Ab initio REMPI

Erlendur Jónsson

MSc project

• Electronically excited states of HX•••(H2O)n

• After some trial calculations, this morphed into just calculations of HF and later on HCl

Calculations

• The calculations I’ve been using are all approximate methods of solving the Schrödinger equation

H E

Calculations

• The excited-state calculations are apparently very hard.

• The methods that are used for them are– TD-DFT– CI– CC

TD-DFT

• Time-dependent density functional theory

• The cheapest method

• Results are highly dependent on the selection of functional

• Doesn’t handle non-Rydberg character properly

CI

• Configuration interaction

• Handles correlated electrons

• Can be formally exact

• Extremely expensive

• Common approximation is the CISD– Configuration interaction singles doubles

CC

• Coupled cluster

• Can be formally exact like CI, but cheaper

• CCSD(T) is currently the gold-standard of quantum chemistry

CC

• The S is singly excited electron

• The D are double excited electrons

• A parenthesis, like (T), means that triple excitations are partially calculated via pertubation

• Implementations exist for up to CCSDTQPH

CC - excited states

• EOMCC– Equations of motions coupled cluster

• Fairly reliable

• A lot of research being done at the moment in new methods and extensions of the old methods

CC

• CC methods have a hard time handling bond breaking and high inter-nuclear distance

• To compensate, new extensions have been added, such as the LR-CC and CR-CC (locally and completely renormalized)

Bases

• Systematic basis sets such as the cc-pvNz basis of Dunning, et al. give a very convenient way to improve calculations

• But to handle very electronegative atoms, such as fluorine and chlorine, diffuse functions are needed in the basis which aren’t in the cc-pvNz so I’ve used the aug-cc-pvNz

aug-cc-pvNz

• Augmented correlation consistent polarized valence N zeta

• N can be Double, Triple, Quadruple, 5 (quintuple) or 6 (sextuple)

• Very popular for estimation of Complete Basis Set limit

aug-cc-pcvNz

• Extension of the aug-cc-pvNz where more core-core and core-valence correlation effects are added

• When I tried excited triplet state calculations they proved to work considerably better than the aug-cc-pvNz

HF

• Was able to get fairly good results

• The usual EOMCCSD calculations weren’t able to handle the V state of HF

• Needed CR-EOM-CCSD(T)

• But when that was achieved, the experimental setup didn’t work properly so I started calculations for HCl

MethodX1Σ+

re [Å] ωe [cm-1]B1Σ+

re [Å] ωe [cm-1]

CCSD/aug-cc-pVDZCCSD/aug-cc-pVTZCCSD/aug-cc-pVQZCCSD/d-aug-cc-pVDZCCSD/d-aug-cc-pVTZCCSD/d-aug-cc-pVQZ

0.921930.916420.913840.921510.916690.91380

4116.94184.74211.34111.34186.04201.2

1.988371.980461.987911.989871.979951.98666

1127.71101.91098.91127.01102.11099.4

CCSD(T)/aug-cc-pv5Z[1]MRD-CI[3]Exp[2]

0.91730.923110.91680

4141.94148.644138.32

---2.15162.0908

---1131.21159.18

[1]K.A. Peterson and T.H. Dunning, J. Chem. Phys. 102, 2032,1995[2] Retrieved from http://webbook.nist.gov [3] Bettendorff, M.,et al. Zeitschrift Fur Physik a-Hadrons and Nuclei, 304, 125-135, 1982

160x103

140

120

100

80

60

40

20

0

E /

cm

-1

3.53.02.52.01.51.0r / A

HF, potential curve calculated using EOMCCSD/t-aug-cc-pVQZ level of theoryred: G. Di Lonardo et al., Can J. of Physics, 51, p434, (73)

v=13

HCl

• Harder than HF– More electrons– Larger basis

• I’ve used the experience gained from HF to progress further into the HCl calculations

HCl

• Is C∞v group, but the programs only offer C2v

• This means that the excited state symmetries are a1, a2, b1 and b2

• Which aren’t the real symmetries which we have been seeking

• So it hasn’t been easy finding what state is what in the resulting calculations

HCl

• Our hypothesis is that a1 states have Σ symmetry, a2 Δ symmetry and b1 have Π symmetry

• b1 and b2 are degenerate

Experimental vs. calculations

• We of course need to compare the ab initio calculations to experimental results

• The problems is that we have a potential curve

Experimental vs. calculations

• Currently we just fit the potential and get the various spectroscopic parameters

• These parameters can then be used to simulate a REMPI spectra

T0 De re e exe

F1 CR/5Z 82659 34789 1.308 2786.14 55.78

CR/QZ 83178 46984 1.333 2617.73 36.46

SD/QZ 81270 33526 1.321 2715.19 54.97

Experimental

82847.3 [1]

34464.18 [3]

1.295 [3] 2608.3 [3]

49.35 [3]

C1 CR/5Z 75868 40822 1.335 2847.41 49.65

CR/QZ 76174 44000 1.351 2766.11 43.47

SD/QZ 76266 56002 1.349 2840.25 36.01

Experimental

77485.2 [1]

--- 1.358 [2] 2684.0 [2]

66.0 [2]

X1+ CR/5Z -1511.1 44103 1.270 3090.31 54.13

CR/QZ -1533.5 45288 1.277 3043.09 51.12

SD/QZ -1559.2 45338 1.277 3047.59 51.21

Experimental

-1482.2685

[1]

42330 [1] 1.27455 [2]

2990.946 [2]

52.8186 [2]

The future

• Automate the simulation of the REMPI spectra and if possible remove the fitting part of method– Make a ab initio REMPI simulator

Thank you for your attention