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    <title>Peter Johnston — Notes</title>
    <link href="https://pvjohnston.com/atom.xml" rel="self" />
    <link href="https://pvjohnston.com" />
    <id>https://pvjohnston.com/atom.xml</id>
    <author>
        <name>Peter Johnston</name>
        
        <email>pvjohnst@gmail.com</email>
        
    </author>
    <updated>2026-07-08T00:00:00Z</updated>
    <entry>
    <title>Forbidden and allowed: what symmetry does to a spectrum</title>
    <link href="https://pvjohnston.com/posts/2026-07-08-forbidden-and-allowed-symmetry-selection-rules.html" />
    <id>https://pvjohnston.com/posts/2026-07-08-forbidden-and-allowed-symmetry-selection-rules.html</id>
    <published>2026-07-08T00:00:00Z</published>
    <updated>2026-07-08T00:00:00Z</updated>
    <summary type="html"><![CDATA[Dissolve cobalt chloride in water and the solution is pale pink; add hydrochloric acid and it turns an intense blue — same ion, same kind of transition, a hundredfold jump in intensity. The gap didn't change; the symmetry did. This post pays the pigment series' oldest promissory note and explains what "forbidden" and "allowed" actually mean — one integral, one parity argument, one character table — and why forbidden bands show up anyway.]]></summary>
</entry>
<entry>
    <title>Molecules as circuits — a chromophore as an RLC resonator</title>
    <link href="https://pvjohnston.com/posts/2026-07-06-molecules-as-circuits-rlc-resonator.html" />
    <id>https://pvjohnston.com/posts/2026-07-06-molecules-as-circuits-rlc-resonator.html</id>
    <published>2026-07-06T00:00:00Z</published>
    <updated>2026-07-06T00:00:00Z</updated>
    <summary type="html"><![CDATA[An absorption energy gap is a resonant frequency, a transition dipole is charge sloshing across a capacitor, and a linewidth is a resistance — so a dye molecule is literally a driven RLC circuit. This post makes the analogy pay its way, pinning every circuit element to a number from a real chromophore I synthesized, then shows the three places the model quietly stops describing the physics: the hyperpolarizability, the quantum interference in the wiring, and the many-body order that actually sets device performance.]]></summary>
</entry>
<entry>
    <title>One donor, one acceptor, one new band: push–pull chromophores and charge transfer</title>
    <link href="https://pvjohnston.com/posts/2026-07-05-push-pull-chromophores-charge-transfer.html" />
    <id>https://pvjohnston.com/posts/2026-07-05-push-pull-chromophores-charge-transfer.html</id>
    <published>2026-07-05T00:00:00Z</published>
    <updated>2026-07-05T00:00:00Z</updated>
    <summary type="html"><![CDATA[Aniline and nitrobenzene each absorb only in the ultraviolet. Bolt the amino donor and the nitro acceptor onto the same ring and a new band appears that neither parent owns — lower in energy and brighter than anything either shows alone. This post computes that emergence with TD-DFT, measures the charge-transfer character directly, and uses it to stress-test two density functionals against a failure mode one of them is famous for.]]></summary>
</entry>
<entry>
    <title>The colors on the palette are energy-level gaps: engineering pigments for permanence</title>
    <link href="https://pvjohnston.com/posts/2026-07-04-the-physics-and-chemistry-of-pigments.html" />
    <id>https://pvjohnston.com/posts/2026-07-04-the-physics-and-chemistry-of-pigments.html</id>
    <published>2026-07-04T00:00:00Z</published>
    <updated>2026-07-04T00:00:00Z</updated>
    <summary type="html"><![CDATA[A tube of paint is an electronic-structure problem plus a scattering problem, perceived by an eye. This post builds the mechanism-first taxonomy of color — conjugated π-systems, ligand-field d–d transitions, charge transfer, and semiconductor band gaps — leading with the modern synthetic pigments engineered to fix the lightfastness failures of their historic ancestors, then puts absorption and scattering back together with Kubelka–Munk.]]></summary>
</entry>
<entry>
    <title>How much does correlation really cost? The correlation gap in water, measured</title>
    <link href="https://pvjohnston.com/posts/2026-07-04-the-correlation-gap-in-water-measured.html" />
    <id>https://pvjohnston.com/posts/2026-07-04-the-correlation-gap-in-water-measured.html</id>
    <published>2026-07-04T00:00:00Z</published>
    <updated>2026-07-04T00:00:00Z</updated>
    <summary type="html"><![CDATA[The Hartree–Fock post drew its correlation-gap figure schematically. This post runs the actual calculations — RHF marched up a basis-set ladder to its limit, MP2 and CCSD(T) below it — and reports what electron correlation costs, in hartrees, for one bent molecule of water.]]></summary>
</entry>
<entry>
    <title>One matrix element, two experiments: molar absorptivity and the Pockels effect</title>
    <link href="https://pvjohnston.com/posts/2026-07-03-one-matrix-element-absorptivity-and-the-pockels-effect.html" />
    <id>https://pvjohnston.com/posts/2026-07-03-one-matrix-element-absorptivity-and-the-pockels-effect.html</id>
    <published>2026-07-03T00:00:00Z</published>
    <updated>2026-07-03T00:00:00Z</updated>
    <summary type="html"><![CDATA[A companion to the molar-absorptivity post. The absolute height of an absorption band, the refractive index, and the electro-optic coefficient of a poled material are three readouts of one quantity — the transition dipole. Normalizing every spectrum to 1 throws that quantity away. This traces the same matrix element from Beer's law through the two-level model to the Pockels effect, with worked numbers.]]></summary>
</entry>
<entry>
    <title>Molar absorptivity is a rate constant in disguise</title>
    <link href="https://pvjohnston.com/posts/2026-07-03-molar-absorptivity-is-a-rate-constant.html" />
    <id>https://pvjohnston.com/posts/2026-07-03-molar-absorptivity-is-a-rate-constant.html</id>
    <published>2026-07-03T00:00:00Z</published>
    <updated>2026-07-03T00:00:00Z</updated>
    <summary type="html"><![CDATA[The molar absorptivity in Beer's law looks like a static property of a molecule — a number you read off a table, like a melting point. It is not. The integrated absorption band is proportional to the same transition dipole that fixes the spontaneous-emission rate, so an absorption measurement quietly measures a lifetime. This post follows the chain from Beer's law to the Einstein coefficients and shows why weak absorbers are always slow emitters.]]></summary>
</entry>
<entry>
    <title>Hartree–Fock and the correlation gap: where the orbital energies come from</title>
    <link href="https://pvjohnston.com/posts/2026-07-01-hartree-fock-and-the-correlation-gap.html" />
    <id>https://pvjohnston.com/posts/2026-07-01-hartree-fock-and-the-correlation-gap.html</id>
    <published>2026-07-01T00:00:00Z</published>
    <updated>2026-07-01T00:00:00Z</updated>
    <summary type="html"><![CDATA[A water molecular-orbital diagram quotes orbital energies as if they were just there to be read off. This post derives the ground-state machinery — the Hartree–Fock equations, their self-consistent solution, Koopmans' theorem, and the correlation energy that the mean field leaves behind — that actually computes them.]]></summary>
</entry>
<entry>
    <title>Reading water off the page: geometry, orbitals, acidity, and spectra</title>
    <link href="https://pvjohnston.com/posts/2026-06-30-reading-water-geometry-orbitals-acidity-spectra.html" />
    <id>https://pvjohnston.com/posts/2026-06-30-reading-water-geometry-orbitals-acidity-spectra.html</id>
    <published>2026-06-30T00:00:00Z</published>
    <updated>2026-06-30T00:00:00Z</updated>
    <summary type="html"><![CDATA[Water is the most familiar molecule and one of the strangest. This post builds it up from the bottom — where the atoms sit, what the electrons do, why it is both an acid and a base, and how it talks to light.]]></summary>
</entry>
<entry>
    <title>The anatomy of a Hakyll site, line by line</title>
    <link href="https://pvjohnston.com/posts/2026-06-24-anatomy-of-a-hakyll-site.html" />
    <id>https://pvjohnston.com/posts/2026-06-24-anatomy-of-a-hakyll-site.html</id>
    <published>2026-06-24T00:00:00Z</published>
    <updated>2026-06-24T00:00:00Z</updated>
    <summary type="html"><![CDATA[A complete reference for the Haskell that builds this blog — the package layout, the Hakyll rule set, contexts, feeds, the Pandoc compiler with citations and math, the build-time TikZ filter, and the templates — presented as numbered code blocks with a detailed explanation of each.]]></summary>
</entry>
<entry>
    <title>What are cloud functions? A practical tour with real code</title>
    <link href="https://pvjohnston.com/posts/2026-06-20-what-are-cloud-functions.html" />
    <id>https://pvjohnston.com/posts/2026-06-20-what-are-cloud-functions.html</id>
    <published>2026-06-20T00:00:00Z</published>
    <updated>2026-06-20T00:00:00Z</updated>
    <summary type="html"><![CDATA[A from-scratch explanation of what cloud functions actually are, the problem they solve, and three real-world examples — an image-resize trigger, a scheduled report, and a webhook handler — written in JavaScript, Python, and Go with line-by-line explanations of what each function does.]]></summary>
</entry>
<entry>
    <title>gcloud, Firebase, and why I keep paying for a Workspace account</title>
    <link href="https://pvjohnston.com/posts/2026-06-19-gcloud-firebase-and-google-workspace.html" />
    <id>https://pvjohnston.com/posts/2026-06-19-gcloud-firebase-and-google-workspace.html</id>
    <published>2026-06-19T00:00:00Z</published>
    <updated>2026-06-19T00:00:00Z</updated>
    <summary type="html"><![CDATA[A working tour of Google Cloud and Firebase — what each one actually is, where the line between them sits, how they integrate through a shared project and IAM, and why a paid Google Workspace account ends up being the quiet keystone that ties it all together.]]></summary>
</entry>
<entry>
    <title>The Met API has no random button</title>
    <link href="https://pvjohnston.com/posts/2026-06-18-the-met-api-has-no-random-button.html" />
    <id>https://pvjohnston.com/posts/2026-06-18-the-met-api-has-no-random-button.html</id>
    <published>2026-06-18T00:00:00Z</published>
    <updated>2026-06-18T00:00:00Z</updated>
    <summary type="html"><![CDATA[A year ago I shipped a one-button "random artwork" toy on top of the Met Museum API. It has since grown into a four-screen app — and the interesting part is what you do when the API you're randomizing over has no way to hand you something random. Manufacture it. And once you can manufacture randomness, a deterministic "artwork of the day" falls out for free.]]></summary>
</entry>
<entry>
    <title>A citation, a slot, and the line nobody plots</title>
    <link href="https://pvjohnston.com/posts/2026-06-18-a-citation-a-slot-and-the-line.html" />
    <id>https://pvjohnston.com/posts/2026-06-18-a-citation-a-slot-and-the-line.html</id>
    <published>2026-06-18T00:00:00Z</published>
    <updated>2026-06-18T00:00:00Z</updated>
    <summary type="html"><![CDATA[<p>A 2024 paper in <em>Nature Communications</em> from Andrei Faraon’s group at Caltech — <a href="https://doi.org/10.1038/s41467-024-45544-0">“Dynamic light manipulation via silicon-organic slot metasurfaces”</a> — cites a piece of work I did during my PhD with Wenwei Jin. Getting cited a decade later is a pleasure. As it turns out the citation runs deeper than the authors probably realized, and chasing down <em>why</em> is what makes the one claim they hang on our work worth examining.</p>
<h2 id="what-they-built">What they built</h2>
<p>Their device is a tunable metasurface that modulates a free-space beam. They etch silicon into a periodic array of nanobars, leave ~100 nm slots between them, and fill those slots with an organic electro-optic (OEO) polymer — a proprietary material, HLD, from NLM Photonics. Light couples into a <em>slot mode</em> confined in the gaps, and because the doped silicon doubles as an electrode, a small voltage produces a large field right where the polymer sits. The Pockels effect shifts the resonance, and the reflected intensity is modulated.</p>
<p>It is a nice idea — the slot does double duty, concentrating the optical field in the OEO material <em>and</em> letting the electrodes sit close together for a strong field per volt. They report an in-device electro-optic coefficient of <span class="math inline">\(r_{33}\)</span> = 45.7 pm/V and tuning at modest voltages. Then, in the discussion, they cite us:</p>
<blockquote>
<p><em>“Barrier layer protection has the potential to increase the nonlinear coefficient <span class="math inline">\(r_{33}\)</span> by 4–5 times, reducing the tuning voltage down to CMOS-level.”</em></p>
</blockquote>
<p>The “barrier layer protection” is our 2014 paper on a benzocyclobutene (BCB) layer that suppresses leakage current during electric-field poling. The implication is that their 45.7 is low, and that our technique is the lever to fix it.</p>
<h2 id="the-citation-runs-deeper-than-they-knew">The citation runs deeper than they knew</h2>
<p>Before I say anything about that claim, an admission that cuts against me: I am not a neutral reader of this material. HLD isn’t a stranger to my work — my work is built into it.</p>
<p>Pull the HLD paper (Xu et al., the Diels-Alder crosslinkable binary molecular glasses) and read the device-fabrication section. It uses a benzocyclobutene charge-injection barrier layer, citing our 2014 paper as the method. On poling uncertainty, the authors state that “standard error in <span class="math inline">\(r_{33}\)</span> and poling efficiency were calculated as in reference 5” — reference 5 being, again, our paper. Our structure-function study is in the bibliography too. So when the Caltech group cites our barrier-layer work to point at headroom in HLD, they are pointing at a material our barrier layer helped build and our statistics helped characterize. The citation is more earned than flattering — which is exactly why I want to get the rest of it right.</p>
<h2 id="the-gap-is-real-and-its-a-field-not-a-fudge">The gap is real — and it’s a field, not a fudge</h2>
<p>So is 45.7 pm/V “low”? Yes. And the honest way to see it is to stop quoting endpoint numbers — their 45.7, HLD’s headline “300” — and plot the line between them.</p>
<p>NLM publishes that line. Their data is <span class="math inline">\(r_{33}\)</span> against poling field with a regression through it that climbs about 2.3 pm/V for every V/µm of poling field. Two things fall out of it. At the ~100 V/µm they applied, the line predicts roughly 230 pm/V. And their measured 45.7 sits where that same line crosses only about <strong>20 V/µm</strong>. In other words the device is poling as though it were given a fifth of the field it was nominally given, and recovering that field would lift the coefficient about fivefold — almost exactly the “4–5×” the paper claims.</p>
<p>I want to be clear about that, because it would be cheap to wave the gap away as scatter: it isn’t noise. The headroom is real, it is quantified, and it is consistent with the paper’s own number. What the line also tells you is the <em>kind</em> of gap it is — a poling-field gap. The slot isn’t delivering the field to the molecules. Which turns the entire question into a single one: can that field be recovered, and is our barrier layer the way to do it?</p>
<h2 id="even-the-lever-may-not-fit-or-fix-it">Even the lever may not fit — or fix it</h2>
<p>Two problems sit in the way of reaching for our BCB work as that lever, and they stack.</p>
<p><strong>Mechanism.</strong> BCB does one specific thing: it suppresses bulk charge-injection and leakage current through a film during poling, so the applied field isn’t bled off before the chromophores align. But in a 100 nm slot, bulk leakage is probably not the culprit. The paper’s <em>own</em> reference 41 — on birefringence, dimensionality, and surface influences in organic hybrid electro-optic materials — points where the real limiter likely lives: in a gap this small, the chromophores must order against an enormous surface-to-volume ratio, and <em>that</em>, not leakage, is the plausible reason the effective field collapses to ~20 V/µm. A barrier layer does not fix an interface-ordering problem.</p>
<p><strong>Fabrication.</strong> Even granting that leakage matters, BCB as we built it is a planar film spun between a flat electrode and a micron-thick EO layer — a vertical stack. Their slot is a 100 nm lateral gap between doped-silicon rails. Reproducing a charge-injection barrier in <em>that</em> geometry is not a drop-in; it is an unsolved fabrication problem.</p>
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<p>So “4–5×, to CMOS voltages” is a sound <em>target</em> — the line says the headroom is genuinely there. But the lever the paper reaches for has to clear both bars, and it may clear neither: it likely doesn’t fit the geometry, and by the paper’s own citations it may not address what’s actually limiting the poling.</p>
<h2 id="the-part-im-proud-of">The part I’m proud of</h2>
<p>Here is what lets me say any of this with confidence: the gap is legible at all because the poling was characterized as a <em>relationship</em> and published — not collapsed into a hero number. Read 45.7 against NLM’s curve and it stops being a disappointment and becomes a data point at low effective field, sitting right where the line says it should. That diagnosis is only possible because somebody plotted the line.</p>
<p>Our own barrier-layer paper held to that standard. The poling analysis ran through the weighted least-squares treatment from <em>Numerical Recipes</em>, under three different weighting schemes, specifically to prove the answer didn’t depend on the choice — and it didn’t. Every figure carried 95% confidence bands. Every discarded device was disclosed, with its reason, the same criteria applied across every architecture. The HLD paper computed its own errors by that method — ours. The rigor is in the literature. What gets lost is the line: by the time a coefficient reaches a spec sheet it is “up to 300,” and by the time it reaches a citation it is “4–5× short” — the endpoints quoted, the curve between them left unplotted.</p>
<p>So this isn’t a complaint about being cited — it’s an invitation. The headroom in their device is real; I’ll concede the 4–5× without argument. Whether our barrier layer is the lever to claim it is a different question, and the paper’s own references hint the answer is no — the slot’s limiter looks like interface and dimensionality, not the bulk leakage BCB was built to stop. If you want to know what these materials actually do, don’t quote the endpoints. Plot the line. Read the supporting information — the HLD paper’s, and <a href="https://doi.org/10.1063/1.4884829">ours</a> — and look at the regression, not the record. That line is the thing that makes any single number mean something, and it is the thing almost nobody plots.</p>
<p><small>The cited work: W. Jin, P. V. Johnston, D. L. Elder, et al., “Benzocyclobutene barrier layer for suppressing conductance in nonlinear optical devices during electric field poling,” <em>Appl. Phys. Lett.</em> 104, 243304 (2014). The citing paper: T. Zheng et al., <em>Nat. Commun.</em> 15, 1557 (2024). HLD poling data: NLM Photonics product literature; H. Xu et al., <em>Chem. Mater.</em> 32, 1408 (2020).</small></p>]]></summary>
</entry>
<entry>
    <title>Running my day job on Claude Code — an agent architecture for non-software work</title>
    <link href="https://pvjohnston.com/posts/2026-06-16-running-my-day-job-on-claude-code.html" />
    <id>https://pvjohnston.com/posts/2026-06-16-running-my-day-job-on-claude-code.html</id>
    <published>2026-06-16T00:00:00Z</published>
    <updated>2026-06-16T00:00:00Z</updated>
    <summary type="html"><![CDATA[My day job isn't writing software — it's coordinating insurance-restoration jobs, which is document-heavy and relentlessly repetitive. Over a few months I built a system of Claude Code agents around that workflow. This is the architecture, the decisions that made it hold together, and what I'd change.]]></summary>
</entry>
<entry>
    <title>Reading the source — the circuitikz behind four schematics</title>
    <link href="https://pvjohnston.com/posts/2026-06-15-reading-the-circuitikz-source.html" />
    <id>https://pvjohnston.com/posts/2026-06-15-reading-the-circuitikz-source.html</id>
    <published>2026-06-15T00:00:00Z</published>
    <updated>2026-06-15T00:00:00Z</updated>
    <summary type="html"><![CDATA[A follow-up that opens up the four circuits from the previous post and shows the circuitikz source for each — the RC low-pass filter, the series RLC, the inverting op-amp, and the full-wave bridge rectifier — line by line.]]></summary>
</entry>
<entry>
    <title>Hardening the open CORS proxy — allowlists, SSRF guards, and the bypass I almost left behind</title>
    <link href="https://pvjohnston.com/posts/2026-06-15-hardening-the-cors-proxy.html" />
    <id>https://pvjohnston.com/posts/2026-06-15-hardening-the-cors-proxy.html</id>
    <published>2026-06-15T00:00:00Z</published>
    <updated>2026-06-15T00:00:00Z</updated>
    <summary type="html"><![CDATA[A year after building an open serverless CORS proxy, I closed the open-relay hole it had become — target and origin allowlists, SSRF guards, a resilience layer — and learned a sharp lesson about a forgotten debug endpoint that Vercel was still routing.]]></summary>
</entry>
<entry>
    <title>A light wave from Maxwell's equations, rendered in pure TikZ</title>
    <link href="https://pvjohnston.com/posts/2026-06-14-rich-tikz-with-dvisvgm.html" />
    <id>https://pvjohnston.com/posts/2026-06-14-rich-tikz-with-dvisvgm.html</id>
    <published>2026-06-14T00:00:00Z</published>
    <updated>2026-06-14T00:00:00Z</updated>
    <summary type="html"><![CDATA[Deriving the electromagnetic plane wave from Maxwell's equations, then drawing it with build-time TikZ — and the Haskell pipeline rebuild (lualatex + dvisvgm) that finally renders its transparency.]]></summary>
</entry>
<entry>
    <title>Schematics that compile — circuit diagrams in pure TikZ</title>
    <link href="https://pvjohnston.com/posts/2026-06-14-circuit-diagrams-with-circuitikz.html" />
    <id>https://pvjohnston.com/posts/2026-06-14-circuit-diagrams-with-circuitikz.html</id>
    <published>2026-06-14T00:00:00Z</published>
    <updated>2026-06-14T00:00:00Z</updated>
    <summary type="html"><![CDATA[Teaching the build-time TikZ pipeline to draw electrical schematics with circuitikz, demonstrated with four classic circuits — an RC filter, a series RLC, an inverting op-amp, and a full-wave bridge rectifier.]]></summary>
</entry>
<entry>
    <title>Quantum Tunneling Workflow for Hydrogen Peroxide - PES Scans, kappa Corrections, and Instanton Integration</title>
    <link href="https://pvjohnston.com/posts/2026-01-16-quantum-tunneling-workflow.html" />
    <id>https://pvjohnston.com/posts/2026-01-16-quantum-tunneling-workflow.html</id>
    <published>2026-01-16T00:00:00Z</published>
    <updated>2026-01-16T00:00:00Z</updated>
    <summary type="html"><![CDATA[An ACS-style, AI-authored workflow note that couples a relaxed PES scan with semiclassical tunneling corrections and an i-PI ring-polymer instanton sketch, including charts, tables, and runnable code.]]></summary>
</entry>

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