Hindered and modulated rotations of adsorbed diatomic molecules ...
DIATOMIC MOLECULES: POTENTIAL CURVESthe 60 transition metal (TM) diatomic molecules Mean absolute...
Transcript of DIATOMIC MOLECULES: POTENTIAL CURVESthe 60 transition metal (TM) diatomic molecules Mean absolute...
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Francisco B. C. Machado, Rene Felipe Keidel SpadaInstituto Tecnológico de Aeronáutica , SP, Brazil
DIATOMIC MOLECULES:
POTENTIAL CURVES
Web page: http://www.univie.ac.at/columbus
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1 1
N MA
i A iA
Z
r= =
−1
1N N
i j i ijr=
+H =
2
1
1
2
M
A
A=
− 1 1
M MA B
A B AB
Z Z
R=
+
Nuclear kinetic energy Nuclear-nuclear repulsion
Electron kinetic energyElectron-Electron repulsion
Electron-nuclear attraction
2
1
1
2
N
i
i=
−
H E =
Hamiltonian Operator
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( , ) ( ; ) ( )ele nucr R r R R =
Eletronic Spectra
Vibracional Spectra
Rotational Spectra
( )nuc R
( ; )ele r R
Born-Oppenheimer Approximation
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1 1
N MA
i A iA
Z
r= =
−1
1N N
i j i ijr=
+ˆele
H =2
1
1
2
N
i
i=
−
ˆ ( ; ) ( ) ( ; )ele ele ele eleH r R E R r R =
ˆ ( ) ( )nuc nuc nucH R E R =
ˆnuc
H = 2
1 1 1 1
1 1
2
N N N N MA
i
i i j i i Aij iA
Z
r r= = = =
− + − +
2
1
1
2
M
A
A=
− 1 1
M MA B
A B AB
Z Z
R=
+
I)
II)
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2 3 4 5 6 7 8 9 10 11-1663,92
-1663,90
-1663,88
-1663,86
-1663,84
-1663,82
-1663,80
-1663,78
-1663,76
R (a0)
E(R
) (u
.a)
2 3 4 5 6 7 8 9 10 11-1663,92
-1663,90
-1663,88
-1663,86
-1663,84
-1663,82
-1663,80
-1663,78
-1663,76
R (a0)
E(R
) (u
.a)
<∆E0<∆E0
∆E0
∆E0
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Hydrogen Molecule (H2):
5
R (Å)
E(R
) (u
.a)
0,74
1 2 1 2( , )x x X X =eR R 1 2(1 ') (1 '')jX C s C s= +
1 1(1 ') 0(1 '')X s s +
2 0(1 ') 1(1 '')X s s +
1 2 1 2( , )x x X X =1 2(1 ') (1 '')jX C s C s= +
1
1(1 ') (1 '')
2X s s +
2
1(1 ') (1 '')
2X s s −
5
R (Å)
E(R
) (u
.a)
0,74
eR R
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Hydrogen Molecule (H2):
5
R (Å)
E(R
) (u
.a)
0,74
1 2 1 2( , )x x X X =eR R 1 2(1 ') (1 '')jX C s C s= +
1 1(1 ') 0(1 '')X s s +
2 0(1 ') 1(1 '')X s s +
1 2 1 2( , )x x X X =1 2(1 ') (1 '')jX C s C s= +
1
1(1 ') (1 '')
2X s s +
2
1(1 ') (1 '')
2X s s −
5
R (Å)
E(R
) (u
.a)
0,74
eR R
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Hydrogen Molecule (H2):
5
R (Å)
E(R
) (u
.a)
0,74
1 2 1 2( , )x x X X =eR R 1 2(1 ') (1 '')jX C s C s= +
1 1(1 ') 0(1 '')X s s +
2 0(1 ') 1(1 '')X s s +
1 2 1 2( , )x x X X =1 2(1 ') (1 '')jX C s C s= +
1
1(1 ') (1 '')
2X s s +
2
1(1 ') (1 '')
2X s s −
eR R
E
Re R>>Re
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Multireference Methods
➢In Re Hartree-Fock ≈ 99% Eexact
➢Erro ≈1% ≈ 1 eV ≈ 100 kJ/mol ≈ 25 kcal/mol
➢Chemical bond ≈ 1 eV ≈ 100kJ/mol ≈ 25 kcal/mol
(energy difference)
H. Lischka, et al., Chem. Rev., 118, 7293 (2018)
𝐸𝑐𝑜𝑟𝑟 = 𝐸𝑒𝑥𝑎𝑐𝑡 − 𝐸𝐻𝐹
Correlation energy
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Multireference Methods
• Separation of the whole calculation into two steps: (i) areference configuration set describing the most relevant part(quasi-degeneracies, nondynamic or static electroncorrelation), using the multiconfiguration self consistent field(MCSCF) method and (ii) configuration interaction (CI) withall single and double excitations (dynamic electroncorrelation) – MR-CISD
• Size extensivity corrections: Davidson correction (+Q)
H. Lischka, et al., Chem. Rev., 118, 7293 (2018)
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Multiconfigurational self-consistent field (MCSCF)
H. Lischka, et al., Chem. Rev., 118, 7293 (2018)
I IMCSCFI
c =
1
1,2,....,K
i iX C i K
=
= =
I 1 2... ...i b NX X X X X=
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?I =Active
(CAS)
Inactive
(DOCC)
Not occupiedSometime, easy, dificult, impossible ...
Chemical information about the system
Necessary: MO occupation 0.1 – 1.9
Ideally: MO occupation 0.02 - 1.98
H. Lischka, et al., Chem. Rev., 118, 7293 (2018)
Complete active space self-consistent field (CASSCF)
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Complete active space self-consistent field (CASSCF)
H. Lischka, et al., Chem. Rev., 118, 7293 (2018)
CuB (1S+) – HOMO (9s2) CAS (7s8s9s10s11s3p4p5p1d)
CuB- 2P – HOMO (4p1)
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0
r
a
rs
ab
1 2... ...N N r s kX X X X X+ +
1 2... ...a b NX X X X XOccupeid Orbitals
Virtual Orbitals
1 2... ...a b NX X X X X=
1 2... ...r b NX X X X X=
1 2... ...r s NX X X X X=
Configuration Interaction, CI
1
1,2,....,K
i iX C i K
=
= =H. Lischka, et al., Chem. Rev., 118, 7293 (2018)
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MRSDCI
0 0
r r rs rs
a a ab abMRSDCIa bar
r s
c c
= + +
0 ? =
H. Lischka, et al., Chem. Rev., 118, 7293 (2018)
Davidson correction (+Q)2
0(1 )( )Q CISD HFE c E E = − −
S. R. Langhoff, E. R. Davidson, Inter. J. Quant.Chem., 8, 61, (1974)
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• Methodology
• CASSCF (active space = valence )
• MRCI
• Basis set
• Nuclear Equation – DSITA Program
• Transition Probabilities
• 𝑨𝝂´𝝂´´ = < 𝝂´ 𝝁𝑻𝑴 𝑹 𝝂´´ >𝟐𝝂𝝂´𝝂´´𝟑
𝟐−𝜹𝟎,𝚲´+𝚲´´
𝟐−𝜹𝟎,𝚲´
• Radiative Lifetimes (1/An´n´´)
• photoionization transition
• 𝑰(𝝂´, 𝝂´´) ∼ 𝑴𝒆𝟐 < 𝝂´´ |𝝂´ >
𝟐= 𝑴𝒆
𝟐𝑸𝝂´´𝝂´
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Diatomic Molecules – State of art
➢Natural candidates to test methodologies.
➢Ideally, full CI : Very expensive.
➢Dissociation energies, electronic and rovibrational
Spectroscopy, excited states: require multireference methodologies.
➢ Main group elements: CASSCF/MRCI
➢ More challenge: systems with, at least, one transition metal atom
H. Lischka, et al., Chem. Rev., 118, 7293 (2018)
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MRCI: Performance of the Contract MethodsMolecule State PC-MRCI FIC-MRCI SC-MRCI SC-MRCI(L.Ext) ∆ER
CH 2Π 0.8 1.2 3.9 9.1 0.32∆ 0.8 4.3 9.0 0.32S- 1.6 4.3 9.0 0.6
CN 2S+ 3.7 9.3 23.1 0.62Π 4.1 9.5 24.4 0.9
CO 1S+ 3.3 4.5 11.3 27.5 1.51Π 6.1 15.9 33.4 1.71S- 5.5 12.9 30.5 1.01∆ 5.0 12.9 30.4 0.9
CO+ 2S+ 2.4 3.1 9.0 19.3 0.92Π 4.4 10.6 22.0 1.8
2-2S+ 4.7 11.9 22.8 2.1
N21S+ 3.4 4.1 9.5 25.6 0.81Π 5.6 13.8 30.8 0.91S- 6.1 12.7 30.4 1.0
O21∆ 5.1 6.3 11.8 37.5 1.5
1S+ 5.7 11.2 37.5 1.23S+ 5.7 7.3 13.9 38.0 2.1
OH 2Π 1.6 2.0 5.6 18.3 0.42S+ 2.4 5.8 18.6 0.9
H. Lischka, et al., Chem. Rev., 118, 7293 (2018)
K. Sivalingam, et al., J. Chem. Phys. 145, 054104 (2016).
in [mEh])
(a) the reference relaxationcomputed with uc-MRCI (ΔER) plays a minor role; (b) FIC-MRCI misses 2%−3% of the correlation energy; (c) The error ranges are substantially larger for SC-MRCI with values about 4%−6%; (d) the orbital noninvariance calculatedcomparing SC-MRCI and SC-MRCI with localized virtual orbitals (SC -MRCI[LExt]) does not affect the excitation energies due to error cancellation; (e) the excitation energies are in excellent agreement with the uc-MRCI results
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Deviations in the calculated dissociation energy from the exp. values for the 60 transition metal (TM) diatomic molecules
Mean absolute deviation (MAD) of 3.3 kcal mol−1. Very high. Complexity to describe the bond-
breaking of TM. For some cases it is 15 kcal mol−1.
Suggestion: most of the experimentally derived values require careful revision. H. Lischka, et al., Chem. Rev., 118, 7293 (2018) Y. A. Aoto, et al., J. Chem. Theory Comput. 13, 5291 (2017)
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Electronic excitation energy calculations for diatomic transitionmetal oxides and compared with available experimental data
Erros: Better accurate is around 100 cm−1. Most exceeds1000 cm−1, especially for the higher lying states
H. Lischka, et al., Chem. Rev., 118, 7293 (2018) J. Tennyson, et al., J. Phys. B At. Mol. Opt. Phys., 49, 102001 (2016)
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Characterization: Potential Energy Curves - Strategy
Previous Information?• Ground State Configuration? • Excited State Configuartion?• Molecular Orbital Diagram?• Experimental Assignment?• Assintotic Limit – Atomic Level – in
general available
Wigner-Witmer Rules
G. Herzberg, Molecular Spectra and Molecular Structure. Vol. 1, van Nostrand Reinhold, New York, 1950.
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Wigner-Witmer Rules
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Studied Molecules: AlC, GaC
Electronic states Spin multiplicity Dissociation channels Energy (cm-1)
1st Σ+, Π(2), Δ, Σ−(2) doublet, quartet Al / Ga (2Pu) + C (3Pg) 0
2nd Σ+, Π(3), Δ(2), Σ−(2) doublet Al / Ga (2Pu) + C (1Du) 10192
3rd Σ− Π doublet Al / Ga (2Pu) + C (1Su) 21648
4rd Σ− Π doublet, quartet Al / Ga (2Sg) + C (3Pg) 25347/24788
Electronic states correlated to the first dissociation channels of AlC and GaC molecules.
AlC
Al(2Pu) and C (3Pg)
Active Space: Valence (7e,8o) + 4s (Al) +2s + 1p
Avoided crossing: P statesAl(2Pu) → Al(2Sg)
GaC
Ga (2Pu) and C (3Pg)
AlC: Emission coefficient as function of the wavelength
Chem . Phys. Lett., 687, 171 (2017)
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Studied Molecules: AsCl, GeB
Chem . Phys. Lett., 601, 26 (2014)
GeB
Chem . Phys. Lett., 634, 66 (2015)
AsCl
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Studied Molecules: XB (X = C, Si, Ge, Sn, Pb)
J. Quant. Spectrosc. Radiat. Transfer, 209, 156 (2018)
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Studied Molecules: CuB, CuAl, CuB+, CuAl+
J. Chem. Phys., 139, 124316 (2013)
[core] {active}
◼ Outer valence (OV) Cu [1s22s22p63s23p63d10] {4s14p0}
X [1s2] {2s22pNx}
◼ “Full” valence (FV)
Cu [1s22s22p63s23p6] {3d104s1}
X [1s2] {2s22pNx}◼ Inner valence (IV)
Cu [1s22s22p63s23p6] {3d104s14p0}
X [1s2] {2s22pNx}
FV ~100,000 CFS
OV ~100 CFS
IV ~800 CFS
OV+IV ~900 CFS
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J. Chem. Phys., 139, 124316 (2013)
CuB, CuAl, CuB+, CuAl+
CuAl (X – 1S+). Exp. Morse potential with experimental data for Re, we and De.
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3 4 5 6 7 8 9 10
0
5000
10000
15000
20000
25000
30000
35000
40000
45000
50000
55000
60000
65000
70000
75000
80000
85000
90000
R (a0)
Rela
tive P
ote
ntial E
nerg
y (
cm
−1)
Cu(2S
1/2,g)+B(
2P
3/2,u)
CuB (1S
+)
CuB (1P)
CuB (3S
+)
CuB (3P)
CuB+ (
2S
+)
CuB+ (
2P)
Cu+ (
1S
0,g) + B (
2P
3/2,u)
CuB, CuAl, CuB+, CuAl+
4 6 8 10 12
0
5000
10000
15000
20000
25000
30000
35000
40000
45000
50000
55000
60000
65000
70000Cu (
2S
1/2,g) + Al
+ (
1S
0,g)
Cu(2S
1/2,g)+Al(
2P
3/2,u)
R (a0)
Rela
tive P
ote
ntial E
nerg
y (
cm
−1)
CuAl (1S
+)
CuAl (1P)
CuAl (3S
+)
CuAl (3P)
CuAl+ (
2S
+)
J. Chem. Phys., 139, 124316 (2013)
CuB (left) and CuAl (right) potential energy curves obtained with MRCI+Q/A5Z
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CuB, CuAl, CuB+, CuAl+
Method Reference
set
Te
(cm−1
)
Re
(a0)
we
(cm−1
)
weχe
(cm−
)
D0
(eV)
(X)1S
+
MRCI+Q
OV --- 2.406 261 1.1 1.89
IV --- 2.369 276 1.6 1.97
OV+IV --- 2.369 275 1.4 1.98
FV_select --- 2.389 264 0.5 1.94
MRCI+Q+C.G
OV --- 2.363 277 1.3 2.03
IV --- 2.329 293 1.7 2.13
OV+IV --- 2.329 292 1.5 2.14
FV_select --- 2.348 284 2.9 2.09
Exp.* --- --- 2.339 294 --- 2.3(15)
Method Reference
set
Te
(cm−1
)
Re
(a0)
we
(cm−1
)
weχe
(cm−
)
D0
(eV)
(A)1P
MRCI+Q
OV 13124 2.438 186 3.7 0.28
IV 13227 2.408 200 1.6 0.35
OV+IV 13238 2.389 209 3.3 0.37
FV_select 13205 2.413 198 0.6 0.31
MRCI+Q+C.G
OV 13726 2.382 206 3.6 0.35
IV 14522 2.392 189 -0.9 0.35
OV+IV 13865 2.338 229 3.4 0.44
FV_select 13853 2.360 215 -1.1 0.38
Exp.* --- 14892 2.353 224 --- 0.4(7)
Molecular constants of CuAl electronic ground state. Molecular constants of CuAl first singlet excited state.
J. Chem. Phys., 139, 124316 (2013)
*J. M. Behm, C. A. Arrington, J. D. Langenberg and M. D. Morse J. Chem. Phys., 99, 6394 (1993).
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CuB (left) and CuAl (right) photoionization spectra.
CuB, CuAl, CuB+, CuAl+
J. Chem. Phys., 139, 124316 (2013)
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Previous Information?
Applications : O2 O: term symbol : 3Pu
Exp. 3Sg−
Dh
D2h
HF: 1ag21b1u
22ag22b1u
23ag21b2u
21b3u21b2g
11b3g1 3b1u
0
3B1g
Basis set: 6-31G* Active Space: valenceCAS(12,8) = 2ag2b1u1b2u1b3u1b2g1b3g
Potential curves for 2 states
Exp. Re (A) D0 (cm-1) Te (cm-1)
X3Sg− 1.2075 41260 0.00
A3Su+ 1.5215 5862 35398
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Applications : O2
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Applications : O2
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Applications : O2
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Applications : O2
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Applications : O2
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Applications : O2
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Applications : O2
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Applications : O2
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Applications : O2
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Applications : O2
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Nuclear Equation - DS-ITA
• From Columbus → Solve electronic Schrödinger equation;
• Access Rovibrational spectroscopic information → Solve the Nuclear Hamiltonian;• Energy levels;• Transition Probabilities;• Radiative Lifetimes;
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Nuclear Equation - DS-ITA
DS-ITA
• Modern Fortran → Easy to read the code, easy to right input files and easy to read the outputs;
• Calculate a numerical Hamiltonian through the finitte difference method with “arbitrary” order of approximation;
• Only the desired eigenvalues are calculated;
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Nuclear Equation - DS-ITA
DS-ITA
• The solution trustworth does not deppend on the quality of the potential fit;
• Since the eigenvalues are calculated, there is no need for a first guess (Numerov like methods);
• The code can be linked against OpenBlas and use OpenMP parallelization.
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Nuclear Equation - DS-ITA
DS-ITA
• Available from February for alpha test;
• Contact the developer → Rene F. K. Spada <[email protected]>
• Thanks.