Spin-arrow diagrams

The spin paradigm employs spin arrows to indicate electron pairing and antipairing. Here I compare the spin-arrow diagrams for ethylene to their Gel fand and the valence bond counterparts ... 

The Gel fand, valence bond and spin-arrow diagrams are compared below... 

From a classically motivated view this should in fact be a good approximation to the ground state, and as it turns out it has the correct phase relationship between all the Kekule structures (if we make the restriction to alternants, and choose the phase such that in Pauling s spin -pairing diagrams all spin-pairing arrows are directed from starred to unstarred sites). An improved Ansatz is... 

Freeon dynamics provides a dynamically-correct replacement for the faulty spin paradigm. In particular its freeon Gel fand diagrams are a dynamically correct replacement for spin arrows as a "primitive pattern of understanding". 

Freeon Gel fand diagrams provide primitive patterns of understanding which are superior to and which should replace spin arrows as the primitive patterns of understanding of N particle systems. 

Figure 3.6 A box/arrow diagram indicating the spins of two unpaired electrons in the electronic configuration of the carbon atom the direction of the arrxiws indicate the spin...

Figure 3.5 VB diagrams for a 6-electron system. Each arrow corresponds to the VB function of Eqn (3.1) where i and j label the atomic orbitals that are spin coupled. Diagrams A and B are the familiar Kekule structures while C, D, and E are the Dewar structures.

The electron configuration of the iron atom is ls 2s 2p 3s 3p 3d 4s. All Ihe subshells except the 3J are filled. In placing the six electrons in the 3d subshell, you note that the first five go into separate 3d orbitals with their spin arrows in the same direction. The sixth electron must doubly occupy a 3d orbital. The orbital diagram is... 

For many purposes, electron configurations are sufficient to describe the arrangements of electrons in atoms. Sometimes, however, it is useful to go a step further and show how electrons are distributed among orbitals. In such cases, orbital diagrams are used. Each orbital is represented by parentheses (), and electrons are shown by arrows written f or, depending on spin. 

Figure 2.14. The molecular orbitals of gas phase carbon monoxide, (a) Energy diagram indicating how the molecular orbitals arise from the combination of atomic orbitals of carbon (C) and oxygen (O). Conventional arrows are used to indicate the spin orientations of electrons in the occupied orbitals. Asterisks denote antibonding molecular orbitals, (b) Spatial distributions of key orbitals involved in the chemisorption of carbon monoxide. Barring indicates empty orbitals.5 (c) Electronic configurations of CO and NO in vacuum as compared to the density of states of a Pt(lll) cluster.11 Reprinted from ref. 11 with permission from Elsevier Science.

Fig. 5.5.14 Schematic diagram showing how the double-phase encoded DEPT sequence achieves both spatial and spectral resolution within the reactor, (a) A spin-echo ]H 2D image taken through the column overlayed with a grid showing the spatial location within the column of the two orthogonal phase encoded planes (z and x) used in the modified DEPT sequence. The resulting data set is a zx image with a projection along y. In-plane spatial resol-ution is 156 [Am (z) x 141 [xm (x) for a 3-mm slice thickness. The center of each volume from which the data have been acquired is identified by the intersection of the white lines. The arrow indicates the direction of flow.

There is, however, a system that chemists use alongside electron configurations to help them plot and keep track of electrons in their orbitals. An orbital diagram uses a box for each orbital in any given principal energy level. (Some chemists use a circle or a line instead of a box.) An empty box represents an orbital in which there are no electrons (an unoccupied orbital). A box that has an upward-pointing arrow represents an orbital with an electron that spins in one direction. A box with a downward-pointing arrow represents an orbital with an electron that spins in the opposite direction. You can... 

Fig. 10. Energy diagram of a IS spin system (two spins 1/2). a and P are the usual spin functions. One-quantum transitions (Ji, Sy S2, physically observable) full arrows. ZQ and DQ (dashed arrows) refer to zero-quantum and double-quantum transitions.

Fig. 1 Molecular orbital diagram showing the electronic configuration for the ground state (So), for the first spin-singlet excited state (Si) and for the first spin-triplet excited state (Ti). The arrows indicate the electron spin, the thin horizontal gray line is a guide to the eye. In this representation, coulomb and exchange energies are explicitly included in the positions of the frontier orbitals...

Figure 12.1—Energy diagram comparing fluorescence and phosphorescence. Short arrows correspond to internal conversion without the emission of photons. Fluorescence is an energy transfer between states of the same multiplicity (spin state) while phosphorescence is between states of diiferent multiplicity. The situation is more complex than that shown by this Jablonski diagram.

We can combine this spin concept and our orbital model to build atoms electron by electron. This is done by using what is called an energy-level diagram, shown in Figure 5.22. Each box represents an orbital, each electron is represented by an arrow, and two electrons spinning in opposite directions in the same orbital are shown as two arrows pointing in opposite directions. 

It is convenient for many purposes to draw "box diagrams of electron configurations in which boxes represent individual orbitals, and electrons and their spins are indicated by arrows ... 

Fig. 11.42 Modified d Tanabe-Sugano diagram showing only the D. H. f. and / terms. Arrows represent spin allowed iransitions for high and low spin complexes.

The wavy arrows in the Jablonski diagram of Figure 3.23, p. 50, correspond to the non-radiative transitions of internal conversion (ic) and the short arrows to intersystem crossing (isc) the former are spin allowed, as they take place between energy states of the same multiplicity the latter are spin forbidden and are therefore much slower. The rate constants of ic and isc span extremely large ranges because they depend not only on the spin reversal (for isc) but also on the energy gap between the initial and final states. 

Figure A1.4 Nuclear spin states for a single proton in a magnetic field. At the top the two spin states, a and j8, are shown in an energy-level diagram with the transition indicated by an arrow. Below is the single-line spectrum. With normal populations, the number of molecules in the lower state is slightly greater than the number in the higher state normal net absorption occurs.

Figure A1.8 Nuclear spin states and spectrum for product 5. At the top the four states are again shown in an energy-level diagram. Heavy lines are the states with enhanced populations. A downward-pointing arrow indicates a net transfer of molecules from an overpopulated higher spin state to a less populated lower one, and corresponds to net emission. The spectrum shows the multiplet effect of type El A. From S. H. Pine, J. Chem. Educ., 49, 664 (1972). Reproduced by permission of the Division of Chemical Education.

An orbital-filling diagram indicates the electrons in each orbital as arrows. Note that the three 4p electrons all have the same spin ... 

In the orbital diagram notation, each subshell is divided into individual orbitals drawn as boxes. An arrow pointing upward corresponds to one type of spin (+1/2) and an arrow pointing down corresponds to the opposite spin (-1/2). Electrons in the same orbital with opposed spins are said to be paired, such as the electrons in the Is and 2s orbitals. These orbitals are completely filled orbitals. 

Fig. 7. Mean-field phase diagram of the four-state Ising-Potts model (A/kB = 90 K, J lkB = 125 K). The high-spin (HS) phase, the low-spin (LS) phase, and the ferroelectric-ordered (FO) phase are shown. The arrow line corresponds to Jo/kB = — 36 K, appropriate to the [Mn(taa)] system.

FIGURE 5. Jablonski diagram showing the various processes associated with light absorption and their time scale. Arrows in boxes, the relative spin states of the paired electrons. (Modified from Ref. 2.)... 

FIGURE 1.15 Metal ligand overlap and MO diagram for a Oh high-spin Fe(III) complex. Arrows indicate the LMCT transitions. The bold arrow shows the more intense a CT... 

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