Texto Completo em PDF - Programa de Pós-Graduação em Física ...
Texto Completo em PDF - Programa de Pós-Graduação em Física ...
Texto Completo em PDF - Programa de Pós-Graduação em Física ...
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6 − 311 + +G(3df, 3pd) <br />
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6 − 311 + +G(3df, 3pd) <br />
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eV <br />
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eV
CH4
− <br />
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1 <br />
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2
eV <br />
eV <br />
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+ <br />
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3 Ultraviolet<br />
4 V acuum Ultraviolet<br />
5 T hreshold P hotoeletrons P hotoions Coinci<strong>de</strong>nce
eV <br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
HCOOH + hν → COOH + + H + e − <br />
→ HCOO + + H + e − <br />
→ HCO + + OH + e − <br />
→ COH + + OH + e − <br />
→ H2O + + CO + e − <br />
<br />
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<br />
+
eV <br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
HCOOH + hν → COOH + + H + e − <br />
→ HCOO + + H + e − <br />
→ HCO + + OH + e − <br />
→ COH + + OH + e − <br />
→ H2O + + CO + e − <br />
<br />
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+
Erot x 2 Evib x 4 Eele<br />
<br />
<br />
Erot Evib Eele <br />
x <br />
x =<br />
<br />
m<br />
1<br />
4<br />
M<br />
<br />
m M <br />
x ≈ 10 −1
HMΨ 0 (r, R; t) = i ∂<br />
∂t Ψ0 (r, R; t) <br />
Ψ 0 (r, R; t) t r<br />
R <br />
HM <br />
N M HM <br />
HM = −<br />
+<br />
N<br />
N<br />
j=1<br />
N<br />
2<br />
2me<br />
e 2<br />
rjk<br />
j=1 j>k<br />
∇ 2<br />
j −<br />
+<br />
M<br />
M<br />
L=1<br />
M<br />
L=1 L>A<br />
2<br />
2ML<br />
N<br />
M<br />
∇ 2 e<br />
L −<br />
j=1 L=1<br />
2Zl rjL<br />
e 2 ZLZA<br />
RLA<br />
<br />
rjL j L rjk j<br />
k RLA L A me <br />
−e ML L ZL <br />
∇ 2<br />
j ∇ 2<br />
L <br />
<br />
<br />
<br />
<br />
<br />
1 0
Ψ 0 (r, R; t) = ψ 0 (r, R)T (t) <br />
<br />
<br />
HMψ 0 (r, R)<br />
ψ 0 (r, R)<br />
1 ∂<br />
= i T (t) <br />
T (t) ∂t<br />
<br />
<br />
E <br />
HMψ 0<br />
α(r, R) = Eαψ 0<br />
α(r, R) <br />
iEαt<br />
−<br />
T (t) = e <br />
ψ 0<br />
α(r, R) <br />
α Eα <br />
<br />
<br />
Ψ 0 (r, R; t) = <br />
α<br />
aαψ 0<br />
iEαt<br />
−<br />
α(r, R)e <br />
<br />
<br />
<br />
ψ 0∗<br />
<br />
α (R, r)ψ 0<br />
α<br />
α<br />
′(R, r)dRdr = δαα ′ <br />
ψ 0<br />
α(R, r)ψ 0∗<br />
α (R ′ , r ′ ) = δ(R − R ′ )δ(r − r ′ ) <br />
δαα ′ δ(R − R′ ) δ(r − r ′ )
N M <br />
<br />
H ele = −<br />
N<br />
j=1<br />
2<br />
2me<br />
∇ 2<br />
j −<br />
N<br />
M<br />
j=1 L=1<br />
e 2 ZL<br />
rjL<br />
+<br />
N<br />
N<br />
e 2<br />
rjk<br />
j=1 j>k<br />
<br />
<br />
[H ele , R] = 0 <br />
H ele R <br />
R <br />
<br />
H ele χ ele<br />
n (r; R) = E ele<br />
n (R)χ ele<br />
n (r; R)
χ ele<br />
n n <br />
<br />
<br />
<br />
<br />
<br />
<br />
E ele<br />
n = E ele<br />
n (R) <br />
<br />
<br />
<br />
<br />
<br />
<br />
Vn(R) = E ele<br />
n (R) +<br />
M<br />
M<br />
L=1 A>L<br />
e 2 ZLZA<br />
RLA<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
ψ 0 (r; R) = <br />
n<br />
φ nuc<br />
n (R)χ ele<br />
n (r; R)
M <br />
−<br />
2<br />
∇<br />
2ML<br />
2<br />
<br />
L + Vn(R)<br />
n<br />
<br />
L=1<br />
<br />
Hele +<br />
<br />
n<br />
M<br />
L=1 A>L<br />
φ nuc<br />
n (R)χ ele<br />
M<br />
e 2 ZLZA<br />
RLA<br />
n (r; R) = E <br />
<br />
n<br />
n<br />
φ nuc<br />
n (R)χ ele<br />
n (r; R) =<br />
φ nuc<br />
n (R)χ ele<br />
n (r; R) <br />
Vn(R)φ nuc<br />
n (R)χ ele<br />
n (r; R) <br />
<br />
<br />
M <br />
−<br />
L=1<br />
2<br />
<br />
<br />
∇L · ∇L ·<br />
2ML<br />
n<br />
= <br />
(E − Vn(R))φ nuc<br />
− M <br />
n L=1<br />
2 2<br />
∇<br />
2ML<br />
= <br />
[E − Vn(R)]φ nuc<br />
n<br />
n<br />
Lφ nuc<br />
n<br />
n (R)χ ele<br />
n (R)χ ele<br />
φ nuc<br />
n (R)χ ele<br />
n (r; R)<br />
<br />
n (r; R) <br />
χ ele<br />
n + 2[∇Lφ nuc<br />
n ][∇Lχ ele<br />
n ] + φ nuc<br />
n [∇ 2<br />
Lχ ele<br />
n ] <br />
n (r; R) <br />
χ ele∗<br />
s (r; R) <br />
<br />
− <br />
n<br />
+ φ nuc<br />
n<br />
M<br />
L=1<br />
<br />
2<br />
∇ 2 Lφ nuc<br />
<br />
n<br />
χ ele∗<br />
s χ ele<br />
n dr + 2∇L(φ nuc<br />
<br />
n )<br />
2ML<br />
χ ele∗<br />
s ∇ 2 Lχ ele<br />
n dr = <br />
(E − Vn(R))φ nuc<br />
<br />
n<br />
n<br />
χ ele∗<br />
s ∇Lχ ele<br />
n dr +<br />
χ ele∗<br />
s χ ele<br />
n dr
−<br />
<br />
<br />
<br />
n<br />
M<br />
L=1<br />
M<br />
L=1<br />
2<br />
2ML<br />
2<br />
2ML<br />
∇ 2<br />
Lφ nuc<br />
s + (Vs(R) − E)φ nuc<br />
s =<br />
<br />
2<br />
X L ns(R) =<br />
χ ele∗<br />
s ∇Lχ ele<br />
<br />
n dr ∇L +<br />
M<br />
χ ele∗<br />
s ∇ 2 Lχ ele<br />
<br />
n dr φ nuc<br />
n<br />
<br />
<br />
<br />
Cns =<br />
L=1<br />
2<br />
(X<br />
ML<br />
L ns∇L + Y L<br />
ns) <br />
<br />
Y L<br />
ns(R) = 1<br />
2<br />
<br />
−<br />
M<br />
L=1<br />
2<br />
2ML<br />
<br />
χ ele∗<br />
s (r; R)∇Lχ ele<br />
n (r; R)dr<br />
χ ele∗<br />
s (r; R)∇ 2<br />
Lχ ele<br />
n (r; R)dr <br />
∇ 2<br />
Lφ nuc<br />
s (R) + (Vs(R) − E)φ nuc<br />
s (R) = <br />
n<br />
Cnsφ nuc<br />
n<br />
<br />
Cns <br />
<br />
<br />
Cns <br />
<br />
<br />
<br />
Hnuc(R)φ nuc<br />
s<br />
Hnuc = −<br />
M<br />
L=1<br />
= Eφ nuc<br />
s (R) <br />
2<br />
2ML<br />
∇ 2 L + Vs(R) <br />
<br />
Cns = 0
E <br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
3M − 3
∇ · E = 4πρ <br />
∇ · B = 0 <br />
∇ × E + 1 ∂B<br />
c ∂t<br />
= 0 <br />
∇ × B − 1 ∂E<br />
c ∂t<br />
=<br />
4π<br />
j<br />
c
E(r, t) B(r, t) ρ(r, t) <br />
j(r, t) <br />
φ(r, t) <br />
A(r, t) <br />
<br />
<br />
B(r, t) = ∇ × A(r, t) <br />
<br />
∇ × E + 1<br />
<br />
∂A(r, t)<br />
= 0 <br />
c ∂t<br />
<br />
<br />
<br />
<br />
E(r, t) = −∇φ − 1 ∂A(r, t)<br />
<br />
c ∂t<br />
<br />
<br />
(A, φ) <br />
(A ′ , φ ′ ) <br />
<br />
A ′ (r, t) = A(r, t) + ∇χ(r, t) <br />
φ ′ (r, t) = φ(r, t) − ∂<br />
χ(r, t) <br />
∂t<br />
χ(r, t) <br />
<br />
∇ · A = 0
∇ 2 φ = 0 <br />
∇ 2 A − 1 ∂ 1<br />
∇ φ −<br />
c ∂t c2 ∂2 A<br />
∂t2 = 0 <br />
<br />
<br />
<br />
∇ 2 A − 1<br />
c 2<br />
<br />
∂2A = 0 <br />
∂t2 <br />
<br />
A(r, t) = A ′ 0e i(k·r−ωt) + A ∗ 0e −ı(k·r−ωt) <br />
k = kû k û ω = kc <br />
A ′ 0 = A ∗ 0 <br />
<br />
A(r, t) = 2A ′ 0 cos[(k · r − ωt)] <br />
2A ′ 0 = A0ˆε ˆε <br />
<br />
<br />
A(r, t) = A0ˆε cos[(k · r − ωt)] <br />
E = − ω<br />
c A0ˆεsen(k · r − ωt) <br />
B = −A0(kû × ˆε)sen(k · r − ωt) <br />
A0 <br />
V N <br />
ω
2πN<br />
A0 = 2c<br />
ωV<br />
1<br />
2<br />
<br />
<br />
<br />
<br />
<br />
H =<br />
+<br />
N<br />
<br />
pj + e<br />
cA(rj, t) <br />
2<br />
− eφ(rj) +<br />
2me<br />
M<br />
<br />
PL − eZL<br />
c A(RL, t) <br />
2<br />
+ eZLφ(RL) + V (r, R) <br />
2ML<br />
j=1<br />
L=1<br />
me ML L −e eZL <br />
rj RL pj PL <br />
V (r, R) A φ <br />
<br />
<br />
<br />
<br />
<br />
<br />
HM =<br />
N p2 j<br />
+<br />
2me<br />
j=1<br />
M P 2 L<br />
+ V (r, R) <br />
2ML<br />
L=1<br />
<br />
V (r, R)
H ′ (t) = −<br />
+<br />
N<br />
j=1<br />
M<br />
<br />
eZL<br />
L=1<br />
2cML<br />
e<br />
2mec<br />
<br />
<br />
PL · A(RL, t) + A(RL, t) · PL − eZL<br />
c |A(RL, t)| 2<br />
<br />
pj · A(rj, t) + A(rj, t) · pj + e<br />
c |A(rj, t)| 2<br />
<br />
<br />
− eφ<br />
<br />
− eZLφ +<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
pj PL<br />
−i∇j −i∇L <br />
H ′ (t) = i<br />
− i<br />
M<br />
<br />
eZL<br />
L=1<br />
N<br />
j=1<br />
2cML<br />
<br />
[∇L · A(RL, t) + A(RL, t) · ∇L]<br />
<br />
e<br />
2mec [∇j<br />
<br />
· A(rj, t) + A(rj, t) · ∇j]<br />
<br />
j L ∇ <br />
<br />
ψ(r, R) <br />
<br />
<br />
∇k · Aψ = A · (∇kψ) + ψ∇k · A<br />
= A · (∇kψ) <br />
k = j k = L k
H ′ (t) = i<br />
M<br />
<br />
eZL<br />
A(RL, t) · ∇L − i<br />
cML<br />
L=1<br />
H ′ (t) = i<br />
− i<br />
M<br />
<br />
eZL<br />
L=1<br />
N<br />
j=1<br />
N<br />
j=1<br />
<br />
e<br />
mec A(rj,<br />
<br />
t) · ∇j<br />
A0 cos(k · RL − ωt)ˆε · ∇L<br />
cML<br />
<br />
e<br />
mec A0<br />
<br />
cos(k · rj − ωt)ˆε · ∇j<br />
<br />
<br />
H ′ (t) = i<br />
− i<br />
M<br />
<br />
eZL<br />
L=1<br />
N<br />
j=1<br />
e ik·RL e −iωt + e −ik·RL e iωt ˆε · ∇L<br />
A0<br />
2cML<br />
<br />
e<br />
2mec A0<br />
ik·rj −iωt −ik·rj iωt<br />
e e + e e ˆε · ∇j<br />
e ±ik·r = e ±ikz <br />
<br />
<br />
<br />
<br />
<br />
<br />
e ±ikz = 1 ± ikz ∓ k2<br />
2 z2 ± ... <br />
<br />
<br />
kz = 2πz<br />
λ ≪ 1 eikz <br />
<br />
<br />
H ′ (t) = iA0<br />
2c<br />
H ′ (t) = iA0<br />
c<br />
<br />
M <br />
eZL<br />
cos(ωt)ˆε · ∇L −<br />
L=1<br />
ML<br />
M<br />
<br />
eZL −iωt iωt<br />
e + e <br />
ˆε · ∇L<br />
L=1<br />
ML<br />
N<br />
<br />
e<br />
j=1<br />
− iA0<br />
2c<br />
me<br />
N<br />
<br />
e<br />
j=1<br />
cos(ωt)ˆε · ∇j<br />
me<br />
<br />
e −iωt + e iωt ˆε · ∇j
[HM + H ′ (t)] ψ(R, r, t) = i ∂<br />
ψ(R, r, t) <br />
∂t<br />
<br />
H ′ (t) HM <br />
<br />
<br />
<br />
ψ(R, r, t) = <br />
α<br />
<br />
aα(t)ψ 0<br />
iEαt<br />
−<br />
α(R, r)e <br />
aα(t) <br />
ψ 0<br />
α(R, r) t <br />
<br />
<br />
<br />
α<br />
<br />
α<br />
<br />
aα(t) i ∂<br />
∂t<br />
<br />
|aα(t)| 2 = 1. <br />
α<br />
<br />
ψ 0<br />
α(R, r)e<br />
iEαt<br />
− <br />
<br />
− HMψ 0<br />
α(R, r)e<br />
iEαt<br />
− <br />
<br />
=<br />
<br />
−i d<br />
dt (aα(t)) ψ 0<br />
iEαt<br />
−<br />
α(R, r)e + H ′ (t)aα(t)ψ 0<br />
iEαt<br />
−<br />
α(R, r)e
α<br />
<br />
−i d<br />
dt (aα(t)) ψ 0<br />
iEαt<br />
−<br />
α(R, r)e + H ′ (t)aα(t)ψ 0<br />
iEαt<br />
−<br />
α(R, r)e <br />
<br />
= 0 <br />
ψ 0<br />
α ′<br />
∗ iE<br />
α ′ t<br />
(R, r)e <br />
<br />
<br />
<br />
α<br />
<br />
<br />
α<br />
ψ 0<br />
α ′<br />
<br />
∗ 0<br />
(R, r)ψα(R, r)dRdr e i(E α ′ −Eα)t<br />
<br />
d<br />
dt aα(t)i<br />
<br />
=<br />
ψ 0<br />
α ′<br />
<br />
∗ ′ 0<br />
(R, r)H (t)ψα(R, r)dRdr e i(E α ′ −Eα)t<br />
aα(t)<br />
<br />
<br />
<br />
<br />
ωα ′ α = <br />
<br />
<br />
H ′ α ′ <br />
α =<br />
Eα ′ − Eα<br />
<br />
ψ 0∗<br />
α ′(R, r)H′ (t)ψ 0<br />
α(R, r)dRdr <br />
i d <br />
aα ′(t) =<br />
dt<br />
α<br />
H ′ α ′ αaα(t)e iω α ′ α t <br />
<br />
H ′ (t)<br />
<br />
d<br />
A0 −iωt iωt<br />
aα ′(t) = e + e<br />
dt 2c<br />
ˆε ·<br />
<br />
<br />
ψ 0<br />
α ′<br />
<br />
M<br />
∗ eZL<br />
∇L −<br />
α<br />
L=1<br />
ML<br />
N<br />
e<br />
∇j<br />
me<br />
j=1<br />
<br />
ψ 0<br />
αdRdraα(t)e iω α ′ α t <br />
<br />
<br />
<br />
<br />
aα(t)
t = 0<br />
d<br />
A0 −iωt iωt<br />
aα ′(t) = e + e<br />
dt 2c<br />
ˆε ·<br />
<br />
<br />
ψ 0<br />
α ′<br />
<br />
M<br />
∗ eZL<br />
∇L −<br />
α<br />
L=1<br />
ML<br />
N<br />
e<br />
∇j<br />
me<br />
j=1<br />
<br />
<br />
ψ 0<br />
αdRdraα(0)e iω α ′ α t <br />
<br />
ψ 0<br />
i (R, r) aα(0) α = i <br />
<br />
d A0 −iωt iωt<br />
aα ′(t) = e + e<br />
dt 2c<br />
<br />
ˆε ·<br />
ψ 0<br />
α ′<br />
∗<br />
<br />
M<br />
eZL<br />
∇L −<br />
L=1<br />
ML<br />
N<br />
e<br />
∇j<br />
me<br />
j=1<br />
<br />
ψ 0<br />
i dRdre iω α ′ i t <br />
pj (PL) <br />
<br />
pj = ime<br />
[HM, rj]<br />
<br />
d<br />
aα ′(t)<br />
dt<br />
=<br />
A0<br />
−<br />
2c2 −iωt iωt<br />
e + e <br />
ˆε ·<br />
<br />
−<br />
PL = iML<br />
[HM, RL] <br />
N<br />
e(HMrj − rjHM)<br />
j=1<br />
HM <br />
d<br />
A0<br />
aα ′(t) = −<br />
dt<br />
·<br />
<br />
2c 2<br />
ψ 0<br />
α ′<br />
∗<br />
M<br />
L=1<br />
eZL(HMRL − RLHM)<br />
ψ 0<br />
i dRdre iω α ′ i t <br />
−iωt iωt<br />
e + e (Eα ′ − Ei)ˆε ·<br />
ψ 0<br />
α ′<br />
<br />
M<br />
N<br />
<br />
∗<br />
eZLRL − erj<br />
L=1<br />
j=1<br />
ψ 0<br />
i dRdre iω α ′ i t <br />
<br />
M = −<br />
N<br />
erj +<br />
j=1<br />
M<br />
eZLRL<br />
L=1
Mα ′ <br />
i =<br />
ψ 0<br />
α ′<br />
∗<br />
<br />
−<br />
N<br />
erj +<br />
j=1<br />
M<br />
<br />
eZLRL<br />
L=1<br />
ψ 0<br />
i dRdr <br />
aα ′(t)<br />
d<br />
dt aα ′(t) = −A0ωα ′ i −iωt iωt<br />
e + e<br />
2c<br />
ˆε · Mα ′ ie iωα ′ it <br />
0 t aα ′(0) = 0 α′ = i<br />
<br />
f <br />
af(t) = − A0<br />
2c ωfiˆε<br />
<br />
i(ωfi+ω)t<br />
1 − e 1 − ei(ωfi−ω)t<br />
· Mfi<br />
+<br />
ωfi + ω ωfi − ω<br />
<br />
ωfi f <br />
i <br />
<br />
ω <br />
ωfi <br />
<br />
<br />
af(t) = − A0<br />
2c ωfiˆε · Mfi<br />
<br />
i(ωfi−ω)t<br />
1 − e<br />
ωfi − ω<br />
<br />
<br />
<br />
Pfi = |af(t)| 2 =<br />
<br />
=<br />
<br />
A0 <br />
− 2c ωfiˆε<br />
2<br />
<br />
<br />
i(ωfi−ω)t<br />
· Mfi<br />
<br />
1 − e<br />
ωfi − ω<br />
<br />
<br />
<br />
−A0 c ωfiˆε<br />
2<br />
2<br />
· Mfi<br />
<br />
sen<br />
<br />
(ωfi − ω) t<br />
<br />
2<br />
(ωfi − ω) 2<br />
δ(ωfi − ω) = 2<br />
π lim<br />
t→∞<br />
sen2 (ωfi − ω) t<br />
<br />
2<br />
(ωfi − ω) 2t 2
Pfi = π<br />
2<br />
<br />
<br />
<br />
−A0 c ωfiˆε<br />
<br />
<br />
· Mfi<br />
<br />
2<br />
<br />
tδ(ωfi − ω) <br />
<br />
<br />
<br />
κfi = d<br />
dt Pfi<br />
<br />
A0 <br />
<br />
κfi = 4π2 N<br />
V<br />
ω 2 fi<br />
ω |ˆε · Mfi| 2 δ(ωfi − ω) <br />
<br />
<br />
<br />
σabs <br />
<br />
<br />
ωfi <br />
<br />
U<br />
At<br />
= Nωc<br />
V<br />
<br />
N V ω <br />
<br />
σ(ω) ≡ ωfiκfi<br />
N ωc<br />
V<br />
<br />
<br />
i f <br />
<br />
σ(ω) = 4π2<br />
c<br />
ω 2 fi<br />
ω |ε · Mfi| 2 δ(ωfi − ω)
ω <br />
ψ 0<br />
i (r, R) ψ 0<br />
f(r, R)<br />
σ(ωfi) = 4π2<br />
c ωfi|ε · Mfi| 2
ω <br />
ψ 0<br />
i (r, R) ψ 0<br />
f(r, R)<br />
σ(ωfi) = 4π2<br />
c ωfi|ε · Mfi| 2
eV <br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
cm MeV
e v<br />
E B <br />
<br />
F = e(E + v × B) <br />
F = dp dt dU = v · F p U <br />
dt<br />
<br />
<br />
<br />
dp<br />
dt<br />
dU<br />
dt<br />
= e(E + v × B) <br />
= ev · E <br />
v·(v×B) = 0 <br />
v <br />
<br />
dp<br />
dt<br />
dU<br />
dt<br />
= ev × B <br />
= 0 <br />
<br />
<br />
<br />
p = γm0v = U<br />
c<br />
v <br />
2<br />
U = γm0c 2 <br />
U 2 − p 2 c 2 = m 2 0c 4 <br />
1
m0 γ =<br />
√ 1<br />
1−v2 /c2 <br />
<br />
a <br />
v2<br />
R <br />
dp<br />
dt<br />
= γm0<br />
v2 ˆr <br />
R<br />
R <br />
<br />
<br />
p = eRB <br />
<br />
<br />
<br />
<br />
U = ecBR <br />
<br />
<br />
<br />
<br />
<br />
<br />
S = c<br />
E × B <br />
4π<br />
B = n × E <br />
n <br />
<br />
<br />
A × (B × C) = (A · C)B − (A · B)C <br />
n · E = 0
S = c<br />
4π [E2 n] <br />
r ′ <br />
r <br />
<br />
r >> r ′ <br />
E(r, t) = e<br />
c<br />
n × [(n − β) × ˙ β]<br />
|r − r ′ |[1 − (n · β)] 3<br />
<br />
β ≡ v<br />
c <br />
t ′ t <br />
<br />
dU<br />
dtdA<br />
= [S · n]ret<br />
<br />
ret <br />
<br />
dU<br />
dAdt<br />
⎧<br />
⎨<br />
e2<br />
=<br />
4π ⎩<br />
1<br />
|r − r ′ | 2<br />
<br />
<br />
n<br />
× [(n − β) ×<br />
<br />
<br />
˙ β]<br />
(1 − β · n) 3<br />
2<br />
<br />
<br />
<br />
<br />
⎫ ⎬<br />
⎭<br />
<br />
<br />
r ∆t <br />
t ′ = T1 t ′ = T2 <br />
U =<br />
t=T2+r(T2)/c<br />
t=T1+r(T1)/c<br />
[S · n]retdt <br />
t ′ t <br />
<br />
t = t ′ + r(t′ )<br />
c<br />
<br />
<br />
t ′ =T2<br />
U = [S · n] dt<br />
dt ′ dt′ <br />
t ′ =T1
dP (t ′ )<br />
dA<br />
= [S · n] dt<br />
dt ′<br />
<br />
<br />
dA = r 2 dΩ dt<br />
dt ′ = 1 − β · n<br />
<br />
<br />
dP (t ′ )<br />
dΩ<br />
e2 |n × [(n − β) ×<br />
=<br />
4πc<br />
˙ β]| 2<br />
(1 − β · n) 5<br />
<br />
<br />
<br />
β · ˙ β = 0 β<br />
ˆ k ˙ β î <br />
β = β ˆ k <br />
˙β = ˙ βî <br />
ˆn = senθ cos φî + senθsenφˆj + cos θ ˆ k <br />
<br />
<br />
dP (t ′ )<br />
dΩ<br />
e2<br />
=<br />
4πc3 |ˆv|<br />
(1 − β cos θ) 3<br />
<br />
1 − sen2θ cos2 φ<br />
γ2 (1 − β cos θ) 2<br />
<br />
<br />
γ >> 1 β 1 θ <br />
θ <br />
1 − β cos θ ≈ 1<br />
γ2 2 2<br />
1 + γ θ <br />
senθ ≈ θ <br />
<br />
dP (t ′ )<br />
dΩ<br />
= 2e2<br />
πc 3<br />
γ 6 | ˙v| 2<br />
(1 + γ 2 θ 2 ) 3<br />
<br />
1 − 4γ2θ 2 cos2 φ<br />
(1 + γ2θ 2 ) 2
P (t ′ ) = 2 e<br />
3<br />
2 | ˙v| 2<br />
c3 γ4 <br />
<br />
R <br />
| ˙v| 2 = v2<br />
R<br />
<br />
<br />
P = 2 e<br />
3<br />
2c R β4γ 4 <br />
γ 4 <br />
<br />
<br />
<br />
<br />
<br />
δt =<br />
2πR/v δE = P δt <br />
δE = 4π<br />
3<br />
e 2<br />
R β3 γ 4 <br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
θ
〈θ 2 〉 1/2 = 1<br />
γ<br />
= mc2<br />
E<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
MeV <br />
m <br />
m <br />
MeV <br />
<br />
GeV <br />
mA <br />
KeV <br />
KW h
m m <br />
10 −9 <br />
10 −11 mbar
eV <br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
eV <br />
<br />
<br />
eV <br />
<br />
<br />
<br />
<br />
<br />
<br />
nhν<br />
n = 1, 2, 3, ... hν <br />
hν <br />
<br />
<br />
<br />
<br />
<br />
2
eV <br />
<br />
eV <br />
eV <br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
3
10 −8
4
1 2 1 2 3 4 <br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
4 <br />
2 <br />
3 <br />
1 <br />
1 <br />
2 <br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
5
EI <br />
EII <br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
E <br />
<br />
F = qE <br />
q m <br />
<br />
d2x qE<br />
= <br />
dt2 m<br />
x <br />
ˆx
t = −v0<br />
<br />
± v2 0 + 2qE<br />
(x − x0)<br />
m<br />
qE<br />
m<br />
<br />
<br />
v0 E x−x0 <br />
q m <br />
<br />
<br />
<br />
<br />
<br />
t = tI + tII + tIII<br />
<br />
tI tII tIII <br />
I II III tI <br />
tI =<br />
−v0I +<br />
<br />
v2 2q<br />
0I + m EIS0<br />
qEI<br />
m<br />
<br />
v0I S0 <br />
<br />
<br />
v0II <br />
<br />
<br />
1<br />
2 mv2 0II<br />
1<br />
=<br />
2 mv2 0I + qEIS0<br />
<br />
qEIS0 <br />
<br />
v0II =<br />
<br />
v 2 0I<br />
+ 2q<br />
m EIS0
tII =<br />
<br />
v2 2q<br />
0I + m (EIS0<br />
<br />
+ EIId) − v2 2q<br />
0I + m EIS0<br />
qEII<br />
m<br />
d <br />
<br />
tIII = D<br />
v0III<br />
<br />
<br />
D v0III <br />
<br />
v0III =<br />
<br />
tIII =<br />
<br />
<br />
t =<br />
<br />
v2 2q<br />
0I + m EIS0 − v0I<br />
+<br />
qEI<br />
m<br />
D<br />
v 2 0I<br />
+ 2q<br />
m (EIS0 + EIId) <br />
D<br />
<br />
v2 2q<br />
0I + m (EIS0 + EIId)<br />
+<br />
<br />
v2 2q<br />
0I + m (EIS0 + EIId)<br />
<br />
v2 2q<br />
0I + m (EIS0<br />
<br />
+ EIId) − v2 2q<br />
0I + m EIS0<br />
qEII<br />
m
t =<br />
2q<br />
m EIS0<br />
qEI<br />
m<br />
<br />
α <br />
+<br />
<br />
2q<br />
m (EIS0<br />
<br />
2q<br />
+ EIId) − m EIS0<br />
qEII<br />
m<br />
<br />
m<br />
t = α<br />
q<br />
D<br />
+ <br />
2q<br />
m (EIS0 + EIId)<br />
<br />
2S0 2(EIS0 + EIId) −<br />
α = +<br />
EI<br />
√ EIS0 D<br />
+ <br />
EII<br />
2(EIS0 + EIId)<br />
<br />
<br />
<br />
<br />
<br />
<br />
m<br />
t<strong>de</strong>t = α − β <br />
q<br />
β <br />
<br />
<br />
<br />
<br />
<br />
<br />
β =<br />
<br />
2 e<br />
me EIS0<br />
+<br />
+<br />
<br />
2 e<br />
me (EIS0<br />
<br />
+ E2d2) − 2 e<br />
me EIS0<br />
e<br />
me EI<br />
e<br />
me E2<br />
<br />
2 e<br />
me (EIS0 + E2d2 + E3d3) −<br />
e<br />
me E3<br />
<br />
2 e<br />
me (EIS0 + E2d2)
α β <br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
6
eV
eV <br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
eV
eV <br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
7
eV
N N<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
N N <br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
ab initio <br />
1 <br />
2 T heory
N <br />
M <br />
<br />
N<br />
j=1<br />
− 2<br />
∇<br />
2me<br />
2<br />
j −<br />
N<br />
v(rj) +<br />
j=1<br />
N<br />
N<br />
rjk<br />
j=1 j>k<br />
e2 <br />
χ ele (r; R) = E ele Rχ ele (r; R) <br />
N<br />
j=1 v(rj) r =<br />
(r1, ..., rN) R = (R1, ..., RM) <br />
<br />
N <br />
<br />
χ ele (r; R) <br />
3
N <br />
<br />
<br />
ρ(r1) = N<br />
d 3 <br />
r2...<br />
<br />
d 3 rNχ ele∗ (r)χ ele (r) <br />
N <br />
<br />
ρ(r1)dr1 <br />
<br />
<br />
<br />
<br />
v(r1) <br />
ρ(r1) <br />
<br />
ρ(r1) <br />
v(r1) <br />
<br />
<br />
H H ′ <br />
v(r1) v ′ (r1) <br />
χ ele (r) χ ele′ (r) <br />
<br />
E0 = 〈χ ele |H|χ ele 〉 < 〈χ ele′ |H|χ ele′ 〉 <br />
〈χ ele′ |H ′ |χ ele′ 〉 <br />
E0 < E ′ 0 + 〈χ ele′ |H − H ′ |χ ele′ 〉<br />
< E ′ <br />
0 +<br />
ρ(r1)[v(r1) − v ′ (r1)]dr1
E ′ 0 < E0 −<br />
<br />
<br />
ρ(r)[v(r1) − v ′ (r1)]dr1<br />
E0 + E ′ 0 < E ′ 0 + E0<br />
<br />
<br />
<br />
v(r1) <br />
ρ(r1) N v(r1) <br />
<br />
E[ρ] = T [ρ] + U[ρ] + V [ρ]<br />
<br />
= F [ρ] + ρ(r1)v(r1)dr1<br />
<br />
T [ρ] U[ρ] V [ρ] <br />
<br />
<br />
F [ρ] = T [ρ] + U[ρ]<br />
<br />
V [ρ] = ρ(r1)v(r1)dr1<br />
<br />
F [ρ] <br />
v(r1) <br />
<br />
E0[ρ] ρ(r1) <br />
ρ ′ <br />
E0 ≤ E[ρ ′ ] = T [ρ ′ ] + U[ρ ′ ] + V [ρ ′ ] <br />
ρ ′ = ρ 0 ρ 0
T [ρ]<br />
<br />
Ts[ρ] Tc[ρ] s c<br />
<br />
T [ρ] = Ts[ρ] + Tc[ρ] <br />
Ts[ρ] <br />
φ i(r1) <br />
ρ(r1) <br />
Ts[ρ] = − 2<br />
2me<br />
N<br />
<br />
i<br />
<br />
φ ∗<br />
i (r1)∇ 2 φ i(r1) <br />
<br />
φ i <br />
<br />
Ts[ρ] = Ts[{φ i[ρ]}] <br />
φ i <br />
N <br />
ρ(r1) =<br />
N<br />
i=1<br />
φ ∗<br />
i (r1)φ i(r1) <br />
<br />
Ts[ρ]
F [ρ] = Ts[ρ] + UH[ρ] + Eex[ρ] <br />
UH[ρ] Eex[ρ] <br />
<br />
Eex[ρ] = T [ρ] − Ts[ρ] + U[ρ] − UH[ρ] <br />
<br />
T [ρ] Ts[ρ] <br />
<br />
<br />
E[ρ] = Ts[{φi[ρ]}] + UH[ρ] + Exc[ρ] +<br />
ρ(r1)v(r1)d 3 r1<br />
<br />
Exc[ρ] <br />
<br />
Ts[ρ] <br />
<br />
<br />
<br />
δE<br />
δρ<br />
= δTs<br />
δρ<br />
+ δUH<br />
δρ<br />
+ δExc<br />
δρ<br />
+ δV<br />
δρ<br />
= 0<br />
= δTs<br />
δρ + vH(r1) + vxc(r1) + v(r1) = 0 <br />
δV<br />
δρ = v(r1) δUH<br />
δρ = vH(r1) <br />
δExc[ρ]<br />
<br />
δρ<br />
<br />
Exc[ρ] = vxc(r1) <br />
<br />
δTS<br />
δρ
vs(r1)<br />
<br />
E[ρs] = Ts[{φi[ρs]}] +<br />
<br />
δE<br />
δρs = δTs<br />
δρ s<br />
ρ s(r1)vs(r1)d 3 r1<br />
<br />
<br />
+ vs(r1) <br />
<br />
ρ s(r1) ≡ ρ(r1) vs <br />
vs(r1) = v(r1) + vH(r1) + vxc(r1) <br />
<br />
v(r1) <br />
vs(r1) <br />
<br />
− 2<br />
∇<br />
2me<br />
2 <br />
+ vs(r1) φi(r1) = εiφi(r1) <br />
ρ(r1) <br />
<br />
ρ(r1) ≡ ρ s(r1) =<br />
N<br />
|φi(r1)| 2 <br />
<br />
E[ρ] <br />
<br />
vH vxc <br />
φ i vs <br />
<br />
vs(r1) φ i(r1) <br />
φ i(r1) <br />
<br />
<br />
i
E0 =<br />
N<br />
i<br />
εi − e2<br />
2<br />
<br />
ρ0(r1)ρ0(r ′ 1)<br />
|r1 − r ′ 1| d3r ′ 1d 3 <br />
r1 −<br />
vxc(r1)ρ 0(r1)d 3 r1 + Exc[ρ 0] <br />
E0 <br />
εi <br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
ρ(r1)<br />
v(r1) <br />
<br />
<br />
<br />
4 <br />
<br />
εmax i = −I <br />
5
Exc[ρ] ≈ E LDA<br />
<br />
xc [ρ] =<br />
<br />
ρ(r1) e hom<br />
x [ρ(r1)] + e hom<br />
c [ρ(r1)] d 3 r1 <br />
ehom x <br />
ehom c <br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
ρ(r) ∇ρ(r) <br />
<br />
E GGA<br />
<br />
xc [ρ] =<br />
f(ρ(r), ∇ρ(r))d 3 r <br />
f(ρ(r), ∇ρ(r))<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
6 <br />
7
B3LY P<br />
Exc = E LDA<br />
xc<br />
+ a0(E HF<br />
x<br />
− E LDA<br />
x ) + ax(E GGA<br />
x<br />
− E LDA<br />
x ) + ac(E GGA<br />
c − E LDA<br />
c ) <br />
a0 = 0, 20 ax = 0, 72 ac = 0, 81 <br />
E GGA<br />
x<br />
E GGA<br />
c<br />
<br />
<br />
E LDA<br />
c<br />
<br />
<br />
v(r1) <br />
<br />
<br />
<br />
<br />
up ρ ↑(r1) down ρ ↓(r1) <br />
<br />
ρ(r1) = ρ ↓(r1) + ρ ↑(r1) <br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
8
ρ(r1, t) = N<br />
d 3 <br />
r2...<br />
<br />
d 3 rN|ψ(r1, r2, ..., rN, t)| 2 <br />
ρ(r1, t)d 3 r1 d 3 r1 <br />
r1 t <br />
<br />
d 3 r1ρ(r1, t) = N <br />
N <br />
<br />
<br />
H(t) = − 2<br />
2me<br />
N<br />
j=1<br />
∇ 2<br />
j +<br />
N<br />
N<br />
e 2<br />
rjk<br />
j=1 j>k<br />
+<br />
N<br />
i=1<br />
vext(ri, t) <br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
vext(r1, t) ρ(r, t) <br />
<br />
N <br />
ρ(r1, t) ρ ′ (r1, t) <br />
χ ele (r, t0) v(r1, t)<br />
v ′ (r1, t) <br />
t0
vs[ρ(r1, t)] <br />
<br />
<br />
i ∂φ j(r1, t)<br />
∂t<br />
=<br />
<br />
− 2<br />
∇<br />
2me<br />
2 <br />
+ vs[ρ](r1, t) φj(r1, t) <br />
φ j(r1, t) <br />
<br />
ρ(r1, t) =<br />
<br />
N<br />
|φj(r1, t)| 2 <br />
j=1<br />
vs(r1, t) = vext(r1, t) + vH(r1, t) + vxc(r1, t) <br />
vext(r1, t) vH(r1, t) <br />
vxc(r1, t)<br />
<br />
<br />
vH(r1, t) =<br />
ρ(r1, t)<br />
|r1 − r ′ 1|<br />
<br />
vxc(r1, t) <br />
χ ele (r, t0) <br />
φ(r1, t0)
vxc[ρ](r, t)<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
vext(r1, t) = v (0) (r1) + v (1) (r1, t) <br />
v (1) <br />
<br />
ρ(r1, t) = ρ (0) (r1) + ρ (1) (r1, t) + ρ (2) (r1, t) + ... <br />
ρ (1) (r1, t) ρ(r1, t) v (1) (r1, t) ρ (2) (r1, t)<br />
<br />
<br />
ρ (1) <br />
(r1, ω) =<br />
χ(r, r ′ , ω)v (1) (r ′ 1, ω)d 3 r ′ 1<br />
<br />
<br />
χ(r, r ′ , ω) <br />
χ(r, r ′ , ω) <br />
<br />
<br />
ρ (1) <br />
(r, ω) =<br />
χ S(r, r, ω)v (1)<br />
S (r′ , ω)
χ(r, r, ω) <br />
<br />
χ <br />
<br />
<br />
<br />
<br />
<br />
6 − 311 + +G(3df, 3pd)<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
φ 1(α, n, l, m, r, θ, φ) = Nr (n−1) e −αr Yl,m(θ, φ) <br />
r θ φ α N <br />
Yl,m n l m <br />
<br />
e −βr2<br />
e −αr
6 − 311 + +G(3df, 3pd) <br />
<br />
<br />
<br />
<br />
<br />
<br />
χj = <br />
cjigi(α, r) <br />
i<br />
gi(α, r) <br />
<br />
ψ i = <br />
j<br />
ajiχj = <br />
aji<br />
j<br />
<br />
cjigi(α, r) <br />
<br />
<br />
<br />
i
6 − 311 + +G(3df, 3pd) <br />
<br />
<br />
<br />
<br />
<br />
6 − 311 + +G(3df, 3pd) <br />
<br />
6 − 311 + +G(3df, 3pd) <br />
<br />
<br />
<br />
<br />
<br />
<br />
d <br />
p
× −7 <br />
<br />
<br />
13
11, 12 <br />
22, 01 eV 0, 015 eV s<br />
<br />
eV eV <br />
<br />
eV <br />
eV <br />
eV <br />
<br />
eV <br />
<br />
<br />
eV
et<br />
al <br />
γ <br />
± eV γ(Eexc) = 1 exc <br />
eV <br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
eV <br />
+ <br />
eV <br />
<br />
<br />
+ + <br />
<br />
1 <br />
2 <br />
3
HCOOHH + <br />
HCOOH + <br />
COOH + (HCOO + ) 2 <br />
CO + 2 <br />
HCOH + 2 <br />
COH + (HCO + ) <br />
CO + <br />
H2O + <br />
OH + <br />
H + <br />
<br />
<br />
2 + <br />
2 + <br />
<br />
<br />
<br />
4 2 +
eV
eV <br />
<br />
<br />
<br />
eV <br />
eV s <br />
<br />
<br />
<br />
0, 015eV <br />
s <br />
<br />
<br />
<br />
<br />
<br />
eV 11, 12 14, 65eV <br />
eV
eV <br />
<br />
eV
eV <br />
<br />
<br />
<br />
<br />
<br />
eV <br />
eV + <br />
<br />
eV <br />
<br />
<br />
eV <br />
F ullP ExP ICO
% <br />
% <br />
<br />
<br />
<br />
eV <br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
13
◦ ◦ ◦ ◦<br />
◦ ◦ ◦ ◦<br />
◦ ◦ ◦ ◦<br />
◦ ◦ ◦ ◦<br />
5 Unrestricted Hartree − F ock
1 1 A ′ 1 2 A ′ <br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
1 2 A ′ <br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
◦ ◦ ◦<br />
◦ ◦ ◦<br />
◦ ◦ ◦<br />
◦ ◦ ◦<br />
<br />
<br />
<br />
<br />
<br />
<br />
6 ab initio <br />
<br />
7 et al
◦ ◦ ◦ ◦<br />
◦ ◦ ◦ ◦<br />
◦ ◦ ◦ ◦<br />
◦ ◦ ◦ ◦<br />
<br />
<br />
<br />
<br />
1 1 A ′ 1 2 A ′ <br />
<br />
<br />
<br />
<br />
<br />
<br />
1 1 A ′ 1 2 A ′<br />
<br />
<br />
<br />
<br />
<br />
◦ ◦<br />
◦ ◦<br />
◦ ◦<br />
◦ ◦
meV <br />
<br />
<br />
meV <br />
meV <br />
<br />
meV <br />
<br />
<br />
<br />
−1<br />
1 1 A ′<br />
<br />
ν(OH) <br />
ν(CH) <br />
ν(C = O) <br />
δ(HCO) <br />
δ(H ′ O ′ C ′ ) <br />
ν(C − O) <br />
δ(OCO ′ ) <br />
δ(CH) <br />
δ(OH) <br />
eV<br />
<br />
<br />
<br />
<br />
<br />
<br />
et al. <br />
<br />
<br />
et al.
= <br />
<br />
<br />
<br />
<br />
<br />
+ <br />
−1<br />
1 2 A ′<br />
<br />
ν <br />
ν <br />
ν <br />
δ <br />
δ <br />
ν <br />
δ <br />
δ <br />
δ <br />
eV<br />
<br />
+<br />
<br />
<br />
<br />
<br />
<br />
eV <br />
eV <br />
eV <br />
8
eV <br />
eV et al. <br />
eV <br />
<br />
Ei <br />
<br />
<br />
<br />
<br />
±0, 1<br />
<br />
<br />
<br />
<br />
et al. <br />
<br />
1 2 A ′ 1 2 A ′′ 3 2 A ′ <br />
2 2 A ′ <br />
2 2 A ′′ <br />
<br />
<br />
<br />
<br />
+
eV<br />
<br />
1 2 A ′ <br />
1 2 A ′′ <br />
2 2 A ′ ≈<br />
2 2 A ′′ ≈<br />
3 2 A ′ <br />
4 2 A ′ <br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
+ + <br />
<br />
eV <br />
<br />
+ <br />
<br />
eV +
+ + + e − ±<br />
+ + + e − <br />
+ + + e − ±<br />
+ + +e − <br />
eV + <br />
eV <br />
+ + +<br />
+ eV <br />
eV <br />
<br />
eV <br />
<br />
8a ′ 3 2 A ′ <br />
+ + +<br />
+ <br />
+ + + <br />
+ + + <br />
<br />
hν → + + + e − <br />
et al <br />
<br />
1 2 A ′ <br />
eV <br />
<br />
1 2 A ′′ + <br />
eV + <br />
eV + <br />
+
eV <br />
+ <br />
+ + <br />
eV + <br />
et al. <br />
1 2 A ′′ + <br />
<br />
<br />
<br />
2 + <br />
<br />
<br />
<br />
<br />
<br />
2 + <br />
<br />
<br />
<br />
2 + <br />
<br />
2 +<br />
<br />
hν → 2 + e − <br />
2 hν → 2 + e − <br />
<br />
±<br />
<br />
2 + <br />
<br />
2 + eV 2 +
2 + <br />
<br />
<br />
2 +
eV <br />
<br />
+ − <br />
+ e − <br />
+ e − <br />
2 + e − <br />
<br />
<br />
<br />
+
eV <br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
+
et al. <br />
<br />
<br />
<br />
+ <br />
<br />
<br />
<br />
<br />
<br />
<br />
2 + <br />
<br />
2 + <br />
<br />
<br />
eV
+ e − 30, 4% <br />
+ 2 + <br />
<br />
+ 2 OH + <br />
<br />
2 + <br />
+ <br />
<br />
<br />
<br />
<br />
2 + <br />
+
+ e − 30, 4% <br />
+ 2 + <br />
<br />
+ 2 OH + <br />
<br />
2 + <br />
+ <br />
<br />
<br />
<br />
<br />
2 + <br />
+
M <br />
<br />
<br />
<br />
3M <br />
<br />
<br />
<br />
3M −5 3M −6
E{n1,...,n9} = Eeletronica +<br />
9<br />
<br />
ωi ni + 1<br />
<br />
2<br />
i=1<br />
<br />
<br />
ni = 0 <br />
<br />
9<br />
Ead = E{n1,...,n9} = Eeletronica +<br />
<br />
i=1<br />
1<br />
2 ωi<br />
<br />
<br />
Ecanal = Ead(ion) + Ead(neutro) − Ead(HCOOH) <br />
Ead(ion) Ead(neutro)
E{n1,...,n9} = Eeletronica +<br />
9<br />
<br />
ωi ni + 1<br />
<br />
2<br />
i=1<br />
<br />
<br />
ni = 0 <br />
<br />
9<br />
Ead = E{n1,...,n9} = Eeletronica +<br />
<br />
i=1<br />
1<br />
2 ωi<br />
<br />
<br />
Ecanal = Ead(ion) + Ead(neutro) − Ead(HCOOH) <br />
Ead(ion) Ead(neutro)
+ <br />
+ <br />
+ <br />
+ <br />
+ <br />
2 + <br />
2 <br />
<br />
<br />
<br />
<br />
cm −1 <br />
<br />
<br />
+ <br />
+ <br />
+ <br />
+ <br />
2 + <br />
2
+<br />
<br />
<br />
+<br />
<br />
<br />
+<br />
<br />
<br />
+<br />
<br />
<br />
2 +<br />
<br />
<br />
2
+
+
+
+
+