1. Computer Spectrometers
Nike Dattani
Kyoto University

2. At what number of electrons
do you think theory is no longer able to match the best experiments?
Experimental energy gap is hyperfine structure according to table 4 of:
He (from Table VIII of Experimental: (16)
Theoretical:
Fourth order means: alpha^4 2

3. 1e- : H Hyperfine splitting
(1) mHz (present best experiment)
(present best theory)
Discrepancy is 7.5 milli-Hartree
What’s missing is the effect of the nuclear structure !!!
Experimental energy gap is hyperfine structure according to table 4 of:
He (from Table VIII of Experimental: (16)
Theoretical:
Fourth order means: alpha^4 3

4. 1e- : Mu (p+ in H is replaced by μ+)
Hyperfine splitting
(1) Hz (experiment)
Hz (theory)
Muonium Experimental energy gap is hyperfine structure according to table 19 of:
He (from Table VIII of Experimental: (16)
Theoretical:
Fourth order means: alpha^4 4

5. QED: Electromagnetism
QFD: Weak nuclear interaction
QCD: Strong nuclear interaction
QGD: Gravity
Q5D: “Fifth forces”

6. QED: Electromagnetism
QFD: Weak nuclear interaction
QCD: Strong nuclear interaction
QGD: Gravity (Dream)
Q5D: “Fifth forces” (Nightmare)

7. 1e- : Mu (p+ in H is replaced by μ+)
Hyperfine splitting
(1) Hz (experiment)
Hz (QED)
2e- : He
Hyperfine splitting
(7) cm-1 (experiment)
(5) cm-1 (QED + nuclear structure)
Muonium Experimental energy gap is hyperfine structure according to table 19 of:
He (from Table VIII of Experimental: (16)
Theoretical:
Fourth order means: alpha^4 7

8. QED Electromagnetism QFD Weak nuclear QCD Strong nuclear
Darwin, Mass velocity, spin-spin, spin-orbit, orbit-orbit
Dirac-Coulomb-Breit
Schrodinger Eqn
Lamb shift
α2H2 + α4H4 + α5H5 + α6H6 + α7H7 ...
QED Electromagnetism
QFD Weak nuclear
QCD Strong nuclear

9. Ionization energies in cm-1
Experimental energy gap is hyperfine structure according to table 4 of:
He (from Table VIII of Experimental: (16)
Theoretical:
Fourth order means: alpha^4 9

10. Buy one, get everything! α2H2 + α4H4 + α5H5 + α6H6 + α7H7 ...
Experimental energy gap is hyperfine structure according to table 4 of:
He (from Table VIII of Experimental: (16)
Theoretical:
Fourth order means: alpha^4 10

11. March 2017 Ionization energies in cm-1
Experimental energy gap is hyperfine structure according to table 4 of:
He (from Table VIII of Experimental: (16)
Theoretical:
Fourth order means: alpha^4
March 2017 11

12. March 2017 March 2017 Ionization energies in cm-1
Experimental energy gap is hyperfine structure according to table 4 of:
He (from Table VIII of Experimental: (16)
Theoretical:
Fourth order means: alpha^4
March 2017
March 2017 12

13. Total non-relativistic energy [Hartree]
Method H 1
-1/2
Exact He 2
Hylleraas Li 3
-7.478 060 323 910 134 843 Be 4
 356 494 9
ECG B 5
 867 537 C 6
-37.84

14. Total non-relativistic energy [Hartree]
Method
Error H 1
-1/2
Exact He 2
Hylleraas Li 3
-7.478 060 323 910 134 843
-7.478 060
FCIQMC / aug-cc-pCV8Z
215 μEh Be 4
 356 494 9
ECG
 356
285 μEh B 5
 867 537
 867
308 μEh C 6
-37.84
 229(2)

15. # e-
Total non-relativistic energy
Method
Error Ga 31
(1)
FCI QMC / aug-cc-pCV8Z -
-1921.
CCSD(T)
3 Eh Ge 32
(1)
FCI QMC
-2070.
6 Eh As 33
(19)
5 Eh Se 34
(14)
-2400.
1 Eh Br 35
(58)
-2572. Kr 36
(88)
100 mEh
For Kr atom, FCI is like CCSD..TQPH

16. Carbon (6e-)
June 2017 !

20. Application: Custom-made molecules
Used 1000 digits for maple calculation 20

21. What we need to know
# of
atoms
50 kHz
Energy of
laser ∆E

22. What we need to know ∆E If we know energy to +/- 1 cm-1 +/- 30,000 MHz
120,000 measurements
1.8 years
# of
atoms
50 kHz ∆E

23. (H.B. Schlegel, Gordon Drake)
Best ab initio for Li2 (6e-)
(H.B. Schlegel, Gordon Drake)

24. Vibrational Energies in cm-1
Schlegel & Drake
Present
(FCI QMC)
Empirical BO
∞Li2
Diff.
5.0
(14)
0.14 cm-1
6.0
(32)
0.12 cm-1
6.5
-94.46
-96.39(12)
-96.51
7.0
-64.68
-66.61(14)
-66.51
0.10 cm-1
8.0
-30.20
-31.70(12)
-31.72
0.02 cm-1
9.0
-14.73
-15.51(15)
-15.55
0.04 cm-1 15
-0.63
-0.59(88)
-0.64
0.05 cm-1 20
-0.11
-0.07(170) 30
(1100)
0.003 cm-1

25. Vibrational spectrum:

26. Thank You !!!