Le cariche parziali da usare nel campo di forze si ottengono generalmente da calcoli quantomeccanici. Nel caso di molecole rigide, il calcolo delle cariche è abbastanza semplice. Nel caso di molecole flessibili, occorre valutare quanto le diverse conformazioni influenzano la distribuzione di carica e, quindi, stimare la carica parziale come media pesata tra i vari conformeri. Il calcolo QM fornisce le cosidette cariche di Mulliken. Questo tipo di cariche possono portare ad una elevata inaccuratezza nel riprodurre proprietà chimico-fisiche di piccole molecole. Per evitare questo inconveniente sono state introdotte varie procedure per ottenere delle cariche parziali che tengano conto della diversa capacitá dei singoli atomi di accomodare una diversa distribuzione di carica. Queste procedure vanno sotto il nome di metodi di Electrostatic potential fitting tra cui i più usati solo il RESP e il CHELPG. Vediamo come questi metodi funzionano.
Continue reading “Il calcolo delle cariche parziali atomiche”Month: January 2018
La Dinamica Molecolare: il Campo di Forze
Then from these forces, by other propositions which are also mathematical, I deduce the motions of the planets, the comets, the moon, and the sea. I wish we could derive the rest of the phenomena of Nature by the same kind of reasoning from mechanical principles, for I am induced by many reasons to suspect that they may all depend upon certain forces by which the particles of bodies, by some causes hitherto unknown, are either mutually impelled towards one another, and cohere in regular figures, or are repelled and recede from one another.
Isaac Newton. Philosophiae Naturalis Principia Mathematica. London, 1686.
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La simulazione di Dinamica Molecolare
- Lex. I. Corpus omne perseverare in statu suo quiescendi vel movendi uniformiter in directum, nili quatenus a viribus impressis cogitur statum illum mutare.
- Lex. II. Muationem motus proportionalem esse vi motrici impressae, et fieri fecundum lineam rectam qua vis illa imprimitur.
- Lex. III. Actioni contrariam semper et equalem esse reactionem: sive corporum duorum actiones in se mutuo semper esse aequales et in partes contrarias dirigi.
Isaac Newton. Philosophiae Naturalis Principia Mathematica. London, 1686.
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Awk Programming II: Life in a Shell
The game of Life was invented in the ’70 by the prolific mathematician John H. Conway (on the 11/4/2020 sadly J.H. Conway passed away at the age of 82 after having contracted the COVID-19, see [5] for his biography). The game becomes popular after Martin Gardner described it in his famous column in the Scientific American magazine [1,2]. The game is based on cellular automata conceived by Konrad Zuse and Stanislaw M. Ulam at beginning of the ’50 and then adopted by John von Neumann for his study on self-replicating automata [2,3]. A cellular automaton is composed of interacting units (cells) arranged in a square grid. The system evolves in life cycles where each cell change status and new cells can be born, and others can survive or eventually die. The status of each cell in the next cycle is defined by the interaction with their neighbor cells according to a given set of rules. The interaction occurs with the first neighbors of each cell. As shown in Figure 1, two type of neighbor’s cells (circles) can be used, the game of Life uses the Moore type neighborhood.
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Molecular interactions and force fields
At quite uncertain times and places,
The atoms left their heavenly path,
And by fortuitous embraces,
Engendered all that being hath.
And though they seem to cling together,
And form ‘associations’ here,
Yet, soon or late, they burst their tether,
And through the depths of space career.
James Clerk MaxwellFrom ‘Molecular Evolution’, Nature, 8, 1873. In Lewis Campbell and William Garnett, The Life of James Clerk Maxwell (1882), 637.
Molecular forces are originated by the interactions of the electronic clouds of the atoms in the molecular systems. A full treatment of these interactions also accounting for the dynamics of the nuclei requires the solution of the time-dependent Schroedinger equation (the top of the modeling pyramid). This approach would provide a more accurate physical representation of the behavior of the systems in time. However, as pointed before, nowadays this approach is impracticable due to the enormous amount of computer resources need to accomplish this task even for relatively small peptides in water systems. The solution to this impasse is the application of the so-called lex parsimoniae or Ockham’s razor, a powerful approach in problem-solving to get rid of the redundant complexity. In this case, the law of parsimony suggests changing the level of scale and account of the hidden degree of freedom using an effective or mean field potential. Continue reading “Molecular interactions and force fields”
