The Potential Distribution Theorem and Models of Molecular Solutions

by Tom L. Beck , Michael E. Paulaitis , Lawrence R. Pratt

• ISBN13: 9780521822152
• ISBN10: 0521822157
• Edition: 1st
• Format: Hardcover
• Copyright: 2006-09-18
• Publisher: Cambridge University Press

Summary

The understanding of statistical thermodynamic molecular theory is fundamental to the appreciation of molecular solutions. Though effective monographs on molecular simulation methods are available, down-to-earth presentations of molecular theory are not. This book aims to re-address the balance, using Potential Distrbution Theorem (PDT) as the basis, providing an up-to-date discussion of practical theories in conjunction with simulation results. The authors discuss the field in a concise and simple manner, illustrating the text with useful models of solution thermodynamics and numerous exercises. Modern quasi-chemical theories that permit statistical thermodynamic properties to be studied on the basis of electronic structure calculations are given extended development, as is the testing of those theoretical results with ab initio molecular dynamics simulations. The book is intended for students taking up research problems of molecular science in chemistry, chemical engineering, biochemistry, pharmaceutical chemistry, nanotechnology and biotechnology.

Table of Contents

Preface	vii
Acknowledgements	x
Glossary	xi
Introduction	1	(22)
Molecules in solution	4	(12)
Looking forward	16	(1)
Notation and the theory of molecular liquids	16	(7)
Statistical thermodynamic necessities	23	(9)
The free energy and chemical potentials	23	(9)
Potential distribution theorem	32	(29)
Derivation of the potential distribution theorem	39	(1)
Weak field limit	40	(1)
Potential distribution theorem view of averages	41	(2)
Ensemble dependence	43	(1)
Inhomogeneous systems	44	(3)
Reduced distribution functions	47	(4)
Activity coefficients and solution standard states	51	(2)
Quantum mechanical ingredients and generalizations	53	(8)
Models	61	(39)
Van der Waals model of dense liquids	61	(6)
Dielectric solvation -- Born -- models	67	(6)
Excluded volume interactions and packing in liquids	73	(5)
Flory--Huggins model of polymer mixtures	78	(11)
Electrolyte solutions and the Debye--Huckel theory	89	(5)
Clustering in dilute solutions and Pitzer models	94	(6)
Generalities	100	(23)
Reference systems and umbrella sampling	100	(4)
Overlap methods	104	(1)
Perturbation theory	105	(11)
Thermodynamic integration	116	(2)
Bias	118	(2)
Stratification	120	(3)
Statistical tentacles	123	(19)
The MM and KS expansions	123	(9)
Density functional and classic integral equation theories	132	(8)
Kirkwood-Buff theory	140	(2)
Quasi-chemical theory	142	(30)
Derivation of the basic quasi-chemical formula	143	(3)
Clustering in more detail	146	(3)
An example of a primitive quasi-chemical treatment: Be2+(aq)	149	(4)
Analysis of ab initio molecular dynamics	153	(4)
Packing in classical liquids	157	(3)
Self-consistent molecular field for packing	160	(6)
Historical quasi-chemical calculation	166	(2)
Explicit-implicit solvent models	168	(4)
Developed examples	172	(42)
Polymers	172	(8)
Primitive hydrophobic effects	180	(18)
Primitive hydrophilic phenomena: ion hydration	198	(16)
References	214	(15)
Index	229