Simple molecules as complex systems.
For individual molecules quantum mechanics (QM) offers a simple, natural and elegant way to build large-scale complex networks: quantized energy levels are the nodes, allowed transitions among the levels are the links, and transition intensities supply the weights. QM networks are intrinsic properties of molecules and they are characterized experimentally via spectroscopy; thus, realizations of QM networks are called spectroscopic networks (SN). As demonstrated for the rovibrational states of H2(16)O, the molecule governing the greenhouse effect on earth through hundreds of millions of its spectroscopic transitions (links), both the measured and first-principles computed one-photon absorption SNs containing experimentally accessible transitions appear to have heavy-tailed degree distributions. The proposed novel view of high-resolution spectroscopy and the observed degree distributions have important implications: appearance of a core of highly interconnected hubs among the nodes, a generally disassortative connection preference, considerable robustness and error tolerance, and an "ultra-small-world" property. The network-theoretical view of spectroscopy offers a data reduction facility via a minimum-weight spanning tree approach, which can assist high-resolution spectroscopists to improve the efficiency of the assignment of their measured spectra.
1] Laboratory of Molecular Structure and Dynamics, Institute of Chemistry, Eötvös Loránd University, H-1117 Budapest, Pázmány Péter sétány 1/A, Hungary [2] MTA-ELTE Research Group on Complex Chemical Systems, H-1518 Budapest 112P.O. Box 32, Hungary.
Tibor
T
Furtenbacher
1] MTA-ELTE Research Group on Complex Chemical Systems, H-1518 Budapest 112P.O. Box 32, Hungary [2] Department of Algebra and Number Theory, Institute of Mathematics, Eötvös Loránd University, H-1518 Budapest 112P.O. Box 120, Hungary.
Péter
P
Arendás
Physikalisch-Chemisches Institut, Justus-Liebig-Universität Giessen, Heinrich-Buff-Ring 58, D-35392 Giessen, Germany.
Georg
G
Mellau
1] Laboratory of Molecular Structure and Dynamics, Institute of Chemistry, Eötvös Loránd University, H-1117 Budapest, Pázmány Péter sétány 1/A, Hungary [2] MTA-ELTE Research Group on Complex Chemical Systems, H-1518 Budapest 112P.O. Box 32, Hungary.
Attila G
AG
Császár