Report HUKI 1-89 ISSN 0784-0365 (Electronic version, 8 December, 1989) SOME CONSTANTS AND CONVERSION FACTORS OF USE FOR QUANTUM MECHANICAL CALCULATIONS Pekka Pyykkö and Yongfang Zhao Department of Chemistry, University of Helsinki, [ Et. Hesperiankatu 4, SF-00100 Helsinki, Finland] Current address: POB 55 (A.I. Virtasen aukio 1), FIN-00014 Helsinki, Finland December 1989 Table 1 below contains the starting data from Cohen and Taylor /1/. The newer gas constant value R = 8.314471 (1.4) J/K mol /2/ was not yet adopted). Table 2, analogous to that of Manne /3/, gives energy conversion factors, Table 3 some electromagnetic quantities and Table 4 some miscellaneous data. The "thermochemical calorie" of 4.184 J /4/ is used in Table 2. References: 1. E.R. Cohen and B.N. Taylor, J. Phys. Chem. Ref. Data 17 (1988) 1795. 2. M.R. Moldover, J.P.M. Trusler, T.J. Edwards, J.B. Mehl and R.S. Davis, Phys. Rev. Lett. 60 (1988) 249. 3. R. Manne, "Some Constants and Conversion Factors of Use for Quantum Mechanical Calculations", Unpublished Report, Quantum Chemistry Group, University of Uppsala, June 15, 1963. 4. "Le Systeme International d'Unites (SI)", Bureau International des Poids et Mesures, Sevres, France (1985). Table 1. Summary of the 1986 recommended values of the fundamental physical constants /1/. ================================================================================ Relative uncertainty Quantity Symbol Value Units (ppm) -------------------------------------------------------------------------------- Speed of light in vacuum c= 299792458 a m/s (exact) Permeability of vacuum mu 0= 12.56637061D-07 a N/A*A (exact) (m kg s-2 A-2) Permittivity of vacuum epsil 0= 8.85418782D-12 a F/m (exact) (m-3 kg-1 s4 A2) Newton constant of gravitation G= 6.67259000D-11 a m**3/kg*s2 128 Planck constant h= 6.62607550D-34 a Js 0.60 h/2*pi h/2pi= 1.05457267D-34 b Js 0.60 Elementary charge e= 1.60217733D-19 a C (= s A) 0.30 Magnetic flux quantum h/2e phi 0= 2.06783462D-15 b Wb 0.30 (= V s =m2 kg s-2 A-1) Electron mass me= 9.1093897D-31 a kg 0.59 Proton mass mp= 1.6726231D-27 a kg 0.59 Proton-electron mass ratio me/mp= 1836.1528D+00 b 0.020 Fine-structure constant a= 7.29735301D-03 b 0.045 Inverse fine-structure constant 1/a= 137.03599D+00 b 0.045 Rydberg constant RH= 1.09737313D+07 b 1/m 0.0012 Avogadro constant NA,L= 6.02213670D+23 a 1/mol 0.59 Faraday constant NAe F= 9.64853090D+04 a C/mol 0.30 Molar gas constant R= 8.31451000D+00 a J/mol*K 8.4 Boltzmann constant R/NA k= 1.38065800D-23 a J/K 8.5 Stefan-Boltzmann constant (pi*pi/60)*k**4/bh**3*c*c sigma= 5.67051000D-08 a W/m*m*K**4 34 (Unified) atomic mass unit 1 u=mu=1/12m(12C) u= 1.66054020D-27 a kg 0.59 Bohr magneton beta= 9.27401549D-24 b J/T=m2 A 0.34 Nuclear magneton beta_n= 5.05078647D-27 b J/T 0.34 Bohr radius a 0= 5.2917726D-11 b m 0.045 -------------------------------------------------------------------------------- a "Primary",ref. 1. b Recalculated from the primary ones. Table 2. Conversion of energy units. -------------------------------------------------------------------------------- a.u. J eV kcal/mol ================================================================================ 1 a.u. = 1.00000000D+00 4.35974812D-18 2.72113957D+01 6.27509541D+02 1 J = 2.29371049D+17 1.00000000D+00 6.24150636D+18 1.43932522D+20 1 eV = 3.67493095D-02 1.60217733D-19 1.00000000D+00 2.30605423D+01 1 kcal/mol = 1.59360127D-03 6.94770014D-21 4.33641146D-02 1.00000000D+00 1 1/cm = 4.55633538D-06 1.98644746D-23 1.23984245D-04 2.85914392D-03 1 MHz = 1.51982989D-10 6.62607550D-28 4.13566924D-09 9.53707754D-08 1 K = 3.16682974D-06 1.38065800D-23 8.61738569D-05 1.98721587D-03 1 kJ/mol = 3.80879844D-04 1.66054019D-21 1.03642721D-02 2.39005736D-01 -------------------------------------------------------------------------------- -------------------------------------------------------------------------------- 1/cm MHz K kJ/mol ================================================================================ 1 a.u. = 2.19474625D+05 6.57968374D+09 3.15773213D+05 2.62549992D+03 1 J = 5.03411250D+22 1.50918896D+27 7.24292330D+22 6.02213670D+20 1 eV = 8.06554093D+03 2.41798834D+08 1.16044475D+04 9.64853090D+01 1 kcal/mol = 3.49755041D+02 1.04853924D+07 5.03216592D+02 4.18400000D+00 1 1/cm = 1.00000000D+00 2.99792458D+04 1.43876866D+00 1.19626582D-02 1 MHz = 3.33564095D-05 1.00000000D+00 4.79921566D-05 3.99031324D-07 1 K = 6.95038770D-01 2.08367381D+04 1.00000000D+00 8.31451121D-03 1 kJ/mol = 8.35934612D+01 2.50606892D+06 1.20271652D+02 1.00000000D+00 -------------------------------------------------------------------------------- Table 3. Conversion of electromagnetic quantities. -------------------------------------------------------------------------------- S.I. e.s.u. ================================================================================ El. field gradient q 1 a.u.= 9.71736408D+21 V/m**2 3.24136376D+15 esu cm-3 Multipole moment Q1 1 a.u.= 8.47835805D-30 C m**1 2.54174780D-18 esu cm**1 Multipole moment Q2 1 a.u.= 4.48655426D-40 C m**2 1.34503513D-26 esu cm**2 Multipole moment Q3 1 a.u.= 2.37418248D-50 C m**3 7.11762002D-35 esu cm**3 Multipole moment Q4 1 a.u.= 1.25636337D-60 C m**4 3.76648264D-43 esu cm**4 Multipole moment Q5 1 a.u.= 6.64838925D-71 C m**5 1.99313695D-51 esu cm**5 Multipole moment Q6 1 a.u.= 3.51817639D-81 C m**6 1.05472275D-59 esu cm**6 Multipole moment Q7 1 a.u.= 1.86173893D-91 C m**7 5.58135291D-68 esu cm**7 Multipole moment Q8 1 a.u.= 9.85189902-102 C m**8 2.95352502D-76 esu cm**8 -------------------------------------------------------------------------------- Table 4. Miscellaneous. -------------------------------------------------------------------------------- ================================================================================ 1 fermi = 10**-15 m 1 barn = 10**-28 m**2 1 oersted = (1000/4 pi) A/m 1 gauss = 10**-4 T (T = Wb/m**2 = kg s-2 A-1) 1 erg = 10**-7 J 1 dyn = 10**-5 N 1 Hz = 3.85000804D-20*gAgB*K S.I. = 3.85000804D-01*gAgB*(K /10**19 m-2 kg s-2 A-2) (in NMR nuclear spin-spin coupling; gX = nuclear g-factor K = reduced coupling constant) Electron g-factor g_e = 2.002319304386(20) 1 e = 4.80320680D-10 esu 1 Debye = 10**-18 esu cm (1 au of q)x(1 barn of Q) = 234.964730D+00 MHz of nuclear quadrupole coupling --------------------------------------------------------------------------------