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eV
+
+ +

eV
+
+ +

eV
+
+ +

6 − 311 + +G(3df, 3pd)
+

6 − 311 + +G(3df, 3pd)
+
2 +
eV
+

eV
eV
eV
eV
eV
eV

CH4

−
1
2

eV
eV
+
3 Ultraviolet
4 V acuum Ultraviolet
5 T hreshold P hotoeletrons P hotoions Coincidence

eV
HCOOH + hν → COOH + + H + e −
→ HCOO + + H + e −
→ HCO + + OH + e −
→ COH + + OH + e −
→ H2O + + CO + e −
+

eV
HCOOH + hν → COOH + + H + e −
→ HCOO + + H + e −
→ HCO + + OH + e −
→ COH + + OH + e −
→ H2O + + CO + e −
+

Erot x 2 Evib x 4 Eele
Erot Evib Eele
x
x =
m
1
4
M
m M
x ≈ 10 −1

HMΨ 0 (r, R; t) = i ∂
∂t Ψ0 (r, R; t)
Ψ 0 (r, R; t) t r
R
HM
N M HM
HM = −
+
N
N
j=1
N
2
2me
e 2
rjk
j=1 j>k
∇ 2
j −
+
M
M
L=1
M
L=1 L>A
2
2ML
N
M
∇ 2 e
L −
j=1 L=1
2Zl rjL
e 2 ZLZA
RLA
rjL j L rjk j
k RLA L A me
−e ML L ZL
∇ 2
j ∇ 2
L
1 0

Ψ 0 (r, R; t) = ψ 0 (r, R)T (t)
HMψ 0 (r, R)
ψ 0 (r, R)
1 ∂
= i T (t)
T (t) ∂t
E
HMψ 0
α(r, R) = Eαψ 0
α(r, R)
iEαt
−
T (t) = e
ψ 0
α(r, R)
α Eα
Ψ 0 (r, R; t) =
α
aαψ 0
iEαt
−
α(r, R)e
ψ 0∗
α (R, r)ψ 0
α
α
′(R, r)dRdr = δαα ′
ψ 0
α(R, r)ψ 0∗
α (R ′ , r ′ ) = δ(R − R ′ )δ(r − r ′ )
δαα ′ δ(R − R′ ) δ(r − r ′ )

N M
H ele = −
N
j=1
2
2me
∇ 2
j −
N
M
j=1 L=1
e 2 ZL
rjL
+
N
N
e 2
rjk
j=1 j>k
[H ele , R] = 0
H ele R
R
H ele χ ele
n (r; R) = E ele
n (R)χ ele
n (r; R)

χ ele
n n
E ele
n = E ele
n (R)
Vn(R) = E ele
n (R) +
M
M
L=1 A>L
e 2 ZLZA
RLA
ψ 0 (r; R) =
n
φ nuc
n (R)χ ele
n (r; R)

M
−
2
∇
2ML
2
L + Vn(R)
n
L=1
Hele +
n
M
L=1 A>L
φ nuc
n (R)χ ele
M
e 2 ZLZA
RLA
n (r; R) = E
n
n
φ nuc
n (R)χ ele
n (r; R) =
φ nuc
n (R)χ ele
n (r; R)
Vn(R)φ nuc
n (R)χ ele
n (r; R)
M
−
L=1
2
∇L · ∇L ·
2ML
n
=
(E − Vn(R))φ nuc
− M
n L=1
2 2
∇
2ML
=
[E − Vn(R)]φ nuc
n
n
Lφ nuc
n
n (R)χ ele
n (R)χ ele
φ nuc
n (R)χ ele
n (r; R)
n (r; R)
χ ele
n + 2[∇Lφ nuc
n ][∇Lχ ele
n ] + φ nuc
n [∇ 2
Lχ ele
n ]
n (r; R)
χ ele∗
s (r; R)
−
n
+ φ nuc
n
M
L=1
2
∇ 2 Lφ nuc
n
χ ele∗
s χ ele
n dr + 2∇L(φ nuc
n )
2ML
χ ele∗
s ∇ 2 Lχ ele
n dr =
(E − Vn(R))φ nuc
n
n
χ ele∗
s ∇Lχ ele
n dr +
χ ele∗
s χ ele
n dr

−
n
M
L=1
M
L=1
2
2ML
2
2ML
∇ 2
Lφ nuc
s + (Vs(R) − E)φ nuc
s =
2
X L ns(R) =
χ ele∗
s ∇Lχ ele
n dr ∇L +
M
χ ele∗
s ∇ 2 Lχ ele
n dr φ nuc
n
Cns =
L=1
2
(X
ML
L ns∇L + Y L
ns)
Y L
ns(R) = 1
2
−
M
L=1
2
2ML
χ ele∗
s (r; R)∇Lχ ele
n (r; R)dr
χ ele∗
s (r; R)∇ 2
Lχ ele
n (r; R)dr
∇ 2
Lφ nuc
s (R) + (Vs(R) − E)φ nuc
s (R) =
n
Cnsφ nuc
n
Cns
Cns
Hnuc(R)φ nuc
s
Hnuc = −
M
L=1
= Eφ nuc
s (R)
2
2ML
∇ 2 L + Vs(R)
Cns = 0

E
3M − 3

∇ · E = 4πρ
∇ · B = 0
∇ × E + 1 ∂B
c ∂t
= 0
∇ × B − 1 ∂E
c ∂t
=
4π
j
c

E(r, t) B(r, t) ρ(r, t)
j(r, t)
φ(r, t)
A(r, t)
B(r, t) = ∇ × A(r, t)
∇ × E + 1
∂A(r, t)
= 0
c ∂t
E(r, t) = −∇φ − 1 ∂A(r, t)
c ∂t
(A, φ)
(A ′ , φ ′ )
A ′ (r, t) = A(r, t) + ∇χ(r, t)
φ ′ (r, t) = φ(r, t) − ∂
χ(r, t)
∂t
χ(r, t)
∇ · A = 0

∇ 2 φ = 0
∇ 2 A − 1 ∂ 1
∇ φ −
c ∂t c2 ∂2 A
∂t2 = 0
∇ 2 A − 1
c 2
∂2A = 0
∂t2
A(r, t) = A ′ 0e i(k·r−ωt) + A ∗ 0e −ı(k·r−ωt)
k = kû k û ω = kc
A ′ 0 = A ∗ 0
A(r, t) = 2A ′ 0 cos[(k · r − ωt)]
2A ′ 0 = A0ˆε ˆε
A(r, t) = A0ˆε cos[(k · r − ωt)]
E = − ω
c A0ˆεsen(k · r − ωt)
B = −A0(kû × ˆε)sen(k · r − ωt)
A0
V N
ω

2πN
A0 = 2c
ωV
1
2
H =
+
N
pj + e
cA(rj, t)
2
− eφ(rj) +
2me
M
PL − eZL
c A(RL, t)
2
+ eZLφ(RL) + V (r, R)
2ML
j=1
L=1
me ML L −e eZL
rj RL pj PL
V (r, R) A φ
HM =
N p2 j
+
2me
j=1
M P 2 L
+ V (r, R)
2ML
L=1
V (r, R)

H ′ (t) = −
+
N
j=1
M
eZL
L=1
2cML
e
2mec
PL · A(RL, t) + A(RL, t) · PL − eZL
c |A(RL, t)| 2
pj · A(rj, t) + A(rj, t) · pj + e
c |A(rj, t)| 2
− eφ
− eZLφ +
pj PL
−i∇j −i∇L
H ′ (t) = i
− i
M
eZL
L=1
N
j=1
2cML
[∇L · A(RL, t) + A(RL, t) · ∇L]
e
2mec [∇j
· A(rj, t) + A(rj, t) · ∇j]
j L ∇
ψ(r, R)
∇k · Aψ = A · (∇kψ) + ψ∇k · A
= A · (∇kψ)
k = j k = L k

H ′ (t) = i
M
eZL
A(RL, t) · ∇L − i
cML
L=1
H ′ (t) = i
− i
M
eZL
L=1
N
j=1
N
j=1
e
mec A(rj,
t) · ∇j
A0 cos(k · RL − ωt)ˆε · ∇L
cML
e
mec A0
cos(k · rj − ωt)ˆε · ∇j
H ′ (t) = i
− i
M
eZL
L=1
N
j=1
e ik·RL e −iωt + e −ik·RL e iωt ˆε · ∇L
A0
2cML
e
2mec A0
ik·rj −iωt −ik·rj iωt
e e + e e ˆε · ∇j
e ±ik·r = e ±ikz
e ±ikz = 1 ± ikz ∓ k2
2 z2 ± ...
kz = 2πz
λ ≪ 1 eikz
H ′ (t) = iA0
2c
H ′ (t) = iA0
c
M
eZL
cos(ωt)ˆε · ∇L −
L=1
ML
M
eZL −iωt iωt
e + e
ˆε · ∇L
L=1
ML
N
e
j=1
− iA0
2c
me
N
e
j=1
cos(ωt)ˆε · ∇j
me
e −iωt + e iωt ˆε · ∇j

[HM + H ′ (t)] ψ(R, r, t) = i ∂
ψ(R, r, t)
∂t
H ′ (t) HM
ψ(R, r, t) =
α
aα(t)ψ 0
iEαt
−
α(R, r)e
aα(t)
ψ 0
α(R, r) t
α
α
aα(t) i ∂
∂t
|aα(t)| 2 = 1.
α
ψ 0
α(R, r)e
iEαt
−
− HMψ 0
α(R, r)e
iEαt
−
=
−i d
dt (aα(t)) ψ 0
iEαt
−
α(R, r)e + H ′ (t)aα(t)ψ 0
iEαt
−
α(R, r)e

α
−i d
dt (aα(t)) ψ 0
iEαt
−
α(R, r)e + H ′ (t)aα(t)ψ 0
iEαt
−
α(R, r)e
= 0
ψ 0
α ′
∗ iE
α ′ t
(R, r)e
α
α
ψ 0
α ′
∗ 0
(R, r)ψα(R, r)dRdr e i(E α ′ −Eα)t
d
dt aα(t)i
=
ψ 0
α ′
∗ ′ 0
(R, r)H (t)ψα(R, r)dRdr e i(E α ′ −Eα)t
aα(t)
ωα ′ α =
H ′ α ′
α =
Eα ′ − Eα
ψ 0∗
α ′(R, r)H′ (t)ψ 0
α(R, r)dRdr
i d
aα ′(t) =
dt
α
H ′ α ′ αaα(t)e iω α ′ α t
H ′ (t)
d
A0 −iωt iωt
aα ′(t) = e + e
dt 2c
ˆε ·
ψ 0
α ′
M
∗ eZL
∇L −
α
L=1
ML
N
e
∇j
me
j=1
ψ 0
αdRdraα(t)e iω α ′ α t
aα(t)

t = 0
d
A0 −iωt iωt
aα ′(t) = e + e
dt 2c
ˆε ·
ψ 0
α ′
M
∗ eZL
∇L −
α
L=1
ML
N
e
∇j
me
j=1
ψ 0
αdRdraα(0)e iω α ′ α t
ψ 0
i (R, r) aα(0) α = i
d A0 −iωt iωt
aα ′(t) = e + e
dt 2c
ˆε ·
ψ 0
α ′
∗
M
eZL
∇L −
L=1
ML
N
e
∇j
me
j=1
ψ 0
i dRdre iω α ′ i t
pj (PL)
pj = ime
[HM, rj]
d
aα ′(t)
dt
=
A0
−
2c2 −iωt iωt
e + e
ˆε ·
−
PL = iML
[HM, RL]
N
e(HMrj − rjHM)
j=1
HM
d
A0
aα ′(t) = −
dt
·
2c 2
ψ 0
α ′
∗
M
L=1
eZL(HMRL − RLHM)
ψ 0
i dRdre iω α ′ i t
−iωt iωt
e + e (Eα ′ − Ei)ˆε ·
ψ 0
α ′
M
N
∗
eZLRL − erj
L=1
j=1
ψ 0
i dRdre iω α ′ i t
M = −
N
erj +
j=1
M
eZLRL
L=1

Mα ′
i =
ψ 0
α ′
∗
−
N
erj +
j=1
M
eZLRL
L=1
ψ 0
i dRdr
aα ′(t)
d
dt aα ′(t) = −A0ωα ′ i −iωt iωt
e + e
2c
ˆε · Mα ′ ie iωα ′ it
0 t aα ′(0) = 0 α′ = i
f
af(t) = − A0
2c ωfiˆε
i(ωfi+ω)t
1 − e 1 − ei(ωfi−ω)t
· Mfi
+
ωfi + ω ωfi − ω
ωfi f
i
ω
ωfi
af(t) = − A0
2c ωfiˆε · Mfi
i(ωfi−ω)t
1 − e
ωfi − ω
Pfi = |af(t)| 2 =
=
A0
− 2c ωfiˆε
2
i(ωfi−ω)t
· Mfi
1 − e
ωfi − ω
−A0 c ωfiˆε
2
2
· Mfi
sen
(ωfi − ω) t
2
(ωfi − ω) 2
δ(ωfi − ω) = 2
π lim
t→∞
sen2 (ωfi − ω) t
2
(ωfi − ω) 2t 2

Pfi = π
2
−A0 c ωfiˆε
· Mfi
2
tδ(ωfi − ω)
κfi = d
dt Pfi
A0
κfi = 4π2 N
V
ω 2 fi
ω |ˆε · Mfi| 2 δ(ωfi − ω)
σabs
ωfi
U
At
= Nωc
V
N V ω
σ(ω) ≡ ωfiκfi
N ωc
V
i f
σ(ω) = 4π2
c
ω 2 fi
ω |ε · Mfi| 2 δ(ωfi − ω)

ω
ψ 0
i (r, R) ψ 0
f(r, R)
σ(ωfi) = 4π2
c ωfi|ε · Mfi| 2

ω
ψ 0
i (r, R) ψ 0
f(r, R)
σ(ωfi) = 4π2
c ωfi|ε · Mfi| 2

eV
cm MeV

e v
E B
F = e(E + v × B)
F = dp dt dU = v · F p U
dt
dp
dt
dU
dt
= e(E + v × B)
= ev · E
v·(v×B) = 0
v
dp
dt
dU
dt
= ev × B
= 0
p = γm0v = U
c
v
2
U = γm0c 2
U 2 − p 2 c 2 = m 2 0c 4
1

m0 γ =
√ 1
1−v2 /c2
a
v2
R
dp
dt
= γm0
v2 ˆr
R
R
p = eRB
U = ecBR
S = c
E × B
4π
B = n × E
n
A × (B × C) = (A · C)B − (A · B)C
n · E = 0

S = c
4π [E2 n]
r ′
r
r >> r ′
E(r, t) = e
c
n × [(n − β) × ˙ β]
|r − r ′ |[1 − (n · β)] 3
β ≡ v
c
t ′ t
dU
dtdA
= [S · n]ret
ret
dU
dAdt
⎧
⎨
e2
=
4π ⎩
1
|r − r ′ | 2
n
× [(n − β) ×
˙ β]
(1 − β · n) 3
2
⎫ ⎬
⎭
r ∆t
t ′ = T1 t ′ = T2
U =
t=T2+r(T2)/c
t=T1+r(T1)/c
[S · n]retdt
t ′ t
t = t ′ + r(t′ )
c
t ′ =T2
U = [S · n] dt
dt ′ dt′
t ′ =T1

dP (t ′ )
dA
= [S · n] dt
dt ′
dA = r 2 dΩ dt
dt ′ = 1 − β · n
dP (t ′ )
dΩ
e2 |n × [(n − β) ×
=
4πc
˙ β]| 2
(1 − β · n) 5
β · ˙ β = 0 β
ˆ k ˙ β î
β = β ˆ k
˙β = ˙ βî
ˆn = senθ cos φî + senθsenφˆj + cos θ ˆ k
dP (t ′ )
dΩ
e2
=
4πc3 |ˆv|
(1 − β cos θ) 3
1 − sen2θ cos2 φ
γ2 (1 − β cos θ) 2
γ >> 1 β 1 θ
θ
1 − β cos θ ≈ 1
γ2 2 2
1 + γ θ
senθ ≈ θ
dP (t ′ )
dΩ
= 2e2
πc 3
γ 6 | ˙v| 2
(1 + γ 2 θ 2 ) 3
1 − 4γ2θ 2 cos2 φ
(1 + γ2θ 2 ) 2

P (t ′ ) = 2 e
3
2 | ˙v| 2
c3 γ4
R
| ˙v| 2 = v2
R
P = 2 e
3
2c R β4γ 4
γ 4
δt =
2πR/v δE = P δt
δE = 4π
3
e 2
R β3 γ 4
θ

〈θ 2 〉 1/2 = 1
γ
= mc2
E
MeV
m
m
MeV
GeV
mA
KeV
KW h

m m
10 −9
10 −11 mbar

eV
eV
eV
nhν
n = 1, 2, 3, ... hν
hν
2

eV
eV
eV
3

10 −8

4

1 2 1 2 3 4
4
2
3
1
1
2
5

EI
EII
E
F = qE
q m
d2x qE
=
dt2 m
x
ˆx

t = −v0
± v2 0 + 2qE
(x − x0)
m
qE
m
v0 E x−x0
q m
t = tI + tII + tIII
tI tII tIII
I II III tI
tI =
−v0I +
v2 2q
0I + m EIS0
qEI
m
v0I S0
v0II
1
2 mv2 0II
1
=
2 mv2 0I + qEIS0
qEIS0
v0II =
v 2 0I
+ 2q
m EIS0

tII =
v2 2q
0I + m (EIS0
+ EIId) − v2 2q
0I + m EIS0
qEII
m
d
tIII = D
v0III
D v0III
v0III =
tIII =
t =
v2 2q
0I + m EIS0 − v0I
+
qEI
m
D
v 2 0I
+ 2q
m (EIS0 + EIId)
D
v2 2q
0I + m (EIS0 + EIId)
+
v2 2q
0I + m (EIS0 + EIId)
v2 2q
0I + m (EIS0
+ EIId) − v2 2q
0I + m EIS0
qEII
m

t =
2q
m EIS0
qEI
m
α
+
2q
m (EIS0
2q
+ EIId) − m EIS0
qEII
m
m
t = α
q
D
+
2q
m (EIS0 + EIId)
2S0 2(EIS0 + EIId) −
α = +
EI
√ EIS0 D
+
EII
2(EIS0 + EIId)
m
tdet = α − β
q
β
β =
2 e
me EIS0
+
+
2 e
me (EIS0
+ E2d2) − 2 e
me EIS0
e
me EI
e
me E2
2 e
me (EIS0 + E2d2 + E3d3) −
e
me E3
2 e
me (EIS0 + E2d2)

α β
6

eV

eV
eV

eV
7

eV

N N
N N
ab initio
1
2 T heory

N
M
N
j=1
− 2
∇
2me
2
j −
N
v(rj) +
j=1
N
N
rjk
j=1 j>k
e2
χ ele (r; R) = E ele Rχ ele (r; R)
N
j=1 v(rj) r =
(r1, ..., rN) R = (R1, ..., RM)
N
χ ele (r; R)
3

N
ρ(r1) = N
d 3
r2...
d 3 rNχ ele∗ (r)χ ele (r)
N
ρ(r1)dr1
v(r1)
ρ(r1)
ρ(r1)
v(r1)
H H ′
v(r1) v ′ (r1)
χ ele (r) χ ele′ (r)
E0 = 〈χ ele |H|χ ele 〉 < 〈χ ele′ |H|χ ele′ 〉
〈χ ele′ |H ′ |χ ele′ 〉
E0 < E ′ 0 + 〈χ ele′ |H − H ′ |χ ele′ 〉
< E ′
0 +
ρ(r1)[v(r1) − v ′ (r1)]dr1

E ′ 0 < E0 −
ρ(r)[v(r1) − v ′ (r1)]dr1
E0 + E ′ 0 < E ′ 0 + E0
v(r1)
ρ(r1) N v(r1)
E[ρ] = T [ρ] + U[ρ] + V [ρ]
= F [ρ] + ρ(r1)v(r1)dr1
T [ρ] U[ρ] V [ρ]
F [ρ] = T [ρ] + U[ρ]
V [ρ] = ρ(r1)v(r1)dr1
F [ρ]
v(r1)
E0[ρ] ρ(r1)
ρ ′
E0 ≤ E[ρ ′ ] = T [ρ ′ ] + U[ρ ′ ] + V [ρ ′ ]
ρ ′ = ρ 0 ρ 0

T [ρ]
Ts[ρ] Tc[ρ] s c
T [ρ] = Ts[ρ] + Tc[ρ]
Ts[ρ]
φ i(r1)
ρ(r1)
Ts[ρ] = − 2
2me
N
i
φ ∗
i (r1)∇ 2 φ i(r1)
φ i
Ts[ρ] = Ts[{φ i[ρ]}]
φ i
N
ρ(r1) =
N
i=1
φ ∗
i (r1)φ i(r1)
Ts[ρ]

F [ρ] = Ts[ρ] + UH[ρ] + Eex[ρ]
UH[ρ] Eex[ρ]
Eex[ρ] = T [ρ] − Ts[ρ] + U[ρ] − UH[ρ]
T [ρ] Ts[ρ]
E[ρ] = Ts[{φi[ρ]}] + UH[ρ] + Exc[ρ] +
ρ(r1)v(r1)d 3 r1
Exc[ρ]
Ts[ρ]
δE
δρ
= δTs
δρ
+ δUH
δρ
+ δExc
δρ
+ δV
δρ
= 0
= δTs
δρ + vH(r1) + vxc(r1) + v(r1) = 0
δV
δρ = v(r1) δUH
δρ = vH(r1)
δExc[ρ]
δρ
Exc[ρ] = vxc(r1)
δTS
δρ

vs(r1)
E[ρs] = Ts[{φi[ρs]}] +
δE
δρs = δTs
δρ s
ρ s(r1)vs(r1)d 3 r1
+ vs(r1)
ρ s(r1) ≡ ρ(r1) vs
vs(r1) = v(r1) + vH(r1) + vxc(r1)
v(r1)
vs(r1)
− 2
∇
2me
2
+ vs(r1) φi(r1) = εiφi(r1)
ρ(r1)
ρ(r1) ≡ ρ s(r1) =
N
|φi(r1)| 2
E[ρ]
vH vxc
φ i vs
vs(r1) φ i(r1)
φ i(r1)
i

E0 =
N
i
εi − e2
2
ρ0(r1)ρ0(r ′ 1)
|r1 − r ′ 1| d3r ′ 1d 3
r1 −
vxc(r1)ρ 0(r1)d 3 r1 + Exc[ρ 0]
E0
εi
ρ(r1)
v(r1)
4
εmax i = −I
5

Exc[ρ] ≈ E LDA
xc [ρ] =
ρ(r1) e hom
x [ρ(r1)] + e hom
c [ρ(r1)] d 3 r1
ehom x
ehom c
ρ(r) ∇ρ(r)
E GGA
xc [ρ] =
f(ρ(r), ∇ρ(r))d 3 r
f(ρ(r), ∇ρ(r))
6
7

B3LY P
Exc = E LDA
xc
+ a0(E HF
x
− E LDA
x ) + ax(E GGA
x
− E LDA
x ) + ac(E GGA
c − E LDA
c )
a0 = 0, 20 ax = 0, 72 ac = 0, 81
E GGA
x
E GGA
c
E LDA
c
v(r1)
up ρ ↑(r1) down ρ ↓(r1)
ρ(r1) = ρ ↓(r1) + ρ ↑(r1)
8

ρ(r1, t) = N
d 3
r2...
d 3 rN|ψ(r1, r2, ..., rN, t)| 2
ρ(r1, t)d 3 r1 d 3 r1
r1 t
d 3 r1ρ(r1, t) = N
N
H(t) = − 2
2me
N
j=1
∇ 2
j +
N
N
e 2
rjk
j=1 j>k
+
N
i=1
vext(ri, t)
vext(r1, t) ρ(r, t)
N
ρ(r1, t) ρ ′ (r1, t)
χ ele (r, t0) v(r1, t)
v ′ (r1, t)
t0

vs[ρ(r1, t)]
i ∂φ j(r1, t)
∂t
=
− 2
∇
2me
2
+ vs[ρ](r1, t) φj(r1, t)
φ j(r1, t)
ρ(r1, t) =
N
|φj(r1, t)| 2
j=1
vs(r1, t) = vext(r1, t) + vH(r1, t) + vxc(r1, t)
vext(r1, t) vH(r1, t)
vxc(r1, t)
vH(r1, t) =
ρ(r1, t)
|r1 − r ′ 1|
vxc(r1, t)
χ ele (r, t0)
φ(r1, t0)

vxc[ρ](r, t)
vext(r1, t) = v (0) (r1) + v (1) (r1, t)
v (1)
ρ(r1, t) = ρ (0) (r1) + ρ (1) (r1, t) + ρ (2) (r1, t) + ...
ρ (1) (r1, t) ρ(r1, t) v (1) (r1, t) ρ (2) (r1, t)
ρ (1)
(r1, ω) =
χ(r, r ′ , ω)v (1) (r ′ 1, ω)d 3 r ′ 1
χ(r, r ′ , ω)
χ(r, r ′ , ω)
ρ (1)
(r, ω) =
χ S(r, r, ω)v (1)
S (r′ , ω)

χ(r, r, ω)
χ
6 − 311 + +G(3df, 3pd)
φ 1(α, n, l, m, r, θ, φ) = Nr (n−1) e −αr Yl,m(θ, φ)
r θ φ α N
Yl,m n l m
e −βr2
e −αr

6 − 311 + +G(3df, 3pd)
χj =
cjigi(α, r)
i
gi(α, r)
ψ i =
j
ajiχj =
aji
j
cjigi(α, r)
i

6 − 311 + +G(3df, 3pd)
6 − 311 + +G(3df, 3pd)
6 − 311 + +G(3df, 3pd)
d
p

× −7
13

11, 12
22, 01 eV 0, 015 eV s
eV eV
eV
eV
eV
eV
eV

et
al
γ
± eV γ(Eexc) = 1 exc
eV
eV
+
eV
+ +
1
2
3

HCOOHH +
HCOOH +
COOH + (HCOO + ) 2
CO + 2
HCOH + 2
COH + (HCO + )
CO +
H2O +
OH +
H +
2 +
2 +
4 2 +

eV

eV
eV
eV s
0, 015eV
s
eV 11, 12 14, 65eV
eV

eV
eV

eV
eV
eV +
eV
eV
F ullP ExP ICO

%
%
eV
13

◦ ◦ ◦ ◦
◦ ◦ ◦ ◦
◦ ◦ ◦ ◦
◦ ◦ ◦ ◦
5 Unrestricted Hartree − F ock

1 1 A ′ 1 2 A ′
1 2 A ′
◦ ◦ ◦
◦ ◦ ◦
◦ ◦ ◦
◦ ◦ ◦
6 ab initio
7 et al

◦ ◦ ◦ ◦
◦ ◦ ◦ ◦
◦ ◦ ◦ ◦
◦ ◦ ◦ ◦
1 1 A ′ 1 2 A ′
1 1 A ′ 1 2 A ′
◦ ◦
◦ ◦
◦ ◦
◦ ◦

meV
meV
meV
meV
−1
1 1 A ′
ν(OH)
ν(CH)
ν(C = O)
δ(HCO)
δ(H ′ O ′ C ′ )
ν(C − O)
δ(OCO ′ )
δ(CH)
δ(OH)
eV
et al.
et al.

=
+
−1
1 2 A ′
ν
ν
ν
δ
δ
ν
δ
δ
δ
eV
+
eV
eV
eV
8

eV
eV et al.
eV
Ei
±0, 1
et al.
1 2 A ′ 1 2 A ′′ 3 2 A ′
2 2 A ′
2 2 A ′′
+

eV
1 2 A ′
1 2 A ′′
2 2 A ′ ≈
2 2 A ′′ ≈
3 2 A ′
4 2 A ′
+ +
eV
+
eV +

+ + + e − ±
+ + + e −
+ + + e − ±
+ + +e −
eV +
eV
+ + +
+ eV
eV
eV
8a ′ 3 2 A ′
+ + +
+
+ + +
+ + +
hν → + + + e −
et al
1 2 A ′
eV
1 2 A ′′ +
eV +
eV +
+

eV
+
+ +
eV +
et al.
1 2 A ′′ +
2 +
2 +
2 +
2 +
hν → 2 + e −
2 hν → 2 + e −
±
2 +
2 + eV 2 +

2 +
2 +

eV
+ −
+ e −
+ e −
2 + e −
+

eV
+

et al.
+
2 +
2 +
eV

+ e − 30, 4%
+ 2 +
+ 2 OH +
2 +
+
2 +
+

+ e − 30, 4%
+ 2 +
+ 2 OH +
2 +
+
2 +
+

M
3M
3M −5 3M −6

E{n1,...,n9} = Eeletronica +
9
ωi ni + 1
2
i=1
ni = 0
9
Ead = E{n1,...,n9} = Eeletronica +
i=1
1
2 ωi
Ecanal = Ead(ion) + Ead(neutro) − Ead(HCOOH)
Ead(ion) Ead(neutro)

E{n1,...,n9} = Eeletronica +
9
ωi ni + 1
2
i=1
ni = 0
9
Ead = E{n1,...,n9} = Eeletronica +
i=1
1
2 ωi
Ecanal = Ead(ion) + Ead(neutro) − Ead(HCOOH)
Ead(ion) Ead(neutro)

+
+
+
+
+
2 +
2
cm −1
+
+
+
+
2 +
2

+
+
+
+
2 +
2

+

+

+

+

+