INTERNATIONAL UNION OF PURE AND APPLIED CHEMISTRY

Physical and Biophysical Chemistry Division

IUPAC

Vc^llclllul LICb . U 111 Lb cillCl Oy 111 DOlo in Physical Chemistry

Third Edition

Prepared for publication by

E. Richard Cohen Tomislav Cvitas Jeremy G. Frey

BcTt.il Holmstrom Kozo Kuchitsu R,oberto Marquardt

Ian Mills Franco Pavese Martin Quack

Jiirgen Stohner Herbert L. Strauss Michio Takanii

Anders J Thor

The first and second editions were prepared for publication by

Ian Mills Tomislav Cvitas Klaus Homann Nikola Kallay Kozo Kuchitsu

IUPAC 2007 RSC Publishing CONTENTS v

PREFACE ix

HISTORICAL INTRODUCTION xi

1 PHYSICAL QUANTITIES AND UNITS 1 1.1 Physical quantities and quantity calculus 3 1.2 Base quantities and derived quantities 4 1.3 Symbols for physical quantities and units 5 1.3.1 General rules for symbols for quantities 5 1.3.2 General rules for symbols for units 5 1.4 Use of the words "extensive", "intensive", "specific", and "molar" 6 1.5 Products and quotients of physical quantities and units 7 1.6 The use of italic and Roman fonts for symbols in scientific publications 7

2 TABLES OF PHYSICAL QUANTITIES 11 2.1 Space and time 13 2.2 Classical mechanics 14 2.3 Electricity and magnetism 16 2.4 Quantum mechanics and quantum chemistry 18 2.4.1 Ab initio Hartree-Fock self-consistent field theory (ab initio SCF) 20

2.4.2 Hartree-Fock-Roothaan SCF theory, using molecular orbitals expanded as linear combinations of atomic-orbital basis . functions (LCAO-MO theory) . 21 2.5 Atoms and molecules 22 2.6 Spectroscopy 25 2.6.1 Symbols for angular momentum operators and quantum numbers 30 2.6.2 Symbols for symmetry operators and labels for symmetry species 31 2.6.3 Other symbols and conventions in optical spectroscopy 32 2.7 Electromagnetic radiation 34 2.7.1 Quantities and symbols concerned with the measurement of absorption intensity 38 2.7.2 Conventions for absorption intensities in condensed phases 40 2.8 Solid state 42 2.8.1 Symbols for planes and directions in crystals 44 2.9 Statistical thermodynamics 45 2.10 General chemistry 47 2.10.1 Other symbols and conventions in chemistry 49 2.11 Chemical thermodynamics 56 2.11.1 Other symbols and conventions in chemical thermodynamics 59 2.12 Chemical kinetics and photochemistry 63 2.12.1 Other symbols, terms, and conventions used in chemical kinetics 68 2.13 Electrochemistry 70 2.13.1 Sign and notation conventions in electrochemistry 73 2.14 Colloid and surface chemistry 77 2.14.1 Surface structure 79 2.15 Transport properties 81 2.15.1 Transport characteristic numbers: Quantities of dimension one 82

v 3 DEFINITIONS AND SYMBOLS FOR UNITS 83

3.1 The International System of Units (SI) 85 3.2 Names and symbols for the SI base units 86 3.3 Definitions of the SI base units 87

3.4 SI derived units with special names and symbols 89 3.5 SI derived units for other quantities 90 3.6 SI prefixes and prefixes for binary multiples 91

3.7 Non-SI units accepted for use with the SI 92 3.8 Coherent units and checking dimensions 93

3.9 Fundamental physical constants used as units 94 3.9.1 Atomic units 94

3.9.2 The equations of quantum chemistry expressed in terms of reduced quantities using atomic units 95 3.10 Dimensionless quantities 97 3.10.1 Fractions (relative values, yields, and efficiencies) 97

3.10.2 Deprecated usage 97

3.10.3 Units for logarithmic quantities: neper, bel, and decibel 98

4 RECOMMENDED MATHEMATICAL SYMBOLS 101

4.1 Printing of numbers and mathematical symbols 103

4.2 Symbols, operators, and functions 105

5 FUNDAMENTAL PHYSICAL CONSTANTS 109

6 PROPERTIES OF PARTICLES, ELEMENTS, AND NUCLIDES 113

6.1 Properties of selected particles 115 6.2 Standard atomic weights of the elements 2005 117 6.3 Properties of nuclides 121

7 CONVERSION OF UNITS 129

7.1 The use of quantity calculus 131 7.2 Conversion tables for units 135 7.3 The esu, emu, Gaussian, and atomic unit systems in relation to the SI 143 7.4 Transformation of equations of electromagnetic theory between the ISQ(SI) and Gaussian forms 145

8 UNCERTAINTY 149 8.1 for Reporting uncertainty a single measured quantity 151 8.2 of for Propagation uncertainty uncorrelated measurements 153 8.3 Reporting uncertainties in terms of confidence intervals 154

9 ABBREVIATIONS AND ACRONYMS 155

10 REFERENCES 165 10.1 Primary sources -,qj 10.2 sources Secondary ,

vi 11 GREEK ALPHABET 179

12 INDEX OF SYMBOLS 181

13 SUBJECT INDEX 195

NOTES 231

PRESSURE CONVERSION FACTORS 233

NUMERICAL ENERGY CONVERSION FACTORS

IUPAC PERIODIC TABLE OF THE ELEMENTS

vn