_18 blank"></span>l<span class="_12 blank"></span>a<span class="_12 blank"></span>t<span class="_12 blank"></span>i<span class="_12 blank"></span>o<span class="_18 blank"></span>n<span class="_12 blank"></span>s<span class="_3 blank"></span>..... ..... ..... ..... ..... .<span class="_15 blank"> </span>6</div><div class="t m0 xd hb y2e ff1 fs7 fc0 sc0 ls55 wsd6">1<span class="_12 blank"></span>.<span class="_12 blank"></span>5<span class="_18 blank"></span>.<span class="_12 blank"></span>3<span class="_19 blank"> </span>M<span class="_12 blank"></span>o<span class="_12 blank"></span>d<span class="_18 blank"></span>e<span class="_12 blank"></span>l<span class="_12 blank"></span>i<span class="_12 blank"></span>n<span class="_18 blank"></span>gt<span class="_12 blank"></span>h<span class="_18 blank"></span>eS<span class="_12 blank"></span>o<span class="_18 blank"></span>l<span class="_12 blank"></span>i<span class="_12 blank"></span>d<span class="_0 blank"> </span>S<span class="_12 blank"></span>t<span class="_12 blank"></span>a<span class="_18 blank"></span>t<span class="_12 blank"></span>e<span class="_1a blank"> </span>............ ..... ..... ..... .<span class="_15 blank"> </span>6</div><div class="t m0 xd hb y2f ff1 fs7 fc0 sc0 ls55 wsd6">1<span class="_12 blank"></span>.<span class="_12 blank"></span>5<span class="_18 blank"></span>.<span class="_12 blank"></span>4<span class="_19 blank"> </span>M<span class="_12 blank"></span>o<span class="_12 blank"></span>l<span class="_12 blank"></span>e<span class="_18 blank"></span>c<span class="_12 blank"></span>u<span class="_12 blank"></span>l<span class="_12 blank"></span>a<span class="_18 blank"></span>rM<span class="_12 blank"></span>e<span class="_18 blank"></span>c<span class="_12 blank"></span>h<span class="_12 blank"></span>a<span class="_12 blank"></span>n<span class="_18 blank"></span>i<span class="_12 blank"></span>c<span class="_12 blank"></span>s............... ..... ..... ..... .<span class="_15 blank"> </span>7</div><div class="t m0 xd hb y30 ff1 fs7 fc0 sc0 ls55 wsd6">1<span class="_12 blank"></span>.<span class="_12 blank"></span>5<span class="_18 blank"></span>.<span class="_12 blank"></span>5<span class="_19 blank"> </span>M<span class="_12 blank"></span>o<span class="_12 blank"></span>l<span class="_12 blank"></span>e<span class="_18 blank"></span>c<span class="_12 blank"></span>u<span class="_12 blank"></span>l<span class="_12 blank"></span>a<span class="_18 blank"></span>rS<span class="_12 blank"></span>i<span class="_12 blank"></span>m<span class="_18 blank"></span>u<span class="_12 blank"></span>l<span class="_12 blank"></span>a<span class="_12 blank"></span>t<span class="_18 blank"></span>i<span class="_12 blank"></span>o<span class="_12 blank"></span>n<span class="_3 blank"></span>.................... ..... ..... .<span class="_15 blank"> </span>7</div><div class="t m0 xd hb y31 ff1 fs7 fc0 sc0 ls55 wsd6">1<span class="_12 blank"></span>.<span class="_12 blank"></span>5<span class="_18 blank"></span>.<span class="_12 blank"></span>6<span class="_19 blank"> </span>S<span class="_12 blank"></span>t<span class="_12 blank"></span>a<span class="_12 blank"></span>t<span class="_12 blank"></span>i<span class="_12 blank"></span>s<span class="_12 blank"></span>t<span class="_18 blank"></span>i<span class="_12 blank"></span>c<span class="_12 blank"></span>a<span class="_12 blank"></span>l<span class="_0 blank"> </span>M<span class="_18 blank"></span>e<span class="_12 blank"></span>c<span class="_12 blank"></span>h<span class="_12 blank"></span>a<span class="_18 blank"></span>n<span class="_12 blank"></span>i<span class="_12 blank"></span>c<span class="_12 blank"></span>s<span class="_8 blank"> </span>.......... ..... ..... ..... ..... .<span class="_15 blank"> </span>8</div><div class="t m0 xd hb y32 ff1 fs7 fc0 sc0 ls3a ws36">1.5.7<span class="_14 blank"> </span>Thermodynamics<span class="_10 blank"> </span>. . . <span class="ls55 wsd6">..... ..... ..... ..... ..... ..... .<span class="_15 blank"> </span>8</span></div><div class="t m0 xd hb y33 ff1 fs7 fc0 sc0 ls55 wsd6">1<span class="_12 blank"></span>.<span class="_12 blank"></span>5<span class="_18 blank"></span>.<span class="_12 blank"></span>8<span class="_19 blank"> </span>S<span class="_12 blank"></span>t<span class="_12 blank"></span>r<span class="_12 blank"></span>u<span class="_18 blank"></span>c<span class="_12 blank"></span>t<span class="_12 blank"></span>u<span class="_12 blank"></span>r<span class="_18 blank"></span>e<span class="_12 blank"></span>-<span class="_12 blank"></span>P<span class="_12 blank"></span>r<span class="_18 blank"></span>o<span class="_12 blank"></span>p<span class="_12 blank"></span>e<span class="_18 blank"></span>r<span class="_12 blank"></span>t<span class="_12 blank"></span>yR<span class="_12 blank"></span>e<span class="_12 blank"></span>l<span class="_12 blank"></span>a<span class="_12 blank"></span>t<span class="_18 blank"></span>i<span class="_12 blank"></span>o<span class="_12 blank"></span>n<span class="_12 blank"></span>s<span class="_18 blank"></span>h<span class="_12 blank"></span>i<span class="_12 blank"></span>p<span class="_12 blank"></span>s<span class="_4 blank"> </span>.......... ..... ..... .<span class="_15 blank"> </span>8</div><div class="t m0 xd hb y34 ff1 fs7 fc0 sc0 ls55 wsd6">1<span class="_12 blank"></span>.<span class="_12 blank"></span>5<span class="_18 blank"></span>.<span class="_12 blank"></span>9<span class="_19 blank"> </span>S<span class="_12 blank"></span>y<span class="_12 blank"></span>m<span class="_12 blank"></span>b<span class="_18 blank"></span>o<span class="_12 blank"></span>l<span class="_12 blank"></span>i<span class="_18 blank"></span>cC<span class="_12 blank"></span>a<span class="_12 blank"></span>l<span class="_12 blank"></span>c<span class="_18 blank"></span>u<span class="_12 blank"></span>l<span class="_12 blank"></span>a<span class="_12 blank"></span>t<span class="_12 blank"></span>i<span class="_18 blank"></span>o<span class="_12 blank"></span>n<span class="_12 blank"></span>s<span class="_1b blank"> </span>.............. ..... ..... ..... .<span class="_15 blank"> </span>9</div><div class="t m0 xd hb y35 ff1 fs7 fc0 sc0 ls56 wsdb">1.5.10<span class="_1c blank"> </span>Arti\ufb01cial Intelligence<span class="_7 blank"> </span><span class="ls55 wsd6">..... ..... ..... ..... ..... ..... .<span class="_15 blank"> </span>9</span></div><div class="t m0 xd hb y36 ff1 fs7 fc0 sc0 ls55 wsdc">1<span class="_12 blank"></span>.<span class="_12 blank"></span>5<span class="_18 blank"></span>.<span class="_12 blank"></span>1<span class="_12 blank"></span>1<span class="_1d blank"> </span>T<span class="_12 blank"></span>h<span class="_12 blank"></span>e D<span class="_18 blank"></span>e<span class="_12 blank"></span>s<span class="_12 blank"></span>i<span class="_12 blank"></span>g<span class="_12 blank"></span>n o<span class="_18 blank"></span>f a C<span class="_12 blank"></span>o<span class="_12 blank"></span>m<span class="_18 blank"></span>p<span class="_12 blank"></span>u<span class="_12 blank"></span>t<span class="_18 blank"></span>a<span class="_12 blank"></span>t<span class="_12 blank"></span>i<span class="_12 blank"></span>o<span class="_12 blank"></span>n<span class="_18 blank"></span>a<span class="_12 blank"></span>lR<span class="_12 blank"></span>e<span class="_18 blank"></span>s<span class="_11 blank"></span>e<span class="_18 blank"></span>a<span class="_12 blank"></span>r<span class="_12 blank"></span>c<span class="_18 blank"></span>hP<span class="_18 blank"></span>r<span class="_12 blank"></span>o<span class="_12 blank"></span>g<span class="_18 blank"></span>r<span class="_12 blank"></span>a<span class="_12 blank"></span>m<span class="_4 blank"> </span>......<span class="_15 blank"> </span>9</div><div class="t m0 xd hb y37 ff1 fs7 fc0 sc0 ls55 wsd6">1<span class="_12 blank"></span>.<span class="_12 blank"></span>5<span class="_18 blank"></span>.<span class="_12 blank"></span>1<span class="_12 blank"></span>2<span class="_1d blank"> </span>V<span class="_1e blank"></span>i<span class="_12 blank"></span>s<span class="_12 blank"></span>u<span class="_12 blank"></span>a<span class="_12 blank"></span>l<span class="_18 blank"></span>i<span class="_12 blank"></span>z<span class="_12 blank"></span>a<span class="_12 blank"></span>t<span class="_12 blank"></span>i<span class="_18 blank"></span>o<span class="_12 blank"></span>n<span class="_1b blank"> </span>.. ..... ..... ..... ..... ..... ..... ..... .<span class="_1f blank"> </span>1<span class="_12 blank"></span>0</div><div class="t m0 xc hb y38 ff1 fs7 fc0 sc0 ls30 wsdd">1.6<span class="_16 blank"> </span>Journal<span class="_3 blank"></span>s and<span class="_9 blank"> </span>Book Series Focusing</div><div class="t m0 xd hb y39 ff1 fs7 fc0 sc0 ls5a wsde">o<span class="_12 blank"></span>n<span class="_0 blank"> </span>C<span class="_12 blank"></span>o<span class="_12 blank"></span>m<span class="_18 blank"></span>p<span class="_12 blank"></span>u<span class="_18 blank"></span>t<span class="_12 blank"></span>a<span class="_12 blank"></span>t<span class="_12 blank"></span>i<span class="_12 blank"></span>o<span class="_18 blank"></span>n<span class="_12 blank"></span>a<span class="_12 blank"></span>lC<span class="_12 blank"></span>h<span class="_18 blank"></span>e<span class="_12 blank"></span>m<span class="_12 blank"></span>i<span class="_12 blank"></span>s<span class="_12 blank"></span>t<span class="_18 blank"></span>r<span class="_12 blank"></span>y<span class="_1b blank"> </span>. ..... ..... ..... ..... ..... ..... .<span class="_1f blank"> </span>1<span class="_12 blank"></span>0</div><div class="t m0 xc hb y3a ff1 fs7 fc0 sc0 ls37 wsdf">1.7<span class="_16 blank"> </span>Journal<span class="_3 blank"></span>s and<span class="_9 blank"> </span>Book Series</div><div class="t m0 xd hb y3b ff1 fs7 fc0 sc0 ls5b wse0">O<span class="_12 blank"></span>f<span class="_12 blank"></span>t<span class="_12 blank"></span>e<span class="_18 blank"></span>n I<span class="_12 blank"></span>n<span class="_18 blank"></span>c<span class="_12 blank"></span>l<span class="_12 blank"></span>u<span class="_18 blank"></span>d<span class="_12 blank"></span>i<span class="_12 blank"></span>n<span class="_18 blank"></span>gC<span class="_12 blank"></span>o<span class="_12 blank"></span>m<span class="_12 blank"></span>p<span class="_18 blank"></span>u<span class="_12 blank"></span>t<span class="_12 blank"></span>a<span class="_18 blank"></span>t<span class="_12 blank"></span>i<span class="_12 blank"></span>o<span class="_12 blank"></span>n<span class="_18 blank"></span>a<span class="_12 blank"></span>lC<span class="_12 blank"></span>h<span class="_12 blank"></span>e<span class="_18 blank"></span>m<span class="_12 blank"></span>i<span class="_12 blank"></span>s<span class="_12 blank"></span>t<span class="_12 blank"></span>r<span class="_18 blank"></span>y<span class="_3 blank"></span>............... ..... .<span class="_1f blank"> </span>1<span class="_12 blank"></span>1</div><div class="t m0 xc hb y3c ff1 fs7 fc0 sc0 ls3a wse1">1.8<span class="_16 blank"> </span>Common R<span class="_3 blank"></span>eference Books A<span class="_3 blank"></span>v<span class="_3 blank"></span>ailable</div><div class="t m0 xd hb y3d ff1 fs7 fc0 sc0 ls5a wsde">o<span class="_12 blank"></span>n<span class="_0 blank"> </span>C<span class="_12 blank"></span>o<span class="_12 blank"></span>m<span class="_18 blank"></span>p<span class="_12 blank"></span>u<span class="_18 blank"></span>t<span class="_12 blank"></span>a<span class="_12 blank"></span>t<span class="_12 blank"></span>i<span class="_12 blank"></span>o<span class="_18 blank"></span>n<span class="_12 blank"></span>a<span class="_12 blank"></span>lC<span class="_12 blank"></span>h<span class="_18 blank"></span>e<span class="_12 blank"></span>m<span class="_12 blank"></span>i<span class="_12 blank"></span>s<span class="_12 blank"></span>t<span class="_18 blank"></span>r<span class="_12 blank"></span>y<span class="_1b blank"> </span>. ..... ..... ..... ..... ..... ..... .<span class="_1f blank"> </span>1<span class="_12 blank"></span>1</div><div class="t m0 xc hb y3e ff1 fs7 fc0 sc0 ls5b wse0">1<span class="_12 blank"></span>.<span class="_12 blank"></span>9<span class="_17 blank"> </span>C<span class="_12 blank"></span>o<span class="_12 blank"></span>m<span class="_12 blank"></span>p<span class="_18 blank"></span>u<span class="_12 blank"></span>t<span class="_12 blank"></span>a<span class="_18 blank"></span>t<span class="_12 blank"></span>i<span class="_12 blank"></span>o<span class="_12 blank"></span>n<span class="_18 blank"></span>a<span class="_12 blank"></span>lC<span class="_12 blank"></span>h<span class="_18 blank"></span>e<span class="_12 blank"></span>m<span class="_12 blank"></span>i<span class="_12 blank"></span>s<span class="_18 blank"></span>t<span class="_12 blank"></span>r<span class="_12 blank"></span>y o<span class="_18 blank"></span>nt<span class="_18 blank"></span>h<span class="_12 blank"></span>e I<span class="_18 blank"></span>n<span class="_12 blank"></span>t<span class="_12 blank"></span>e<span class="_12 blank"></span>r<span class="_18 blank"></span>n<span class="_12 blank"></span>e<span class="_12 blank"></span>t........... ..... ..... .<span class="_1f blank"> </span>1<span class="_12 blank"></span>3</div><div class="t m0 xc hb y3f ff1 fs7 fc0 sc0 ls29 wse2">1.10<span class="_20 blank"> </span>Some T<span class="_6 blank"></span>opics of Research Interest Rel<span class="_3 blank"></span>ated</div><div class="t m0 xd hb y40 ff1 fs7 fc0 sc0 ls5a wsde">t<span class="_12 blank"></span>o<span class="_0 blank"> </span>C<span class="_12 blank"></span>o<span class="_18 blank"></span>m<span class="_12 blank"></span>p<span class="_12 blank"></span>u<span class="_18 blank"></span>t<span class="_12 blank"></span>a<span class="_12 blank"></span>t<span class="_12 blank"></span>i<span class="_12 blank"></span>o<span class="_18 blank"></span>n<span class="_12 blank"></span>a<span class="_12 blank"></span>lC<span class="_12 blank"></span>h<span class="_18 blank"></span>e<span class="_12 blank"></span>m<span class="_12 blank"></span>i<span class="_18 blank"></span>s<span class="_11 blank"></span>t<span class="_18 blank"></span>r<span class="_12 blank"></span>y<span class="_a blank"> </span>........... ..... ..... ..... ..... .<span class="_1f blank"> </span>1<span class="_12 blank"></span>4</div><div class="t m0 xc hb y41 ff1 fs7 fc0 sc0 ls55 wsd6">R<span class="_12 blank"></span>e<span class="_12 blank"></span>f<span class="_12 blank"></span>e<span class="_12 blank"></span>r<span class="_18 blank"></span>e<span class="_12 blank"></span>n<span class="_12 blank"></span>c<span class="_18 blank"></span>e<span class="_12 blank"></span>s<span class="_0 blank"> </span>... ..... .... ..... ..... ..... ..... ..... ..... ..... ..... .<span class="_1f blank"> </span>1<span class="_12 blank"></span>5</div><div class="t m0 xe hc y45 ff1 fs8 fc0 sc0 ls3f">xi</div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div>
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