Benchmark calculations
Computational
method CASSCF(5,10) / icMRCI (5 active electronsin 10 active orbitals) [3]
basis set d-aug-cc-pVTZprogram package MOLPRO 2000.1
[3] H.-J. Werner and P. J. Knowles, J. Chem. Phys. 89, 5803 (1988); P. J. Knowles and H.-J. Werner, Chem. Phys. Letters 145, 514 (1988)
Results
Potential energy curves for the electronic ground state and the first two excited states calculated for C2v geometries
○ – our calculations
+ – M. F. Satterwhite and G. I. Gellene, J. Phys. Chem. 99, 1339 (1995)subplots – comparison with literatura data
Potential energy surfaces for C2v geometries
A detailed plot of the C2v PES for the electronic ground state
Ab initioAb initio calculation on He calculation on He33++ of interest for semiempirical of interest for semiempirical
modelling of Hemodelling of Henn++
Ivana PaidarovIvana Paidarováá a)a), Rudolf Pol, Rudolf Poláákk a)a), Franti, Františšek Karlickek Karlický ý b)b), Daniel Hriv, Daniel Hrivňákňák bb)), and René Kalus , and René Kalus bb))
a) a) J. HeyrovskJ. Heyrovskýý Institute of Physical Chemistry, Praha, Institute of Physical Chemistry, Praha, b) b) University of Ostrava, OstravaUniversity of Ostrava, Ostrava
Aim
The principal aim of the present calculations is to provide highly The principal aim of the present calculations is to provide highly accurate potential energy surfaces (PES) for the electronic ground accurate potential energy surfaces (PES) for the electronic ground state and the first two excited states of the Hestate and the first two excited states of the He33
++ ion to be employed ion to be employed
in subsequent semiempirical modellings of larger helium cluster in subsequent semiempirical modellings of larger helium cluster cations, Hecations, Henn
++. It is well known that the . It is well known that the diatomics-in-moleculediatomics-in-molecule (DIM) (DIM)
approach, which performs well for the heavier rare gases, fails approach, which performs well for the heavier rare gases, fails remarkably even for the smallest Heremarkably even for the smallest Henn
++. It is argued that this is mainly . It is argued that this is mainly
due to the neglect of three-body interactions due to the neglect of three-body interactions [1][1] within the DIM within the DIM framework and, consequently, the three-body contributions to the framework and, consequently, the three-body contributions to the HeHenn
++ interaction energy have to be extracted from interaction energy have to be extracted from ab initioab initio
calculations and included in semiemirical models for them to become calculations and included in semiemirical models for them to become acceptably accurate. This can be done, acceptably accurate. This can be done, e. g.e. g., within the , within the triatomics-in-triatomics-in-moleculesmolecules (TRIM) approach (TRIM) approach [2][2], which represents a natural , which represents a natural generalization of the DIM method.generalization of the DIM method.
[1] [1] P.J. Knowles, J.N. Murrell, E.J. Hodge, Mol. Phys. 85, 243 (1995)P.J. Knowles, J.N. Murrell, E.J. Hodge, Mol. Phys. 85, 243 (1995)[2] this poster session, D. Hriv[2] this poster session, D. Hrivňák ňák et al.et al., , Semiempirical modelling of HeSemiempirical modelling of Henn
++ clusters. clusters.
Grant No. 203/04/2146 of the Grant Agency of the Czech Republic
Potential energy surface
Computational
Coordinates
where r1 ≤ r2 ≤ r3 are inter-atomic distances.
Analytical formula
Computationally cheap Morse potential (Easymp → 0)
with (X = D, A, R)
Configurations
○ - anticipated three-body configurations in Hen+ clusters (n ≤ 13)
● - configurations included in fitting procedure
Least-square fits
rough optimization: genetic algorithm (with binary encodedstrings)
fine-tuning: Levenberg-MarquardtNewton-Raphson (program by V. Špirko)
Results
Examples of 1D fits for a representative set of geometries and for the electronic ground state
● - ab initio points from economy calculations—— - least-square fitssubplots - deviations of the least-square fits from the ab initio data
Distribution of the least-square fits residues for electronic ground state points
Dependence of the Morse potential parameters on He3+
shape (electronic ground state)
Economy calculations
Computational
method Equation-Of-Motion Coupled Clusters [4]
basis set d-aug-cc-pVTZ [5]
program package ACES II
[4] J.F. Stanton and R.J. Bartlett, J. Chem. Phys. 98, 7029 (1993)[5] Basis set converged results were obtained with daug-cc-pVTZ basis set, in the series of aug-cc-pVXZ calculations, X=D,T,Q.
Results
Comparison of potential energy curves for the first three electronic states and for selected C2v geometries with the benchmark results
● – economy calculations
○ – benchmark calculations
subplots – a detailed view of local minimum
Differences between the economy and benchmark calculations for two selected geometries (C2v and D∞h)
A detailed plot of the C∞v PES for the electronic ground state
The C∞v PES is extremely flat for the electronic ground state
Grant No. 203/06/XXXX (submitted) of the Grant Agency of the Czech Republic
Equilibrium structure of He3+
(comparison with literature)
method Emin Re De[hartree] [bohr] [eV]
QICSD(T), aug-cc-pVTZ [6]-7.896672 2.340 2.598 QICSD(T), aug-cc-pVQZ [6] -7.902103 2.336 2.640
MRD-CI, cc-pVTZ [7] -7.8954 2.34 2.59
this work, benchmark -7.897021 2.339 2.639 this work, economy -7.896084 2.341 2.639 (?)
[6] M. F. Satterwhite and G. I. Gellene, J. Phys. Chem. 99, 1339 (1995) [7] E. Buonomo et al., Chem. Phys. Letters 259, 641 (1996)
23
45
-7.90
-7.88
-7.86
-7.84
-7.82
-7.80
-7.78
-7.76
-7.74
-7.72
-7.70
100
120
140160
180
2B2(1)
2A1(2)
2A1(1)
23
45
-7.90
-7.88
-7.86
-7.84
-7.82
-7.80
-7.78
-7.76
-7.74
-7.72
-7.70
100
120
140160
180
2B2(1)
E [hart
ree]
23
45
-7.90
-7.88
-7.86
-7.84
-7.82
-7.80
-7.78
-7.76
-7.74
-7.72
-7.70
100
120
140160
180
2A1(1)
E [hart
ree]
23
45
-7.90
-7.88
-7.86
-7.84
-7.82
-7.80
-7.78
-7.76
-7.74
-7.72
-7.70
100
120
140160
180
2A1(2)
E [hart
ree]
2.12.2
2.32.4
2.52.6
2.72.8
100120
140
160
180
-7.895
-7.890
-7.885
-7.880
-7.875
-7.870
-7.865
-7.860
R [bohr] [deg.]
E [h
artr
ee]
-7.896
-7.894
-7.892
-7.891
-7.889
-7.887
-7.886
-7.884
-7.882
-7.881
-7.879
-7.877
-7.876
-7.876
-7.871
-7.869
2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8
100
120
140
160
180
global minimumR
1 = R
2 = 2.339 bohr
Emin
= -7.8970 hartree
[d
eg.]
R [bohr]
-7.8949
-7.8955
2.0 2.2 2.4 2.6 2.8 3.02.0
2.2
2.4
2.6
2.8
3.0
R2 [
bo
hr]
R1 [bohr]
-7.8944
global minimumR
1 = R
2 = 2.341 bohr
Emin
= -7.8961 hartree
2.02.2
2.42.6
2.83.0
-7.895
-7.890
-7.885
-7.880
-7.875
-7.870
2.0
2.2
2.4
2.6
2.83.0
E [h
artr
ee]
R 2 [b
ohr]
R1 [bohr]
2.02.2
2.42.6
2.8
3.0
-8.0
-7.8
-7.6
-7.4
2.0
2.2
2.4
2.62.8
3.0
E [h
artr
ee]
R 2 [b
ohr]R1 [bohr]
-8.0
-7.8
-7.6
-7.4
-7.2
-7.0
-6.8
1 2 3 4 5 6 7-8.0
-7.8
-7.6
-7.4
-7.2
-7.0
-6.8
1 2 3 4 5 6 7
2.0 2.2 2.4 2.6
-7.896
-7.893
-7.890
-7.887
2.0 2.2 2.4 2.6
-7.896
-7.893
-7.890
-7.887
2.0 2.2 2.4 2.6-7.893
-7.890
-7.887
-7.884
2.2 2.4 2.6 2.8-7.878
-7.875
-7.872
-7.869
E [h
artr
ee]
= 90o = 120o
= 150o
R [bohr]
= 180o
-8.0
-7.8
-7.6
-7.4
-7.2
-7.0
-6.8
1 2 3 4 5 6 7-8.0
-7.8
-7.6
-7.4
-7.2
-7.0
-6.8
1 2 3 4 5 6 7
2.0 2.2 2.4 2.6
-7.896
-7.893
-7.890
-7.887
2.0 2.2 2.4 2.6
-7.896
-7.893
-7.890
-7.887
E [h
artr
ee]
= 90o = 120o
= 150o
R [bohr]
= 180o
2 3 4 5 6 71 2 3 4 5 6 7 8-20
0
20
40
60
80
100 = 180o
R [bohr]
E2
E1
E3
Eec
onom
y -
Ebe
nchm
ark
[meV
] = 90o
1 1 1 2 2 3 2 1, / , ( ) /r r r r r r SIZE SHAPE
1 1 2 e 1 1( , , ) exp 2 ( ) 2exp ( )e e e eV r D A r R A r R
( )e 1 2 .X k m
kmk m n
X
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1
isosce
les config
s ( >
60
o)
2
asymmetric <-- linear configs --> symmetric
isosceles configs ( < 60o)
pe
rpe
ndic
ula
r <
-- d
isso
cia
ted
co
nfig
s -
-> c
olin
ea
r
0.00
0.05
0.10
0.15
0.20
0.25
0.00
0.02
0.04
0.06
0.08
0.10
1 2 3 4 5 6 7
0.1
0.2
0.3
0.4
0.5
0.6
1 2 3 4 5 6 7
0.00
0.02
0.04
0.06
0.08
0.10
1 2 3 4 5 6 7-60
-30
0
30
60
1 2 3 4 5 6 7-60
-30
0
30
60
1 2 3 4 5 6 7-60
-30
0
30
60
1 2 3 4 5 6 7-60
-30
0
30
60
E [h
artr
ee]
1 = 1.0,
2 = 1.0 (D
inf,h)
1 = 0.7,
2 = 1.0 (C
inf,v)
1 = 1.0,
2 = 0.0 (D
3,h)
R1 [bohr]
1 = 0.7,
2 = 0.5 (C
s)
resi
du
es
[me
V]
re
sid
ue
s [m
eV
]
re
sid
ue
s [m
eV
]
re
sid
ue
s [m
eV
]
-100 -80 -60 -40 -20 0 20 40 600
2
4
6
8
10
ab
un
da
nce
[%
]
residues [meV]
0.00.2
0.40.6
0.81.0
0.04
0.06
0.08
0.10
0.5
0.6
0.7
0.8
0.91.0
De
[har
tree
]
1
2
0.00.2
0.40.6
0.81.0
2.0
2.2
2.4
2.6
2.8
3.0
0.5
0.6
0.7
0.8
0.91.0
Re [b
oh
r]
1
2
0.00.2
0.40.6
0.81.0
1.05
1.10
1.15
1.20
1.25
0.5
0.6
0.7
0.8
0.91.0
Ae
[1/b
ohr]
1
2