View source for Inter system crossing

= Why the need for "inter system crossing" and what it is = 

== The need for flipping spins to make some covalent reactions happen ==

In [[piezochemical mechanosynthesis]] sometimes one wants to intentionally flip a spin. <br>
Without the spin being flipped the lowest possible electronic energy state (in the timeframe of the mechanosynthetisation reaction) <br>
might not be the ground state. That means when pressing the bonding partners together they might not form a covalently bonding orbital. <br>
This is due to the pauli-principle not allowint two electrons with the same spin sitting in the same (lowest energy state) orbital.

'''Spin-flipping less critical for heavier atoms like transition metals:''' <br>
This is especially the case with light elements like carbon where filled high-energy antibinding orbitals often make a bond impossible. <br>
Transition metals can from bonds with electrons in antibinding orbitals (albeit weaker bonds) and these eventually de-excite to become bonds of full strength. <br>
Still this is not at all desirable since this is a high energy dissipation mechanism. Devaluating a lot of un-bond Helmholtz free energy. 

== Flipping a spin means flipping (preserverd) angular momentum => drain needed ==

Since 
* spin is linked to angular momentum (gyromagnetic factor) and
* there is conservation of angular momentum 
we need to find a recipient for that angular momentum that is both 
* capable of taking that angular momentum up quickly and 
* "willing" to take it up quickly.

== Listing potential means for flipping spins ==

What we seek are effects that make some angular momentumm carrying "particles" interact with electron spins in the form of a magnetic torque. <br>
Options for potential sinks for unwanted angular momentum that comes with spin include:
* (?photons in the form of phosphorescence? – way too slow end dissipating energy)
* nuclear spins (energy conservation too)
* external magnetic field
* '''orbital configuration change''' – via "spin orbit coupling"
It seems the last one is best (to check what's the issue with the others)

== Why spins are "frobidden" to flip without relativistic quantum mechanics ==

Unfortunately paired spins (singlet-state wave function) and unpaired spins (triplet-state wave function) are orthogonal wave functions <br>
meaning their [[overlap integral]] is zero – meaning they don't interact – meaning the transition is "forbidden". <br>
<small>(Meaning Fermis golden rule predict infinitely long transition time?)</small> <br>
So there's a problem with the "willingness" part. <br>
This is just to first approximation though.

=== Relativistic quantum mechanics saving the day ===

Taking into account effects of relativistic quantum mechanics, <br>
<small>(these fall out of the Dirac equation – the relativistic generalization of the Schrödinger equation)</small> <br>
One gets a spin-orbit coupling energy term in the Hamiltonian. Exactly what we want. <br>
In the non-relativistic picture this effect can be fudged in as a perturbation term. Spin orbit coupling term (SO).

<math> H_{SO} = - \frac{Z^4 e^2}{8 \pi \epsilon_0 m_e^2 c^2} \vec l \cdot \vec s </math>

Note that the '''interaction strength is proportional to the fourth power of the atomic number Z'''. <br>
Doubling the atomic number causes a 16-fold increase in interaction strength. <br>
So '''the Elements of the 3rd row and higher are good "drains" for getting rid of unwanted angular momentum'''. <br>
* This is called the '''"heavy atom effect"'''. <br>
* It even works if there is no direct covalent bond '''"external heavy atom effect"''' <br>
How does the latter one work? There needs to be some overlap of electron wave functions right? <br>
<small>A highly electronically isolating connection (like plain diamond can be, or a nonbonding VdW contact can be, or a minimal vacuum gap can be) is probably a bad idea right?</small>

== Side-notes to spinning flips via ISC ==
 
* Beside "spin flipping" there is also "spin rephaseing" as a possible transition (precession speed ...) ???
* This topic is related to spectroscopy and optical effects
<br>
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= Inter system crossing in (piezochemical) mechanosynthesis =

Design target: Increasing inter system crossing rates. Goals:
* avoiding errors
* increasing reaction speeds
* reducing energy dissipation

== Avoiding errors (omitted reactions, misreactions) due to too low singlet-triplet energy gap ==

* Singlet transition geometries often resemble triplet equilibrium geometries (Salem and Rowland 1972 – referenced by [[Nanosystems]])
* Singlet state (paired) to low lying triplet state is undesired
To avoid that 
* either (conservatively) get the energy gap up to above 145zJ ( = k * 300K * ln(10^15) )
* or (weaker prerequisite) get the accumulated ramp-on ISC transition rate to a probability above ln(P_err) prior <br>to theΔV_s,t point where the geometry is no longer suitable for bond formation

== Inadvertently slowing down by pressing to hard ==

Citations from [[Nanosystems]]: 
* "As the radicals approach the gap between the triplet and singlet state energies grows, but this ''decreases'' the rate of intersystem crossing". <br>
* "The condition that ΔV_s,t ≥145maJ imposes a significant constraint  because k_isc varies inversely with the electronic energy difference ΔV_isc which (in the absence of mechanical relaxation) would equal the difference in equilibrium energies ΔV_s,t, and will frequently be of similar magnitude"

== Avoiding dissipation during bond cleavage by speeding up ISC ==

If inter system crossing is slow compared to (tensile) bond cleavage then cleavage gives a singlet diradical <br>
When pulling the cleaved parts further apart then the singlet triplet energy gap vanishes <br>
and thermal excitations fill the triplet state (a loss in Helmholtz free energy of minus ln(2)kT – a loss of one bit information – undesired dissipation)

{{todo|That would cause local cooling that goes unused and thus gets dissipated by ambient heat flowing in? Could that be partially recuperated by a heat pump? Abd or exploited for deliberate cooling?}}

If inter system crossing is fast compared to (tensile) bond cleavage then
* thermal excitations fill the (repulsive) triplet state already during bond cleavage 
* => there is a reduction of the mean-force bond potential energy (?)
* there is no significant dissipation ☺

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An other means for reducing dissipation is: [[Dissipation sharing]]

== ISC rates in pi-bond twisting ==

Abstraction of a moiety to yield an aklene (accelerating Diels Adler and related reactions)
* resembles radical coupling
* requires spin pairing
* raises questions about inter-system crossing rates

== Employing the "external heavy atom effect" to accelerate ISC ==

Nearby site integration of heavy elements. <br>
E.g. Bismuth (Z=83) – since it likes to form 3 weak covalent bonds (?) (suggested in [[Nanosystems]])

Given known examples for the "external heavy atom effect" ([[Nanosystems]] page 216) it should be possible to have:
* k_isc>10^9 with ΔV_s,t >145zJ and thus
* t_trans<10^-7s with P_err<10^-15

= [[Nanosystems]] references =

* 8.3.4. Preview: molecular manufacturing and reliability constraints – e. Meeting constraints on omitted reactions in a single trial. (P210 center)
* 8.4.4. Carbon radicals – b. Radical coupling and inter system crossing (P215 bottom, P216)
* 8.5.3. Tensile bond cleavage – c. Spin, dissipation, and reversibility. (P224 bottom)
* 8.5.6. Pi bond torsion (P231 bottom)

= Related =

* [[Piezochemical mechanosynthesis]]
* [[Mechanosynthesis]]
* [[Fun with spins]] – influencing spins by ligand-fields (crystal-fields) rather than spin-orbit coupling
* [[Quantum mechanics]]
* [[Photonics]]
* [[Electronic transitions]]

= External links =

'' (Wikipedia: [http://en.wikipedia.org/wiki/Intersystem_crossing| Intersystem crossing]) <br>
* Source of info in the intro: Video: [https://www.youtube.com/watch?v=rHbxqduwc_E]

= Table of contents =

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