2009.06.22OSU MI07 Coy,Wong,Kay,Field1 New effective one-electron potential for CaF based on ab-initio calculations CaF is a prototype for all Rydberg

2009.06.22 OSU MI07 Coy,Wong,Kay,Field 1

New effective one-electron potential for CaF based on ab-

initio calculations

• CaF is a prototype for all Rydberg systems. All bound electronic states of this molecule are members of some Rydberg series.• CaF investigations are continuing in Bob Field’s and Christian Jungen’s groups, with several recent papers, and a new QDT fit paper in progress.• We have talked previously about CaF: MQDT calculation techniques, shape resonance, photoionization cross section anisotropy.• Currently, a new QDT fit is in progress (Jeff Kay), and new ab-initio calculations are available (Bryan Wong), so we focus today on the new ab-initio results, their implications for the CaF+ - e- potential, and the relationship to experimental results.

Stephen L. Coy, Bryan M. Wong, Jeffrey J. Kay, and Robert W. FieldMIT Dept. of Chemistry and Sandia National Labs (BMW)


• Calculations of the energy levels for comparison with experiment have been based on MQDT theory as developed by Serhan Altunata based on work by Christian Jungen, Chris Greene, Seaton, and others. (Altunata et. al.).

• Calc. have used a one-electron effective potential optimized only for the equilibrium internuclear separation, Req=3.54. (AJ potential, Arif et. al.).

• Multipole moments from the AJ potential agree with those from ab-initio near Req, but begin to differ as a function of R.

• Ab-initio moments have been calculated from two different types of calculations, then fitted to R-dependent Ca and F polarizabilities in the AJ one-electron effective potential.

• Ca polarizability is almost independent of R while F polarizability increases with R. This inferred R variation can be understood in terms of the differing atomic orbital structures of Ca and F.

New effective one-electron potential for CaF based on ab-initio calculations

Summary Outline


The one-electron effective potential for CaF

Hamiltonian terms1. Coulomb2. e--induced dipole3. nuclei-induced dipole4. induced dipole – induced dipole5. Ca core correction


Terms in Arif, Jungen, Roche effective 1-e- potentialM. Arif, Ch. Jungen, and A. L. Roche, J. Chem. Phys. 106 (10), 4102, 8 March 1997

a) the Coulomb interaction between Z1 , Z2 , and e2;b) the energy of the electric dipole induced on each ion by the electron and by the charge of the other ion;c) the dipole–dipole interaction energy of each electron induced dipole on one center with the ion-induced dipole on the other center;d) the dipole–dipole interaction energy of the twoelectron-induced dipoles;

Coulomb (e-nuclei) e - (e-ind. dip) e-(ion-ind. dip)

e) a small metal core correction potential which will be specified in Sec. III B;f) OMITTED: all the terms that are independent of the position of the electron , but may be dependent on R, such as e.g. the dipole–dipole interaction energy between the dipoles induced on each ion by the other ion) are part of the energy of the ion core and are therefore not considered explicitly

(e-ind. dip) – (ion-ind dip) (e-ind. dip) – (e-ind dip) e in core corr.

V for r>r1a (Ca atomic zone rad)

angles are zero at the midpoint.


Two different types of calculations have been completed. Others are currently in progress.

1. Point potential calculation. A test charge is placed in the vicinity of the ion core, and the energy calculated.a. All point charge calculations were obtained by sequentially placing

a negative point charge around the center of mass of the CaF+ ion. Each of the single-point energies was calculated using the coupled cluster with singles and double substitutions with perturbative triples (CCSD(T)) level of theory.

2. CaF+ ion core calculationa. Electric multipole moment values for the CaF+ ion were obtained

by computing the expectation value of the tensor operators using the CCSD density matrix.

The ion core calculation did not include triples corrections, but that calculation is now in progress.

Both point charge and ion core calc utilized a new cc-pCVTZ basis recently published for the Ca atom [ref].

[Ca atomic core]: M. A. Iron, M. Oren, and J. M. L. Martin. Mol. Phys., 101:1345, 2003. and

Iron MA, Oren M, Martin JML, "Alkali and alkaline earth metal compounds: core-valence basis sets and importance of subvalence correlation", Mol. Phys. 101 (9): 1345-1361 MAY 2003

CaF ab-initio calculations


CaF ab-initio calculations

Ab-initio point potential energies are rather smooth away from the ion cores


2.5 3 3.5 4 4.50

0.1

0.2

0.3

0.4

0.5

R

Ene

rgy/

hartre

e

Morse fit to CaF+ energies

De, R

e, , V+777

(0.1906, 3.56, 0.778, 0.24191)

Dee-2(R-R

e) - 2D

ee-(R-R

e) + V

calcfitMorse

CaF+ morse vibrational freq ωe = 0.003134 Eh = 687.85 cm-1

Xee = 0.00411ΩX = 2.82752 cm-1

CaF reduced mass 12.8889 amu

Morse fit to CaF ab-initio calculations

The energies from the ion calculation fit well to a Morse potential form, with a vibrational frequency that is close to the experimental value.


CaF dipole moments

The AJ potential assumes that polarizabilities are independent of R.

The dipole moment increases less than expected with R, therefore polarizabilities, which decrease the dipole moment, are increasing with R.

Multipole moments are calculated from the point-sampled potential using a band-limited Fourier interpolation method that gives accurate results through the octopole moment.


CaF higher moments, Expt’l value

Only d^2 – Q is known experimentally with the current data set, as discussed inJ.J.Kay et. al. JCP 128, 194301(2008).


The two ab-initio calculations differ. Possible reasons include

1. No triples correction in ion core calc.• Ion core calc with triples is in

progress.2. r1 = 20 for the charge location

may be affecting the potential.• Calculation for r1=30 is in

progress.3. In the point potential, the

Rydberg electron is represented by a stationary negative charge. The stationary charge may have a greater effect on the core electrons than the Rydberg electron. In the ion calc, the ion core is unperturbed by external charges. The experimental value is intermediate, with location that can depend on relative timescales of Rydberg and core, and thus on n,l.

CaF ab-initio calculation comparison

Until these results are analyzed, take a linear combination of ion and point potential moments, matching d2-Q, to determine the R dependence of the α(Ca), and α(F) values in the AJ form.


With d2-Q matching the experimental value

Polarizabilities of Ca and F in AJ potential from ab-initio

moments

Qualitative behavior is the same for both point and ion calc

α(Ca) remains nearly constant with R, while α(F)Increase strongly.


Orbital-mixing model of polarizabilities of Ca and F

The polarizability coefficient describes the mixing between atomic orbitals that occurs due to the presence of a nearby charge. The affected levels in F are closer together than those in Ca. If the mixing is so close that the levels become completely mixed, α will decrease as R decreases, because the polarizability is saturated.

1. The Ca polarizability coefficient remains nearly constant with R,thus the mixing of the orbitals is not near saturation.2. The F coeffient increases as R increases, indicating that it iscoming out of saturation as R becomes large.3. The Ca coefficient is smaller than the F coefficient, againindicating that it is further from saturation. The induction on the Cais lower that on F because the mixed levels are further apart.4. The F polarizability is almost linearly increasing with Rin this restricted range. Can this scaling come out of the two-level orbitalmodel? TBD.


• The polarizabilities in a one-electron effective potential derived from ab-initio calculations appear reasonable and can be given a physical basis.

• Further calculations are in progress.• We will now perform MQDT calculations using this updated potential for

comparison with the massive fit being completed by Jeff Kay. The AJ potential gave good agreement with his results near Req, but deviated at other R values.

New effective one-electron potential for CaF based on ab-initio calculations

Summary and Future Plans

MQDT calc with AJ potential is compared to expt. (eigenchannel decomposition) and shows deviations away from Req = 3.54.

Documents

2009.06.22OSU MI07 Coy,Wong,Kay,Field1 New effective one-electron potential for CaF based on ab-initio calculations CaF is a prototype for all Rydberg