1. Discovery Bay, Hong Kong
MD by X-Rays?
Thomas Prevenslik
QED Radiations
Discovery Bay, Hong Kong
Enter speaker notes here. 1
11th European Conf. Theo. and Comp. Chemistry - EUCO-TCC - Barcelona, Sept. 4-7, 2017

2. Introduction
Chemical reactions are strongly affected by vibrational excitations through changes in the positions of the atoms. Recently, RIXS was shown [1] to provide vibrational control in photochemical reactions. X-rays may be tuned in resonance with stretching while another tuning excites bending modes RIXS = resonant inelastic X-ray scattering spectroscopy
[1] R. C. Couto, et al., “Selective gating to vibrational modes through resonant X-ray scattering,” Nature Communications, 8, 14165, 2017. 2
11th European Conf. Theo. and Comp. Chemistry - EUCO-TCC - Barcelona, Sept. 4-7, 2017

3. Purpose
RIXS shows X-ray pulse interaction with molecules provides control of vibration modes of atoms,
but
also provides the experimental basis for asking the question:
Are X-rays naturally created in atoms controlling ordinary chemical atoms?
The purpose of this presentation is to answer this question 3
11th European Conf. Theo. and Comp. Chemistry - EUCO-TCC - Barcelona, Sept. 4-7, 2017

4. Proposal
X-rays are created in ordinary chemical reactions using heat from the thermal surroundings by simple QED
Simple QED is not the complex light-matter interaction by Feynman and others.
Simple QED assumes QM governs atomic heating and not classical physics.
QM stands for quantum mechanics.
By QM, heating an atom does not increase temperature as the EM confinement of its high surface-to-volume ratio requires the atom heat capacity to vanish.
Consider the Planck law at 300 K 4
11th European Conf. Theo. and Comp. Chemistry - EUCO-TCC - Barcelona, Sept. 4-7, 2017

5. Heat Capacity of the Atom
Classical physics (kT > 0)
kT eV QM
(kT < 0)
Molecules
Under EM confinement at  < 0.1 microns, QM requires atoms in molecules to have vanishing heat capacity 5
11th European Conf. Theo. and Comp. Chemistry - EUCO-TCC - Barcelona, Sept. 4-7, 2017

6. MD by Classical Physics
By the Planck law, MD simulations of the bulk performed under periodic boundary conditions (PBC) assume atoms have heat capacity for  > 100 microns
In the macroscopic bulk by PBC, all atoms do indeed have heat capacity
MD programs, e.g., A&T, are valid for bulk PBC simulations, but invalid for discrete molecules having  < 100 microns while vanishing for  < 0.1 microns
A&T = Allen & Tildesley 6
11th European Conf. Theo. and Comp. Chemistry - EUCO-TCC - Barcelona, Sept. 4-7, 2017

7. Validity of the Equipartition Theorem
Based on statistical mechanics, MD assumes heating a molecule increases the thermal energy of constituent atoms that is converted to kinetic energy by the equipartition theorem providing the vibrational motion of atoms.
By QM, the equipartition theorem for molecules having kinetic energy < KE > = 3 N kT / 2 is invalid as the temperature T of constituent atoms cannot change.
Before considering atoms,
how do nanostructures conserve heat? 7
11th European Conf. Theo. and Comp. Chemistry - EUCO-TCC - Barcelona, Sept. 4-7, 2017

8. Nanostructures
By simple QED, atoms in a NS are placed under high EM confinement as absorbed heat is concentrated almost totally confined in the NS surface NS = nanostructure Simple QED conserves surface heat by creating EM radiation standing across the NS f = ( c/n ) /  ,  = 2d , E = h f where, d is the minimum dimension across the nanostructure, and the velocity of light c is corrected for the slower speed in the NS by its refractive index n But in an atom, there is no surface !!! 8
11th European Conf. Theo. and Comp. Chemistry - EUCO-TCC - Barcelona, Sept. 4-7, 2017

9. Atoms 9 Like a NS, simple QED is applied to an atom by
standing waves of electrons in a circular ring [2]
The standing electron waves consist of n wavelengths  around the circumference of a ring or radius R,
n = 2  R, n = 1,2,3,...
The Planck energy E of electron emission,
E = ko/R = hc/2 R J
where ko = 3.26x 10 −26 J-m
[2] D. Bergman, Electron Wave Function - Electromagnetic Waves Emitted by Ring Electrons, Foundations of Science, 2005 9
11th European Conf. Theo. and Comp. Chemistry - EUCO-TCC - Barcelona, Sept. 4-7, 2017

10. X-rays from Atoms 10 Q=4 R 2 (KT o /R) = 4 K R To  J/s
Since QM precludes atoms from temperature changes, heat flow Q into the atom is conserved by creating X-rays.
In RIXS, the atom is excited with X-ray lasers, but of interest is creation of X-rays under ordinary conditions
Taking a bath of water at 310 K typical of atoms in the human body at 40 C, the conductivity K = 0.61 W/m-K.
The heat Q into an atom as a spherical cavity of radius R in a water bath at absolute temperature To is,
Q=4 R 2 (KT o /R) = 4 K R To  J/s
The time  to create a single X-ray photon is,
 = E / Q  s 10
11th European Conf. Theo. and Comp. Chemistry - EUCO-TCC - Barcelona, Sept. 4-7, 2017

11. X-rays and Ring Radius 11 Q = 4KRTo  = E / Q X-ray time X-ray energy
11th European Conf. Theo. and Comp. Chemistry - EUCO-TCC - Barcelona, Sept. 4-7, 2017

12. Application 12 F= K s x −d/2 ,where d is the bond length
Nitrogen in the stretch mode
As in RIXS, QM precludes atoms from temperature changes, heat flow Q into the atom is conserved by stretch vibrations by specifying momenta of atoms
N2 is modeled by bead-spring with force F,
F= K s x −d/2 ,where d is the bond length
The momentum P imparted to the mass m is,
P= 2mE = mV
Perform MD specifying initial velocity V = 2E/m 12
11th European Conf. Theo. and Comp. Chemistry - EUCO-TCC - Barcelona, Sept. 4-7, 2017

13. Nitrogen by L- J f= 1 2 2K s m = 6.99x 10 13 Hz = 2330 / cm 13
The L- J parameters ( ,  ) for N2 from A&T are:  / k = 37.3 and  = nm having a stretch stiffness
K s = 72 2 1/3  2 =9337 Nt m
But experimentally, K s =2261 Nt/m giving
f= 1 2 2K s m = 6.99x Hz = 2330 / cm
Problem is L-J applies to weak interactions between closed-shell atoms, not to covalent bonds
How does MD by QM compare? 13
11th European Conf. Theo. and Comp. Chemistry - EUCO-TCC - Barcelona, Sept. 4-7, 2017

14. Nitrogen by QM
The N2 molecule was simulated in A&T with the anti-node fixed
Like RIXS, momentum P is applied in the stretch direction.
Only a fraction  of the X-ray energy E is inelastic
Eo =  E, but  is not known
Vibrations are inelastically excited at   50 meV
Assuming Eo = 10 meV, V = 371 m/s
Perform MD with Iterations with t = 10 −16 s
The N2 frequency  = 6.8 x Hz = 2330 / cm
agrees with experiment
No need to invoke the equipartition theorem 14
11th European Conf. Theo. and Comp. Chemistry - EUCO-TCC - Barcelona, Sept. 4-7, 2017

15. Nitrogen by QM 15 X = +/- 50 pm V = +/- 371 m/s Amplitude - X - pm
Velocity - V - m/s
Amplitude - X - pm
X = +/- 50 pm
V = +/- 371 m/s 15
11th European Conf. Theo. and Comp. Chemistry - EUCO-TCC - Barcelona, Sept. 4-7, 2017

16. Nitrogen by Equipartition Theorem
One MD method of fixing the kinetic temperarure is to rescale the velociites at ech step by
Factor = T F 1/2
T = desired temperature F = current temperature
Equipartition  F = 2.0 * K / Boltz / 3.
V = V * Factor
However, for fast transients, as the Nitogen stretch mode the equipartition theorem gives meaningless results, but if no scaling the results are identical to QM 16
11th European Conf. Theo. and Comp. Chemistry - EUCO-TCC - Barcelona, Sept. 4-7, 2017

17. Equipartition Results
The scaling of velocities in the Nitrogen stretch mode was made by constraining the temperature to 310 K, the resuts differing from QM
Temperatures +/- 500 K (310 K)
Amplitude +/- 40 pm (50 pm)
Velocites +/- 74 m/s (371 m/s) 17
11th European Conf. Theo. and Comp. Chemistry - EUCO-TCC - Barcelona, Sept. 4-7, 2017

18. Vibration Analysis
RIXS shows N2 stretch vibrations (0.2 eV) superposed on X-ray (434 eV) response?
2 DOF N2 atom – electron model M1 K1 K2 M2
Anti-node F A2 A1
M1 , M2 = Mass of N2 atom and electron
K1 , K2 = Vibration stiffness of N2 atom and electron
F = Vibration force of N2 atom
A1 , A2 = Amplitude of N2 atom and electron vibrations 18
11th European Conf. Theo. and Comp. Chemistry - EUCO-TCC - Barcelona, Sept. 4-7, 2017

19. Vibration Results 19 E2 = 434*q J f2 = E2/h = 1.05x 10 17 Hz
M2 = 9.31x 10 −31 kg
K2 = M2 (2f2) 2 = Nt/m
A2 = 4x 10 −9 m
K1 = 2*2261 Nt/m
M1 = 14/Avag
M1 = 2.32x 10 −26 kg
A1 = 0.04 m
Electron is excited by N2 vibrations. But for F = 1 Nt , the N2 amplitude A1 = 0.04 m gives an electron amplitude A2 = 4x 10 −9 m  A2 / A1 = 1x 10 −7  small ! 19
11th European Conf. Theo. and Comp. Chemistry - EUCO-TCC - Barcelona, Sept. 4-7, 2017

20. RIXS Chemistry
RIXS chemistry differs from ordinary chemistry as an external X-ray source excites the molecule.
The difference between the X-rays (in and out) may be inelastic, the latter exciting vibrational modes as QM precludes changes in temperature
MD simulations of RIXS by QM require imposing momenta on all atoms in the direction of the X-ray
At present, the inelastic fraction  of the X-ray energy E converted to vibration energy Eo can only be estimated, but in principle could be compiled for all atomic elements. 20
11th European Conf. Theo. and Comp. Chemistry - EUCO-TCC - Barcelona, Sept. 4-7, 2017

21. Ordinary Chemistry
Atoms in a molecule continually absorb heat Q from the surroundings including X-rays from other atoms
By QM, heat Q into the atom cannot be conserved by a temperature increase.
Hence, heat Q may only be conserved by non-thermal Planck energy E in the core electrons at E > 100 eV
But heat Q << 100 eV !
Over time < 10 ns, heat Q accumulates until E = 100 eV inducing X-ray emission that excites vibrational states , or
is absorbed by other atoms in the molecule!
The process is forever continuous 21
11th European Conf. Theo. and Comp. Chemistry - EUCO-TCC - Barcelona, Sept. 4-7, 2017

22. MD under PBC is valid by QM
Conclusions
MD under PBC is valid by QM
MD for discrete molecules by PBC is meaningless, but may be modified to be consistent with QM
MD by X-rays requires modifying computer programs for QM by replacing chemical reactions driven by temperatures by specifying momenta of atoms
MD by X-rays requires assumptions of the inelastic fractions  of the X-ray energy E in the vibration mode of all atoms in the molecule, at least initially
The N2 molecule in the stretch mode is used as a simple example of how MD programs may be modified for X-rays to simulate RIXS and ordinary chemistry 22
11th European Conf. Theo. and Comp. Chemistry - EUCO-TCC - Barcelona, Sept. 4-7, 2017

23. Questions & Papers
Enter speaker notes here. 23
11th European Conf. Theo. and Comp. Chemistry - EUCO-TCC - Barcelona, Sept. 4-7, 2017