Danail D. Bonchev – författare

As we were at pains to point out in the companion volume to this mo- graph, entitled Complexity in Chemistry: Introduction and Fundamentals, complexity is to be encountered just about everywhere. All that is needed forustoseeitisasuitablytrainedeyeanditthenappearsalmostmagically in all manner of guises. Because of its ubiquity, complexity has been and currentlystillisbeingde?nedinanumberofdifferentways. Someofthese de?nitions have led us to major and powerful new insights. Thus, even in the present monograph, the important distinction is drawn between the - terpretations of the concepts of complexity and complication and this is shown to have a signi?cant bearing on how systems are modeled. Having said this, however, we should not fail to mention that the broad consensus that now gained acceptance is that all of the de?nitions of complexity are in the last analysis to be understood in essentially intuitive terms. Such de?nitions will therefore always have a certain degree of fuzziness as- ciated with them. But this latter desideratum should in no way be viewed as diminishing the great usefulness of the concept in any of the many scienti?c disciplines to which it can be applied. In the chapters that are included in this monograph the fact that differing concepts of complexity can be utilized in a variety of disciplines is made explicit. The speci?c d- ciplines that we embrace herein are chemistry, biochemistry, biology, and ecology. Chapter 1, “On the Complexity of Fullerenes and Nanotubes,” is wr- ten by an international team of scientists led by Milan Randic.

As we were at pains to point out in the companion volume to this mo- graph, entitled Complexity in Chemistry: Introduction and Fundamentals, complexity is to be encountered just about everywhere. All that is needed forustoseeitisasuitablytrainedeyeanditthenappearsalmostmagically in all manner of guises. Because of its ubiquity, complexity has been and currentlystillisbeingde?nedinanumberofdifferentways. Someofthese de?nitions have led us to major and powerful new insights. Thus, even in the present monograph, the important distinction is drawn between the - terpretations of the concepts of complexity and complication and this is shown to have a signi?cant bearing on how systems are modeled. Having said this, however, we should not fail to mention that the broad consensus that now gained acceptance is that all of the de?nitions of complexity are in the last analysis to be understood in essentially intuitive terms. Such de?nitions will therefore always have a certain degree of fuzziness as- ciated with them. But this latter desideratum should in no way be viewed as diminishing the great usefulness of the concept in any of the many scienti?c disciplines to which it can be applied. In the chapters that are included in this monograph the fact that differing concepts of complexity can be utilized in a variety of disciplines is made explicit. The speci?c d- ciplines that we embrace herein are chemistry, biochemistry, biology, and ecology. Chapter 1, “On the Complexity of Fullerenes and Nanotubes,” is wr- ten by an international team of scientists led by Milan Randic.

The progress in computer technology during the last 10-15 years has enabled the performance of ever more precise quantum mechanical calculations related to structure and interactions of chemical compounds. However, the qualitative models relating electronic structure to molecular geometry have not progressed at the same pace. There is a continuing need in chemistry for simple concepts and qualitatively clear pictures that are also quantitatively comparable to ab initio quantum chemical calculations. Topological methods and, more specifically, graph theory as a fixed-point topology, provide in principle a chance to fill this gap. With its more than 100 years of applications to chemistry, graph theory has proven to be of vital importance as the most natural language of chemistry. The explosive development of chemical graph theory during the last 20 years has increasingly overlapped with quantum chemistry. Besides contributing to the solution of various problems in theoretical chemistry, this development indicates that topology is an underlying principle that explains the success of quantum mechanics and goes beyond it, thus promising to bear more fruit in the future.

As we were at pains to point out in the companion volume to this mo- graph, entitled Complexity in Chemistry: Introduction and Fundamentals, complexity is to be encountered just about everywhere. All that is needed forustoseeitisasuitablytrainedeyeanditthenappearsalmostmagically in all manner of guises. Because of its ubiquity, complexity has been and currentlystillisbeingde?nedinanumberofdifferentways. Someofthese de?nitions have led us to major and powerful new insights. Thus, even in the present monograph, the important distinction is drawn between the - terpretations of the concepts of complexity and complication and this is shown to have a signi?cant bearing on how systems are modeled. Having said this, however, we should not fail to mention that the broad consensus that now gained acceptance is that all of the de?nitions of complexity are in the last analysis to be understood in essentially intuitive terms. Such de?nitions will therefore always have a certain degree of fuzziness as- ciated with them. But this latter desideratum should in no way be viewed as diminishing the great usefulness of the concept in any of the many scienti?c disciplines to which it can be applied. In the chapters that are included in this monograph the fact that differing concepts of complexity can be utilized in a variety of disciplines is made explicit. The speci?c d- ciplines that we embrace herein are chemistry, biochemistry, biology, and ecology. Chapter 1, “On the Complexity of Fullerenes and Nanotubes,” is wr- ten by an international team of scientists led by Milan Randic.

The progress in computer technology during the last 10-15 years has enabled the performance of ever more precise quantum mechanical calculations related to structure and interactions of chemical compounds. However, the qualitative models relating electronic structure to molecular geometry have not progressed at the same pace. There is a continuing need in chemistry for simple concepts and qualitatively clear pictures that are also quantitatively comparable to ab initio quantum chemical calculations. Topological methods and, more specifically, graph theory as a fixed-point topology, provide in principle a chance to fill this gap. With its more than 100 years of applications to chemistry, graph theory has proven to be of vital importance as the most natural language of chemistry. The explosive development of chemical graph theory during the last 20 years has increasingly overlapped with quantum chemistry. Besides contributing to the solution of various problems in theoretical chemistry, this development indicates that topology is an underlying principle that explains the success of quantum mechanics and goes beyond it, thus promising to bear more fruit in the future.