RHF-RCCSD-T CALCULATIONS FOR THE RHF-RCCSD-T CALCULATIONS FOR THE B2 AND A1 STATESB2 AND A1 STATES

AB INITIOAB INITIO AND DIM MODEL AND DIM MODEL

INCLUSION OF THE SPIN-ORBIT COUPLINGINCLUSION OF THE SPIN-ORBIT COUPLINGTHROUGH DIM (for the ground-state surface)THROUGH DIM (for the ground-state surface)

6 8 1 0 1 2 1 4- 0 . 1 0

- 0 . 0 5

0 . 0 0

0 . 0 5

0 . 1 0

0 . 1 5

0 . 2 0

0 . 2 5

6 8 1 0 1 2 1 4- 1 5 0

- 1 2 5

- 1 0 0

- 7 5

- 5 0

- 2 5

0

En

erg

y [a

.u.]

R [ a . u . ]

a n g l e = 3 0 o

E

ne

rgy

[me

V]

R [ a . u . ]

S p i n - o r b i t c o r r e c t i o n t o t h e a b i n i t i o p o i n t s

4 6 8 1 0 1 2 1 4

- 0 . 0 6

- 0 . 0 5

- 0 . 0 4

- 0 . 0 3

- 0 . 0 2

- 0 . 0 1

0 . 0 0

0 . 0 1

0 . 0 2

4 6 8 1 0 1 2 1 4- 2 5 0

- 2 0 0

- 1 5 0

- 1 0 0

- 5 0

0

En

erg

y [a

.u.]

R [ a . u . ]

a n g l e = 6 2 o

S p i n - o r b i t c o r r e c t i o n t o t h e a b i n i t i o p o i n t s

E

ne

rgy

[me

V]

R [ a . u . ]

4 6 8 1 0 1 2 1 4

- 0 . 0 6

- 0 . 0 5

- 0 . 0 4

- 0 . 0 3

- 0 . 0 2

- 0 . 0 1

0 . 0 0

0 . 0 1

0 . 0 2

4 6 8 1 0 1 2 1 4- 2 5 0

- 2 0 0

- 1 5 0

- 1 0 0

- 5 0

0

En

erg

y [a

.u.]

R [ a . u . ]

a n g l e = 9 0 o

S p i n - o r b i t c o r r e c t i o n t o t h e a b i n i t i o p o i n t s

E

ne

rgy

[me

V]

R [ a . u . ]

4 6 8 1 0 1 2 1 4

- 0 . 0 6

- 0 . 0 5

- 0 . 0 4

- 0 . 0 3

- 0 . 0 2

- 0 . 0 1

0 . 0 0

0 . 0 1

0 . 0 2

4 6 8 1 0 1 2 1 4- 2 5 0

- 2 0 0

- 1 5 0

- 1 0 0

- 5 0

0

En

erg

y [a

.u.]

R [ a . u . ]

a n g l e = 1 2 0 o

S p i n - o r b i t c o r r e c t i o n t o t h e a b i n i t i o p o i n t s

E

ne

rgy

[me

V]

R [ a . u . ]

4 6 8 1 0 1 2 1 4

- 0 . 0 6

- 0 . 0 5

- 0 . 0 4

- 0 . 0 3

- 0 . 0 2

- 0 . 0 1

0 . 0 0

0 . 0 1

0 . 0 2

4 6 8 1 0 1 2 1 4- 2 5 0

- 2 0 0

- 1 5 0

- 1 0 0

- 5 0

0

En

erg

y [a

.u.]

R [ a . u . ]

a n g l e = 1 5 0 o

S p i n - o r b i t c o r r e c t i o n t o t h e a b i n i t i o p o i n t s

E

ne

rgy

[me

V]

R [ a . u . ]

4 6 8 1 0 1 2 1 4

- 0 . 0 6

- 0 . 0 5

- 0 . 0 4

- 0 . 0 3

- 0 . 0 2

- 0 . 0 1

0 . 0 0

0 . 0 1

0 . 0 2

4 6 8 1 0 1 2 1 4- 2 5 0

- 2 0 0

- 1 5 0

- 1 0 0

- 5 0

0

En

erg

y [a

.u.]

R [ a . u . ]

a n g l e = 1 7 9 o

E

ne

rgy

[me

V]

R [ a . u . ]

D i f f e r e n c e s A B I N I T I O ( B 2 ) - D I M ( E 1 )

— — D I M — — D I M + S O

• • • • • D I M + I D - I D • • • • • D I M + S O + I D - I D

• a b i n i t i o , B 2 O a b i n i t i o , B 2 + S O

• a b i n i t i o , A 1 O a b i n i t i o , A 1 + S O

6 8 1 0 1 2 1 4

0 . 0

0 . 5

1 . 0

1 . 5

2 . 0

2 . 5

6 8 1 0 1 2 1 4- 5 0

- 4 0

- 3 0

- 2 0

- 1 0

0

1 0

2 0

En

erg

y [a

.u.]

R [ a . u . ]

a n g l e = 3 0 o

E

ne

rgy

[me

V]

R [ a . u . ]

D i f f e r e n c e s A B I N I T I O ( B 2 ) - D I M ( E 1 )

4 6 8 1 0 1 2 1 4

- 0 . 0 6

- 0 . 0 5

- 0 . 0 4

- 0 . 0 3

- 0 . 0 2

- 0 . 0 1

0 . 0 0

0 . 0 1

0 . 0 2

0 . 0 3

4 6 8 1 0 1 2 1 4- 7 5

- 5 0

- 2 5

0

2 5

5 0

7 5

1 0 0

En

erg

y [a

.u.]

R [ a . u . ]

a n g l e = 6 2 o

E

ne

rgy

[me

V]

R [ a . u . ]

D i f f e r e n c e s A B I N I T I O ( B 2 ) - D I M ( E 1 )

4 6 8 1 0 1 2 1 4

- 0 . 0 6

- 0 . 0 5

- 0 . 0 4

- 0 . 0 3

- 0 . 0 2

- 0 . 0 1

0 . 0 0

0 . 0 1

0 . 0 2

0 . 0 3

4 6 8 1 0 1 2 1 40

2 5

5 0

7 5

1 0 0

1 2 5

1 5 0

1 7 5

2 0 0

En

erg

y [a

.u.]

R [ a . u . ]

a n g l e = 9 0 o

En

erg

y [m

eV

]R [ a . u . ]

D i f f e r e n c e s A B I N I T I O ( B 2 ) - D I M ( E 1 )

4 6 8 1 0 1 2 1 4

- 0 . 0 6

- 0 . 0 5

- 0 . 0 4

- 0 . 0 3

- 0 . 0 2

- 0 . 0 1

0 . 0 0

0 . 0 1

0 . 0 2

0 . 0 3

4 6 8 1 0 1 2 1 40

2 5

5 0

7 5

1 0 0

En

erg

y [a

.u.]

R [ a . u . ]

a n g l e = 1 2 0 o

E

ne

rgy

[me

V]

R [ a . u . ]

D i f f e r e n c e s A B I N I T I O ( B 2 ) - D I M ( E 1 )

4 6 8 1 0 1 2 1 4

- 0 . 0 6

- 0 . 0 5

- 0 . 0 4

- 0 . 0 3

- 0 . 0 2

- 0 . 0 1

0 . 0 0

0 . 0 1

0 . 0 2

0 . 0 3

4 6 8 1 0 1 2 1 4- 2 5

0

2 5

5 0

7 5

1 0 0

En

erg

y [a

.u.]

R [ a . u . ]

a n g l e = 1 5 0 o

E

ne

rgy

[me

V]

R [ a . u . ]

D i f f e r e n c e s A B I N I T I O ( B 2 ) - D I M ( E 1 )

4 6 8 1 0 1 2 1 4

- 0 . 0 6

- 0 . 0 5

- 0 . 0 4

- 0 . 0 3

- 0 . 0 2

- 0 . 0 1

0 . 0 0

0 . 0 1

0 . 0 2

0 . 0 3

4 6 8 1 0 1 2 1 4- 2 5

0

2 5

5 0

7 5

1 0 0

1 2 5

1 5 0

En

erg

y [a

.u.]

R [ a . u . ]

a n g l e = 1 7 9 o

E

ne

rgy

[me

V]

R [ a . u . ]

D i f f e r e n c e s A B I N I T I O ( B 2 ) - D I M ( E 1 )

— — D I M • • • • • D I M + I D - I D

• a b in i t io , B 2 • a b in i t io , A 1

Evaporation energies for KrEvaporation energies for Kr33++(D(Dhh) ) Kr Kr22

++ + Kr + Kr

Method Energy (eV)

Exp. [Hiraoka et al, J.Chem.Phys.92 (1990) 4408] 0.2290.007 Exp. [Fehsenfeld et al, 31st Gaseous El. Conference, NY 1978] 0.27 DIM with SO - De (D0) 0.238 (0.234) DIM with SO and ID-ID - De (D0) 0.245 (0.240) RCCSD-T (De with SO) 0.246

Dissociation energies forDissociation energies for Kr3++(D(Dhh) ) Kr Kr++((22PP3/23/2) + 2 Kr) + 2 Kr

Method Energy (eV)

DIM with SO - De (D0) 1.386 (1.369) DIM with SO and ID-ID - De (D0) 1.392 (1.375) RCCSD-T with SO - De 1.393

CONCLUSIONS AND PERSPECTIVESCONCLUSIONS AND PERSPECTIVES

• The RCCSD-T calculations with the extended basis set provide highly accurate potential energy surfaces for the ground states of Kr3

+. The PESs for the B2 and A1 states (C2v) were obtained over a large range of nuclear configurations. Spin-orbit coupling can be included from the DIM model. For the lowest electronic states the semi-empirical (DIM) and ab initioPESs are in very good agreement.• The MCSCF- CI method provides a manifold of the PESs suitable to test and improve the DIM results. The calculation with the extended basis are very expensive and can be carried on only at selected nuclear configurations for the test purposes. The calculations with the reduce basis set are feasible, they provide qualitatively correct PESs, and can be used for a monitoring of three body effects over a large range of nuclear configurations. The loss of accuracy when passing from the extended to the reduced basis set has a negligible effect on the energy separations of the states. Spin-orbit interaction can be incorporated into the MCSCF-CI data through the DIM model.• The simultaneous use of the DIM and ab initio methods for Kr3

+ can provide reliable PESs that can be expressed analytically and used both in the spectroscopical and dynamical studies.

MULTI REFERENCEMULTI REFERENCEMCSCF-CI CALCULATIONSMCSCF-CI CALCULATIONS

R1=R2=5.38 au linear

MCSCF- CI extended reduced basis set RCCSDTE(1A’) -54.82103 au -54.76111au -54.92414au

2A´-1A´ 44,0 kcal 43,8 kcal 54.8 kcal 3A´-1A´ 57,5 kcal 57,0 kcal 5A´-1A´ 66,1 kcal 66,4 kcal

MCSCF-CI and DIM (without SO) for C2v

First steps towards modelling three - body effects in KrFirst steps towards modelling three - body effects in Krnn++

Petr Milko Petr Milko a) b)a) b), René Kalus , René Kalus c)c), Ivana Paidarová , Ivana Paidarová a)a), and Jan Hru, and Jan Hrušášákk a)a)

a) a) J. HeyrovskJ. Heyrovskýý Institute of Physical Chemistry, Praha, Institute of Physical Chemistry, Praha, b) b) Institute of Chemical Technology, Praha, Institute of Chemical Technology, Praha, c) c) University of Ostrava, OstravaUniversity of Ostrava, Ostrava

AIMThe structure, absorption spectra and the dynamics of the Krn

+ clusters can be efficiently studied by modelling based on the semiempirical diatomics-in-molecules method (DIM) [Kalus et al, Chem.Phys. 294 (2003)141; 298 (2004)155;302(2004)279]. Presented ab initio studies aim to i) provide accurate potential energy surfaces for the lowest electronic state of Kr3

+ for an analysis of rovibrational spectra ii) justify and improve the quality of the DIM potential energy surfaces for the electronic states of Krn

+ participating in computational dynamical simulations by a proper incorporation of the three-body forces effects into the DIM models.

STRATEGYSTRATEGY• Very accurate ab initio calculation of the potential energy

surfaces (PESs) for the lowest electronic states of Kr3+ (B2

and A1 at C2v,) by use of the MOLPRO 2002 program,

RHF-RCCSD-T method with the relativistic effective core

potential and basis set of Niclass et al [J.Chem.Phys.102(1995) 8942

Dolg]] optimized for Kr2+ [Kalus at al, Chem.Phys.294 (2003) 141]

and core polarization potential.• Inclusion of the spin-orbit interaction through the DIM model: Eab initio SO= Eab initio- EDIM+ EDIM+SO

• Multi-reference (MCSCF-CI) calculations for the five A’ and three A’’ electronic states of Kr3

+ with the reduced basis set [8s6p6d6f2g]->[8s6p3d1f] in order to provide reliable PES over a large range of nuclear configurations.

Grant No. 203/02/1204 of the Grant Agency of the Czech Republic