9806 J. Phys. Chem. A, Vol. 104, No. 43, 2000
ADDITIONS AND CORRECTIONS 2000, Volume 104A James A. Miller,* Stephen J. Klippenstein, and Struan H. Robertson: A Theoretical Analysis of the Reaction between Vinyl and Acetylene: Quantum Chemistry and Solution of the Master Equation Page 7527-7528. Although the calculations presented in the paper were performed correctly, there are several errors in the presentation of the theory. Most notably, the partition function Q1(T) was omitted in several equations in the discussion following eq 9. For clarity we repeat that presentation here, making the appropriate corrections. Let xR(t) ) nR(t)/nR(0), xi(E,t) ) ni(E,t)/ne(0), and yi(E,t) ) xi(E,t)/fi(E). Then dividing by nR(0)fi(E), eq 2 becomes
dyi(E) dt
[
)Z
∫E∞
oi
M
1+
{
fi(E′)
Pi(E,E′)
fi(E)
-
] }
∑
From the detailed balance conditions (8) and (9), one can see that eq 10 is symmetric in E and E′ and in i and j. By this we mean that the coefficient of yi(E′) in eq 10 is identical to the coefficient of yi(E) in an analogous equation for dyi(E′)/dt, i.e., for any specific values of E and E′. Likewise, the coefficient of yj(E) in (10) is the same as the coefficient of yi(E) in an analogous equation for dyj(E)/dt for any values of i and j. Multiplying eq 5 by (Keq1nm/Q1(T))1/2/nR(0), we obtain
[( ) ] ( ) ∫ ( )∫
d Keq1nm dt Q1(T)
1/2
xR )
Keq1nm
dt Q1(T)δE
(
N1
1/2
xR )
∑ l)1
( ) Keq1nm
xR
Keq1nm δE Q1(T)
y1(El)
N1
3/2
(δE)
)
1/2
f1(El) kd1(El) -
kd1(El) f12(El) ∑ l)1
1/2
Q1(T)
(12)
where N1 is the number of grid points in the energy space of well 1 and δE is the spacing between grid points. Similarly, if we write eq 10 as a sum, the next-to-last term in the component equation for dy1(El)/dt can be written as
(
Keq1nm
Q1(T)δE
) [( 1/2
xR
Keq1nm δE Q1(T)
)
1/2
f1(El) kd1(El)
]
[
|w(t)〉 f y1(E01), ..., y1(El), ..., yi(E0i), ..., yi(El), ...,
(
δ(E - E′) yi(E′) dE′ +
fj(E) Keqi yj(E) + kdi(E) fi(E) xRnmδi1 kij(E) fi(E) Qi(T) j*i i ) 1, ..., M (10) kpi(E) yi(E) M
[( ) ] Keq1nm
(13)
Now the coefficient of y1(El) in eq 12 is the same as that of (Keq1nm/Q1(T)δE)1/2xR in (13). Then the vector of unknowns becomes
kji(E) + kdi(E)δi1 ∑ j*i Z
d
1/2
∞
0
Q1(T) Keq1nm xR Q1(T)
kd1(E) f1(E) y1(E) dE -
3/2
∞
0
kd1(E) f12(E) dE (11)
Approximating the integrals in eq 11 as sums and rearranging,
Keq1nm
Q1(T)δE
) ] 1/2
T
xR
We apologize if this has caused any inconvenience. 10.1021/jp003193l Published on Web 10/07/2000
2000, Volume 104A Karol Jackowski,* Marcin Wilczek, Magdalena Pecul, and Joanna Sadlej: : Nuclear Magnetic Shielding and SpinSpin Coupling of 1,2-13C-Enriched Acetylene in Gaseous Mixtures with Xenon and Carbon Dioxide Page 5956. In the caption for Figure 1, the absolute shielding of liquid TMS should be σ[Si(CH3)4] ) 186.37 ppm and σ[Si(CH3)4] ) 32.775 ppm. Page 5956. In lines 4 and 5 of column two should be σ(liq TMS) - σ0(CO) ) 185.77 ppm and σ(liq TMS) - σ0(CH4) ) 2.164 ppm. Page 5957. In line 11 of column one “1J (29Si19F) in SF6” should read “1J(29Si19F) in SiF4”. 10.1021/jp003138c Published on Web 09/30/2000
