xraytools.

Charge Flipping

The phases are thrown away and this gets them back. Transform, change the sign of everything below a small threshold, transform back, put the measured amplitudes in again — a few hundred times. Nothing in it knows what an atom is, and the atoms appear anyway.

You supply
One of the named structures, and three numbers with defaults: the flip threshold as a multiple of the map’s rms, how many cycles to run, and which random start. The amplitudes are computed from the published coordinates and the phases are then discarded.
Reading it
Every result is printed beside a floor — what the same test scores on maps built from random phases. The comparison fixes neither the origin nor the hand of the structure, so it searches both, and on a structure whose sites fall on a regular pattern that search fits a noise map perfectly. Where the floor equals the full count, a perfect score is evidence of nothing, and the page says so.

Worked examples: cristobalite · rock salt — a score worth nothing · berlinite — nothing to show

Input

× the map’s rms

Density at or below this changes sign each cycle. Blank means 0.2; the range is -0.5 to 2.

How many times the four steps run. Blank means 400, and 2000 is the most this will do.

Which set of random starting phases, from 1 to 999. It is a lottery: the same structure solves from some starts and not others, and changing this is how you play it again.

What came back

α-cristobalite, SiO2, P41212 — 284 reflections to 0.50 Å, projected onto 12 sites, from random start 1 after 400 cycles.

Not solved: 11 of 12 sites have a peak, against a floor of 6 from random phases. Charge flipping is a lottery — try another random start, or more cycles.

The recovered density

O at 0.104, 0.239Si at 0.200, 0.800O at 0.239, 0.104O at 0.261, 0.604Si at 0.300, 0.300O at 0.396, 0.739O at 0.604, 0.261Si at 0.700, 0.700O at 0.739, 0.396O at 0.761, 0.896Si at 0.800, 0.200O at 0.896, 0.761ab

The shading is the electron density this map recovered; the circles are where the atoms actually are. Nothing about their positions went into the calculation. The map has been shifted and, if necessary, inverted onto the known origin before being drawn — the amplitudes fix neither, because |F(h)| = |F(−h)| and moving the origin changes only the phases.

Getting there

cycle 1
cycle 5
cycle 25
cycle 100
cycle 400

No atom positions are drawn on these, deliberately: the first one is fog, and marking the answer over the top of it would tell you where to look before there is anything there.

The numbers behind the verdict

QuantityValue What it says
Sites recovered 11 of 12 Peaks of this map that land on a known site, one peak to one site, within one grid step.
Floor, from random phases 6 of 12 The same test on maps built from random phases with no flipping at all, worst of 10. Anything at or below this is worth nothing.
Control, from the true phases 12 of 12 What the map shows when it is given the right answer. Below the full count, this projection cannot resolve the structure and nothing here could.
R 0.366 Amplitude residual. Read the note below before believing it.
Grid flipped 71.0 % How much of the map changed sign on the last cycle. At 100 % the algorithm is doing nothing but alternating.
Threshold 0.0402 0.2 × the map’s rms of 0.2010, in electrons per square Ångström of projected cell.

The R factor compares the amplitudes this map implies with the ones that were measured, and it is not the test of success. Push the threshold above the map's maximum and every point flips, so g is exactly −ρ, every |G| equals its |F| and R reaches 0.000 with nothing solved — the coefficients simply change sign every cycle. A number a wrong parameter drives to perfect is not a number to judge a solution by, which is why the count of sites above it is.

Why the floor is here

Charge flipping fixes neither the origin nor the hand of the structure it finds, so a map can only be compared with the answer by trying every origin and both hands and keeping the best fit. That is a search with a great many chances to succeed, and on a structure whose sites fall on a regular pattern it fits anything — including a map made of pure noise.

So the floor is measured rather than assumed, and it is printed beside every result. For some of the structures offered here it equals the full count, which means a perfect score on those is not evidence of anything. Saying so is more useful than four easy successes.

Where this comes from