### Table 5 Perturbation theory analysis of 13C/12C (S,/S,)ffor alkyl ethers quot;

"... In PAGE 5: ...1672 See Table 1. (S2/S,)fmB includes all non-unity C and P factors; (SJS,) f ha includes all non-unity C factors (four stretches, 7-13 bends and two to four torsions) and 27 P factors (12 opposing stretch-bend, three opposing bend-bend and 12 adjacent bend-bend interactions); (S2/S,)fhB includes C factors for four stretches and 7-13 bends and P factors for only 15 interactions (12 opposing stretch-bend and three opposing bend-bend interactions); (S,/S,)f- is obtained from weight-averaged values of C and P factors listed in Table5 ; (S2/Sl)f,,,c, is ... In PAGE 6: ...i.e. C2(l3CH)-0], the pair of P factors will be P;H13CC/C13CO)opp and P;H13CO/C13CC)opp. (ii) The Kpp factors (for various pairs of opposing bends) are calculated from weight- averaged values of P factors (given in Table 3) and labelled as Pop and their values, which would be applicable for any type of apos;,C substitution site, are given in Table5 . (iii) Weight- averaged values of Ci factors (denoted by C), uniformly applicable for primary, secondary and tertiary quot;C substitu- P;H13CH/C13C~)opp and In the CaSe Of CCT-0 tion, for three types of stretch and nine types of bend are obtained from the data in Table 1 and are given in Table 5.... ..."

### Table 5: The convergence of the perturbation theory for mb at n = 14, = mb, s(MZ) = 0:118

### Table 4 Contributions to the removal energy (a.u.) of lithium in perturbation theory. Term

### Table 3. Comparison of Eiy, amp;n calculated by Rayleigh-Schrtidinger perturbation theory and by the asymptotic formula

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### Table 1. Leading-order perturbation theory values of the parameters of polynomial kdjul and kujdl relations, derived for the n 21 spectral index.

"... In PAGE 5: ... Indeed, in our simulations the skewness measured with an 8h21Mpc top-hat filter has the value of 1:77 ^ 0:11: 4 THE FORWARD RELATION With our models, we have tested the polynomial approximation of the mean forward DVDR (equation 4). We compare the coefficients a1, a2 and a3 computed from our simulations with the corresponding third-order perturbation theory (3PT) values ( Table1 ) in Fig. 3.... ..."

### Table 4 Perturbation theory analysis of apos; 3C/1 2C isotope effects in alkyl ethers: (S,/S,)f values at 300 K

"... In PAGE 4: ... 5% perturbation correction. In Table4 are listed the (S,/S,)fvalues obtained from con- sideration of C and P factors arranged in different ways. In this table are also included the (S,/S1)fe,,ct values with which the perturbation theory values are compared.... In PAGE 6: ... (iv) The (S,/S,)f values obtained from C and P factors and labelled as (SZ/Sl)f,.TB, are given in Table4 . The (S2/Sl)fPTB values calculated in such a simple manner [by considering only four C(Stretch), 7-13 C(Bend) and one Popp factors from a short-list of 17 C and P factors] are found to be within ca.... ..."

### Table 2 Perturbation theory analysis of apos;3C/12C(S2/Sl): Break-up of (S2/S,)fb, the Ci factors for torsions at 300 K

"... In PAGE 4: ... The largest A values for Pj- k factors (indicative of strong interactions) belong to the stretch-bend interactions. Table2 lists the Ci factors for torsions which vary in number (from two to four) for different types of substitution site. There is a fixed number of torsions for the sites P-0 (two torsions) and CCT-0 (four torsions).... ..."

### Table 3 Perturbation theory analysis of 13C/ apos;2C (S,/S,)f: Break-up of CORR apos; into individual Pj-k factors (T = 300 K) ~~ ~

"... In PAGE 4: ...e. and Table3 lists some of the various Pj-k factors which form CORR apos;. They consist of 12 opposite stretch-bend inter- actions, three opposite bend-bend interactions and 12 adjac- ent bend-bend interactions.... In PAGE 4: ...e. and CORR;p,) gt; CORR;p,-,, CORR;c amp;o, apos; CORR;c amp;c-o) From the values of C: factors for stretch, bend and torsion (Tables 1 and 2) and those of PjPk factors ( Table3 ), it is seen that the total value of (S,/Sl)fhB is composed of the follow- ing: ca. 73% from four stretches, ca.... In PAGE 6: ...i.e. C2(l3CH)-0], the pair of P factors will be P;H13CC/C13CO)opp and P;H13CO/C13CC)opp. (ii) The Kpp factors (for various pairs of opposing bends) are calculated from weight- averaged values of P factors (given in Table3 ) and labelled as Pop and their values, which would be applicable for any type of apos;,C substitution site, are given in Table 5. (iii) Weight- averaged values of Ci factors (denoted by C), uniformly applicable for primary, secondary and tertiary quot;C substitu- P;H13CH/C13C~)opp and In the CaSe Of CCT-0 tion, for three types of stretch and nine types of bend are obtained from the data in Table 1 and are given in Table 5.... ..."

### Table6 Ease of computation quot; of (S,/S,)f by the perturbation theory approach and accuracyb vis-a-vis (S,/S l)feract: D/H, 6O and 13C/1zC isotope effects apos; in alkyl ethers

"... In PAGE 7: ... The various approximations used in the perturbation theory analysis of isotope effects in ethers reduce substantially the efforts involved in evaluation of a particular isotope effect. The data in Table6 give a qualitative picture of the extent of computa- tional effort (represented by the number of C and P factors needing to be scanned) involved for obtaining an (S,/S,)f value of a certain degree of approximation and its accuracy [represented by 6, its deviation from (S2/S1)fexact] for a mod- erate size molecule, e.... ..."