diff --git a/src/examples/alpha-orbitals/example-data.ts b/src/examples/alpha-orbitals/example-data.ts
new file mode 100644
index 0000000000000000000000000000000000000000..ff4a87270a165cce9bd4172481f08b095d4d9207
--- /dev/null
+++ b/src/examples/alpha-orbitals/example-data.ts
@@ -0,0 +1,60186 @@
+import { Basis } from '../../extensions/alpha-orbitals/cubes';
+import { SphericalBasisOrder } from '../../extensions/alpha-orbitals/orbitals';
+
+export const DemoMoleculeSDF = `60823
+ -OEChem-10232017443D
+
+ 76 79 0 1 0 0 0 0 0999 V2000
+ 4.2325 4.8495 -0.2414 F 0 0 0 0 0 0 0 0 0 0 0 0
+ 3.3901 -2.4373 3.0602 O 0 0 0 0 0 0 0 0 0 0 0 0
+ 5.8234 -0.9362 -0.1694 O 0 0 0 0 0 0 0 0 0 0 0 0
+ -4.0484 -0.0236 1.5867 O 0 0 0 0 0 0 0 0 0 0 0 0
+ 5.9513 -3.8220 -3.4785 O 0 0 0 0 0 0 0 0 0 0 0 0
+ 5.7344 -1.5960 -3.0713 O 0 0 0 0 0 0 0 0 0 0 0 0
+ 0.3212 0.0758 1.5166 N 0 0 0 0 0 0 0 0 0 0 0 0
+ -3.4511 -1.1575 -0.3628 N 0 0 0 0 0 0 0 0 0 0 0 0
+ -0.8535 -0.6250 1.5997 C 0 0 0 0 0 0 0 0 0 0 0 0
+ 1.5803 -0.3344 2.1283 C 0 0 0 0 0 0 0 0 0 0 0 0
+ 0.1278 1.2100 0.7719 C 0 0 0 0 0 0 0 0 0 0 0 0
+ -0.9533 -1.9004 2.3428 C 0 0 0 0 0 0 0 0 0 0 0 0
+ 2.4473 -1.2165 1.2192 C 0 0 0 0 0 0 0 0 0 0 0 0
+ -1.8115 0.0728 0.8978 C 0 0 0 0 0 0 0 0 0 0 0 0
+ -1.1907 1.2338 0.3742 C 0 0 0 0 0 0 0 0 0 0 0 0
+ 3.7416 -1.7120 1.8781 C 0 0 2 0 0 0 0 0 0 0 0 0
+ 4.5791 -2.6487 0.9881 C 0 0 0 0 0 0 0 0 0 0 0 0
+ 1.1949 2.1553 0.5088 C 0 0 0 0 0 0 0 0 0 0 0 0
+ -1.3241 -3.0999 1.4405 C 0 0 0 0 0 0 0 0 0 0 0 0
+ -1.9352 -1.8320 3.5352 C 0 0 0 0 0 0 0 0 0 0 0 0
+ -1.7591 2.2833 -0.4268 C 0 0 0 0 0 0 0 0 0 0 0 0
+ 5.0315 -2.1044 -0.3741 C 0 0 2 0 0 0 0 0 0 0 0 0
+ -3.1792 -0.3427 0.7529 C 0 0 0 0 0 0 0 0 0 0 0 0
+ 5.8126 -3.1249 -1.2008 C 0 0 0 0 0 0 0 0 0 0 0 0
+ 1.9989 2.0028 -0.6208 C 0 0 0 0 0 0 0 0 0 0 0 0
+ 1.4170 3.2178 1.3848 C 0 0 0 0 0 0 0 0 0 0 0 0
+ -2.3259 3.4003 0.1871 C 0 0 0 0 0 0 0 0 0 0 0 0
+ -1.7439 2.1847 -1.8182 C 0 0 0 0 0 0 0 0 0 0 0 0
+ 3.0251 2.9131 -0.8744 C 0 0 0 0 0 0 0 0 0 0 0 0
+ 2.4429 4.1280 1.1313 C 0 0 0 0 0 0 0 0 0 0 0 0
+ -2.8777 4.4186 -0.5902 C 0 0 0 0 0 0 0 0 0 0 0 0
+ -2.2957 3.2032 -2.5955 C 0 0 0 0 0 0 0 0 0 0 0 0
+ 3.2469 3.9758 0.0018 C 0 0 0 0 0 0 0 0 0 0 0 0
+ -4.6784 -1.7492 -0.7544 C 0 0 0 0 0 0 0 0 0 0 0 0
+ 5.8309 -2.7456 -2.6619 C 0 0 0 0 0 0 0 0 0 0 0 0
+ -2.8626 4.3200 -1.9814 C 0 0 0 0 0 0 0 0 0 0 0 0
+ -5.8255 -1.5489 0.0136 C 0 0 0 0 0 0 0 0 0 0 0 0
+ -4.7392 -2.5312 -1.9079 C 0 0 0 0 0 0 0 0 0 0 0 0
+ -7.0333 -2.1307 -0.3717 C 0 0 0 0 0 0 0 0 0 0 0 0
+ -5.9471 -3.1129 -2.2932 C 0 0 0 0 0 0 0 0 0 0 0 0
+ -7.0940 -2.9125 -1.5250 C 0 0 0 0 0 0 0 0 0 0 0 0
+ 2.1382 0.5731 2.3855 H 0 0 0 0 0 0 0 0 0 0 0 0
+ 1.3708 -0.8002 3.0947 H 0 0 0 0 0 0 0 0 0 0 0 0
+ 0.0077 -2.1843 2.7778 H 0 0 0 0 0 0 0 0 0 0 0 0
+ 1.8521 -2.0869 0.9138 H 0 0 0 0 0 0 0 0 0 0 0 0
+ 2.6842 -0.6643 0.3050 H 0 0 0 0 0 0 0 0 0 0 0 0
+ 4.3434 -0.8508 2.1898 H 0 0 0 0 0 0 0 0 0 0 0 0
+ 5.4691 -2.9413 1.5624 H 0 0 0 0 0 0 0 0 0 0 0 0
+ 4.0142 -3.5780 0.8346 H 0 0 0 0 0 0 0 0 0 0 0 0
+ -0.6944 -3.1286 0.5448 H 0 0 0 0 0 0 0 0 0 0 0 0
+ -1.1783 -4.0399 1.9847 H 0 0 0 0 0 0 0 0 0 0 0 0
+ -2.3703 -3.0713 1.1264 H 0 0 0 0 0 0 0 0 0 0 0 0
+ -1.8631 -2.7437 4.1386 H 0 0 0 0 0 0 0 0 0 0 0 0
+ -1.7020 -0.9798 4.1827 H 0 0 0 0 0 0 0 0 0 0 0 0
+ -2.9745 -1.7380 3.2088 H 0 0 0 0 0 0 0 0 0 0 0 0
+ 4.1475 -1.8000 -0.9464 H 0 0 0 0 0 0 0 0 0 0 0 0
+ 6.8506 -3.2027 -0.8609 H 0 0 0 0 0 0 0 0 0 0 0 0
+ 5.3309 -4.1061 -1.1198 H 0 0 0 0 0 0 0 0 0 0 0 0
+ 1.8373 1.1817 -1.3152 H 0 0 0 0 0 0 0 0 0 0 0 0
+ 0.7989 3.3503 2.2697 H 0 0 0 0 0 0 0 0 0 0 0 0
+ 4.2168 -2.6972 3.5013 H 0 0 0 0 0 0 0 0 0 0 0 0
+ -2.3461 3.4925 1.2706 H 0 0 0 0 0 0 0 0 0 0 0 0
+ -1.3066 1.3204 -2.3125 H 0 0 0 0 0 0 0 0 0 0 0 0
+ -2.6662 -1.3612 -0.9788 H 0 0 0 0 0 0 0 0 0 0 0 0
+ 3.6513 2.7948 -1.7537 H 0 0 0 0 0 0 0 0 0 0 0 0
+ 2.6161 4.9554 1.8131 H 0 0 0 0 0 0 0 0 0 0 0 0
+ 5.2440 -0.2436 0.1902 H 0 0 0 0 0 0 0 0 0 0 0 0
+ -3.3191 5.2883 -0.1123 H 0 0 0 0 0 0 0 0 0 0 0 0
+ -2.2842 3.1265 -3.6788 H 0 0 0 0 0 0 0 0 0 0 0 0
+ -3.2921 5.1128 -2.5867 H 0 0 0 0 0 0 0 0 0 0 0 0
+ -5.8624 -0.9592 0.9179 H 0 0 0 0 0 0 0 0 0 0 0 0
+ -3.8528 -2.6952 -2.5153 H 0 0 0 0 0 0 0 0 0 0 0 0
+ 5.9549 -3.5647 -4.4251 H 0 0 0 0 0 0 0 0 0 0 0 0
+ -7.9272 -1.9757 0.2256 H 0 0 0 0 0 0 0 0 0 0 0 0
+ -5.9946 -3.7218 -3.1913 H 0 0 0 0 0 0 0 0 0 0 0 0
+ -8.0344 -3.3656 -1.8250 H 0 0 0 0 0 0 0 0 0 0 0 0
+ 1 33 1 0 0 0 0
+ 2 16 1 0 0 0 0
+ 2 61 1 0 0 0 0
+ 3 22 1 0 0 0 0
+ 3 67 1 0 0 0 0
+ 4 23 2 0 0 0 0
+ 5 35 1 0 0 0 0
+ 5 73 1 0 0 0 0
+ 6 35 2 0 0 0 0
+ 7 9 1 0 0 0 0
+ 7 10 1 0 0 0 0
+ 7 11 1 0 0 0 0
+ 8 23 1 0 0 0 0
+ 8 34 1 0 0 0 0
+ 8 64 1 0 0 0 0
+ 9 12 1 0 0 0 0
+ 9 14 2 0 0 0 0
+ 10 13 1 0 0 0 0
+ 10 42 1 0 0 0 0
+ 10 43 1 0 0 0 0
+ 11 15 2 0 0 0 0
+ 11 18 1 0 0 0 0
+ 12 19 1 0 0 0 0
+ 12 20 1 0 0 0 0
+ 12 44 1 0 0 0 0
+ 13 16 1 0 0 0 0
+ 13 45 1 0 0 0 0
+ 13 46 1 0 0 0 0
+ 14 15 1 0 0 0 0
+ 14 23 1 0 0 0 0
+ 15 21 1 0 0 0 0
+ 16 17 1 0 0 0 0
+ 16 47 1 0 0 0 0
+ 17 22 1 0 0 0 0
+ 17 48 1 0 0 0 0
+ 17 49 1 0 0 0 0
+ 18 25 2 0 0 0 0
+ 18 26 1 0 0 0 0
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+ 19 51 1 0 0 0 0
+ 19 52 1 0 0 0 0
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+ 20 54 1 0 0 0 0
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+ 22 24 1 0 0 0 0
+ 22 56 1 0 0 0 0
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+ 24 57 1 0 0 0 0
+ 24 58 1 0 0 0 0
+ 25 29 1 0 0 0 0
+ 25 59 1 0 0 0 0
+ 26 30 2 0 0 0 0
+ 26 60 1 0 0 0 0
+ 27 31 1 0 0 0 0
+ 27 62 1 0 0 0 0
+ 28 32 2 0 0 0 0
+ 28 63 1 0 0 0 0
+ 29 33 2 0 0 0 0
+ 29 65 1 0 0 0 0
+ 30 33 1 0 0 0 0
+ 30 66 1 0 0 0 0
+ 31 36 2 0 0 0 0
+ 31 68 1 0 0 0 0
+ 32 36 1 0 0 0 0
+ 32 69 1 0 0 0 0
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+ 36 70 1 0 0 0 0
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+ 38 72 1 0 0 0 0
+ 39 41 2 0 0 0 0
+ 39 74 1 0 0 0 0
+ 40 41 1 0 0 0 0
+ 40 75 1 0 0 0 0
+ 41 76 1 0 0 0 0
+M END
+`;
+
+export const DemoOrbitals = {
+ order: 'cca-reverse' as SphericalBasisOrder,
+ basis: <Basis>{
+ 'atoms': [
+ {
+ 'center': [
+ 7.9982659673182726,
+ 9.164227180945113,
+ -0.45617989301045103
+ ],
+ 'shells': [
+ {
+ 'angularMomentum': 0,
+ 'coefficients': [
+ [
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+ -0.05150303336984537,
+ 0.3346271173989955,
+ 0.5621061300983123,
+ 0.17129946969948573
+ ]
+ ],
+ 'exponents': [
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+ 44.725105704361845,
+ 12.568719598666123,
+ 1.7973548076770884,
+ 0.8157501538300561,
+ 0.38902663868632525
+ ]
+ },
+ {
+ 'angularMomentum': 1,
+ 'coefficients': [
+ [
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+ 0.18984000600705359,
+ 0.40498631911504746,
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+ ]
+ ],
+ 'exponents': [
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+ ]
+ }
+ ]
+ },
+ {
+ 'center': [
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+ ],
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+ {
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+ },
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+ ]
+ },
+ {
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+ ],
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+ ]
+ },
+ {
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+ ]
+ ],
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+ {
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+ ],
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+ ]
+ },
+ {
+ 'angularMomentum': 1,
+ 'coefficients': [
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+ ]
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+ {
+ 'center': [
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+ ],
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+ ],
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+ ]
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+ }
+ ]
+};
\ No newline at end of file
diff --git a/src/examples/alpha-orbitals/index.html b/src/examples/alpha-orbitals/index.html
new file mode 100644
index 0000000000000000000000000000000000000000..69b190fd3faadcab58f6f287fa21424c36c96dfa
--- /dev/null
+++ b/src/examples/alpha-orbitals/index.html
@@ -0,0 +1,32 @@
+<!DOCTYPE html>
+<html lang="en">
+ <head>
+ <meta charset="utf-8" />
+ <meta name="viewport" content="width=device-width, user-scalable=no, minimum-scale=1.0, maximum-scale=1.0">
+ <title>Mol* Alpha Orbitals Example</title>
+ <style>
+ * {
+ margin: 0;
+ padding: 0;
+ box-sizing: border-box;
+ }
+ #app {
+ position: absolute;
+ left: 160px;
+ top: 100px;
+ width: 600px;
+ height: 600px;
+ border: 1px solid #ccc;
+ }
+ </style>
+ <link rel="stylesheet" type="text/css" href="molstar.css" />
+ <script type="text/javascript" src="./index.js"></script>
+ </head>
+ <body>
+ <div id='controls'></div>
+ <div id="app"></div>
+ <script>
+ AlphaOrbitalsExample.init('app')
+ </script>
+ </body>
+</html>
\ No newline at end of file
diff --git a/src/examples/alpha-orbitals/index.ts b/src/examples/alpha-orbitals/index.ts
new file mode 100644
index 0000000000000000000000000000000000000000..784e2cfc24dc0e8c552d44548c505c4f7ce9b006
--- /dev/null
+++ b/src/examples/alpha-orbitals/index.ts
@@ -0,0 +1,99 @@
+/**
+ * Copyright (c) 2019 mol* contributors, licensed under MIT, See LICENSE file for more info.
+ *
+ * @author Alexander Rose <alexander.rose@weirdbyte.de>
+ */
+
+import { Basis, computeIsocontourValues } from '../../extensions/alpha-orbitals/cubes';
+import { SphericalBasisOrder } from '../../extensions/alpha-orbitals/orbitals';
+import { createPluginAsync, DefaultPluginSpec } from '../../mol-plugin';
+import { createVolumeRepresentationParams } from '../../mol-plugin-state/helpers/volume-representation-params';
+import { StateTransforms } from '../../mol-plugin-state/transforms';
+import { PluginContext } from '../../mol-plugin/context';
+import { ColorNames } from '../../mol-util/color/names';
+import { DemoMoleculeSDF, DemoOrbitals } from './example-data';
+import './index.html';
+import { CreateOrbitalVolume, StaticBasisAndOrbitals } from './transforms';
+require('mol-plugin-ui/skin/light.scss');
+
+interface DemoInput {
+ moleculeSdf: string,
+ basis: Basis,
+ order: SphericalBasisOrder,
+ orbitals: {
+ energy: number,
+ alpha: number[]
+ }[]
+}
+
+class AlphaOrbitalsExample {
+ plugin: PluginContext;
+
+ async init(target: string | HTMLElement) {
+ this.plugin = await createPluginAsync(typeof target === 'string' ? document.getElementById(target)! : target, {
+ ...DefaultPluginSpec,
+ layout: {
+ initial: {
+ isExpanded: false,
+ showControls: false
+ },
+ controls: { left: 'none', right: 'none', top: 'none', bottom: 'none' }
+ }
+ });
+
+ this.plugin.managers.interactivity.setProps({ granularity: 'element' });
+
+ this.load({
+ moleculeSdf: DemoMoleculeSDF,
+ ...DemoOrbitals
+ });
+ }
+
+ async load(input: DemoInput) {
+ await this.plugin.clear();
+
+ const data = await this.plugin.builders.data.rawData({ data: input.moleculeSdf }, { state: { isGhost: true } });
+ const trajectory = await this.plugin.builders.structure.parseTrajectory(data, 'mol');
+ const model = await this.plugin.builders.structure.createModel(trajectory);
+ const structure = await this.plugin.builders.structure.createStructure(model);
+
+ const all = await this.plugin.builders.structure.tryCreateComponentStatic(structure, 'all');
+ if (all) await this.plugin.builders.structure.representation.addRepresentation(all, { type: 'ball-and-stick', color: 'element-symbol', colorParams: { carbonColor: { name: 'element-symbol', params: { } } } });
+
+ const volumeRef = await this.plugin.build().toRoot()
+ .apply(StaticBasisAndOrbitals, { basis: input.basis, order: input.order, orbitals: input.orbitals })
+ .apply(CreateOrbitalVolume, { index: 44 })
+ .commit();
+
+ if (!volumeRef.isOk) return;
+
+ // TODO: the isovalues are being computed twice. Need to add more flexible support to Volume object
+ // for controlling them
+ const { negative, positive } = computeIsocontourValues(volumeRef.data!.grid.cells.data as any, 0.85);
+
+ const repr = this.plugin.build().to(volumeRef);
+
+
+ if (positive !== void 0) {
+ repr.apply(StateTransforms.Representation.VolumeRepresentation3D, createVolumeRepresentationParams(this.plugin, volumeRef.data!, {
+ type: 'isosurface',
+ typeParams: { isoValue: { kind: 'absolute', absoluteValue: positive } },
+ color: 'uniform',
+ colorParams: { value: ColorNames.blue }
+ }));
+ }
+
+ if (negative !== void 0) {
+ repr.apply(StateTransforms.Representation.VolumeRepresentation3D, createVolumeRepresentationParams(this.plugin, volumeRef.data!, {
+ type: 'isosurface',
+ typeParams: { isoValue: { kind: 'absolute', absoluteValue: negative } },
+ color: 'uniform',
+ colorParams: { value: ColorNames.red }
+ }));
+ }
+
+ await repr.commit();
+ }
+}
+
+(window as any).AlphaOrbitalsExample = new AlphaOrbitalsExample();
\ No newline at end of file
diff --git a/src/examples/alpha-orbitals/transforms.ts b/src/examples/alpha-orbitals/transforms.ts
new file mode 100644
index 0000000000000000000000000000000000000000..0472eb6bceadda3bf33dbe42d5debbb05c43947a
--- /dev/null
+++ b/src/examples/alpha-orbitals/transforms.ts
@@ -0,0 +1,74 @@
+/**
+ * Copyright (c) 2020 mol* contributors, licensed under MIT, See LICENSE file for more info.
+ *
+ * @author David Sehnal <david.sehnal@gmail.com>
+ */
+
+import { PluginStateObject, PluginStateTransform } from '../../mol-plugin-state/objects';
+import { Basis, createSphericalCollocationGrid } from '../../extensions/alpha-orbitals/cubes';
+import { ParamDefinition as PD } from '../../mol-util/param-definition';
+import { Task } from '../../mol-task';
+import { CustomProperties } from '../../mol-model/custom-property';
+import { SphericalBasisOrder } from '../../extensions/alpha-orbitals/orbitals';
+import { Volume } from '../../mol-model/volume';
+
+export class BasisAndOrbitals extends PluginStateObject.Create<{ basis: Basis, order: SphericalBasisOrder, orbitals: { energy: number, alpha: number[] }[] }>({ name: 'Basis', typeClass: 'Object' }) { }
+
+export const StaticBasisAndOrbitals = PluginStateTransform.BuiltIn({
+ name: 'static-basis-and-orbitals',
+ display: 'Basis and Orbitals',
+ from: PluginStateObject.Root,
+ to: BasisAndOrbitals,
+ params: {
+ label: PD.Text('Orbital Data', { isHidden: true }),
+ basis: PD.Value<Basis>(void 0 as any, { isHidden: true }),
+ order: PD.Text<SphericalBasisOrder>('gaussian' as SphericalBasisOrder, { isHidden: true }),
+ orbitals: PD.Value<{ energy: number, alpha: number[] }[]>([], { isHidden: true })
+ },
+})({
+ apply({ params }) {
+ return new BasisAndOrbitals({ basis: params.basis, order: params.order, orbitals: params.orbitals }, { label: params.label });
+ }
+});
+
+export const CreateOrbitalVolume = PluginStateTransform.BuiltIn({
+ name: 'create-orbital-volume',
+ display: 'Orbital Volume',
+ from: BasisAndOrbitals,
+ to: PluginStateObject.Volume.Data,
+ params: (a) => {
+ if (!a) {
+ return { index: PD.Numeric(0) };
+ }
+
+ return {
+ index: PD.Select(0, a.data.orbitals.map((o, i) => [i, `[${i + 1}] ${o.energy.toFixed(4)}`]))
+ };
+ }
+})({
+ apply({ a, params }) {
+ return Task.create('Orbital Volume', async ctx => {
+ const data = await createSphericalCollocationGrid({
+ basis: a.data.basis,
+ cutoffThreshold: 0.0075,
+ alphaOrbitals: a.data.orbitals[params.index].alpha,
+ sphericalOrder: a.data.order,
+ boxExpand: 4.5,
+ gridSpacing: [
+ [55, 0.6],
+ [40, 0.5],
+ [25, 0.4],
+ [0, 0.33],
+ ],
+ }).runInContext(ctx);
+ const volume: Volume = {
+ grid: data.grid,
+ sourceData: { name: 'custom grid', kind: 'custom', data },
+ customProperties: new CustomProperties(),
+ _propertyData: Object.create(null),
+ };
+
+ return new PluginStateObject.Volume.Data(volume, { label: 'Orbital Volume' });
+ });
+ }
+});
\ No newline at end of file
diff --git a/src/extensions/alpha-orbitals/collocation.ts b/src/extensions/alpha-orbitals/collocation.ts
new file mode 100644
index 0000000000000000000000000000000000000000..b202f88d380ab58d483e3344473056e79abc986f
--- /dev/null
+++ b/src/extensions/alpha-orbitals/collocation.ts
@@ -0,0 +1,187 @@
+/**
+ * Copyright (c) 2020 mol* contributors, licensed under MIT, See LICENSE file for more info.
+ *
+ * @author David Sehnal <david.sehnal@gmail.com>
+ */
+
+import { Vec3 } from '../../mol-math/linear-algebra';
+import { RuntimeContext } from '../../mol-task';
+import { arrayMin } from '../../mol-util/array';
+import { Basis, CubeGridInfo, SphericalElectronShell } from './cubes';
+import {
+ normalizeBasicOrder,
+ SphericalFunctions,
+ SphericalBasisOrder,
+} from './orbitals';
+
+export interface CollocationParams {
+ grid: CubeGridInfo;
+ basis: Basis;
+ sphericalOrder: SphericalBasisOrder;
+ cutoffThreshold: number;
+ alphaOrbitals: number[];
+}
+
+export async function sphericalCollocation(
+ {
+ grid,
+ basis,
+ sphericalOrder,
+ cutoffThreshold,
+ alphaOrbitals,
+ }: CollocationParams,
+ taskCtx: RuntimeContext
+) {
+ let baseCount = 0;
+
+ for (const atom of basis.atoms) {
+ for (const shell of atom.shells) {
+ baseCount += 2 * shell.angularMomentum + 1;
+ }
+ }
+
+ const matrix = new Float32Array(grid.npoints);
+
+ let baseIndex = 0;
+ for (const atom of basis.atoms) {
+ for (const shell of atom.shells) {
+ const L = shell.angularMomentum;
+
+ if (L > 4) {
+ // TODO: will L > 4 be required? Would need to precompute more functions in that case.
+ throw new Error('Angular momentum L > 4 not supported.');
+ }
+
+ const alpha = normalizeBasicOrder(
+ L,
+ alphaOrbitals.slice(baseIndex, baseIndex + 2 * L + 1),
+ sphericalOrder
+ );
+ baseIndex += 2 * L + 1;
+
+ collocationBasis(
+ matrix,
+ grid,
+ atom.center,
+ cutoffThreshold,
+ alpha,
+ shell
+ );
+
+ if (taskCtx.shouldUpdate) {
+ await taskCtx.update({
+ message: 'Computing...',
+ current: baseIndex,
+ max: baseCount,
+ isIndeterminate: false,
+ });
+ }
+ }
+ }
+
+ return matrix;
+}
+
+function collocationBasis(
+ matrix: Float32Array,
+ grid: CubeGridInfo,
+ center: Vec3,
+ cutoffThreshold: number,
+ alpha: number[],
+ shell: SphericalElectronShell
+) {
+ const L = shell.angularMomentum;
+ const exponents = shell.exponents;
+ const ncoeff = exponents.length;
+ const coefficients: number[] = sumCoefficients(shell.coefficients);
+ const sphericalFunc = SphericalFunctions[L];
+
+ const cx = center[0],
+ cy = center[1],
+ cz = center[2];
+ const ny = grid.dimensions[1],
+ nz = grid.dimensions[2];
+ const gdx = grid.delta[0],
+ gdy = grid.delta[1],
+ gdz = grid.delta[2];
+ const sx = grid.box.min[0],
+ sy = grid.box.min[1],
+ sz = grid.box.min[2];
+
+ const cutoffRadius =
+ cutoffThreshold > 0
+ ? Math.sqrt(-Math.log(cutoffThreshold) / arrayMin(exponents))
+ : 10000;
+ const cutoffSquared = cutoffRadius * cutoffRadius;
+
+ const radiusBox = getRadiusBox(grid, center, cutoffRadius);
+ const iMin = radiusBox[0][0],
+ jMin = radiusBox[0][1],
+ kMin = radiusBox[0][2];
+ const iMax = radiusBox[1][0],
+ jMax = radiusBox[1][1],
+ kMax = radiusBox[1][2];
+
+ for (let i = iMin; i <= iMax; i++) {
+ const x = sx + gdx * i - cx;
+ const oX = i * ny * nz;
+
+ for (let j = jMin; j <= jMax; j++) {
+ const y = sy + gdy * j - cy;
+ const oY = oX + j * nz;
+
+ for (let k = kMin; k <= kMax; k++) {
+ const z = sz + gdz * k - cz;
+ const R2 = x * x + y * y + z * z;
+
+ if (R2 > cutoffSquared) {
+ continue;
+ }
+
+ let gaussianSum = 0;
+ for (let c = 0; c < ncoeff; c++) {
+ gaussianSum +=
+ coefficients[c] * Math.exp(-exponents[c] * R2);
+ }
+
+ const sphericalSum =
+ L === 0 ? alpha[0] : sphericalFunc(alpha, x, y, z);
+ matrix[k + oY] += gaussianSum * sphericalSum;
+ }
+ }
+ }
+}
+
+function sumCoefficients(coefficients: number[][]) {
+ if (coefficients.length === 1) return coefficients[0];
+
+ const ret: number[] = [];
+ const len = coefficients[0].length;
+ for (let i = 0; i < len; i++) ret[i] = 0;
+
+ for (let j = 0; j < coefficients.length; j++) {
+ const row = coefficients[j];
+ for (let i = 0; i < len; i++) ret[i] += row[i];
+ }
+
+ return ret;
+}
+
+function getRadiusBox(grid: CubeGridInfo, center: Vec3, radius: number) {
+ const r = Vec3.create(radius, radius, radius);
+ const min = Vec3.scaleAndAdd(Vec3(), center, r, -1);
+ const max = Vec3.add(Vec3(), center, r);
+
+ Vec3.sub(min, min, grid.box.min);
+ Vec3.sub(max, max, grid.box.min);
+
+ Vec3.div(min, min, grid.delta);
+ Vec3.floor(min, min);
+ Vec3.max(min, min, Vec3());
+
+ Vec3.div(max, max, grid.delta);
+ Vec3.ceil(max, max);
+ Vec3.min(max, max, Vec3.subScalar(Vec3(), grid.dimensions, 1));
+
+ return [min, max];
+}
diff --git a/src/extensions/alpha-orbitals/cubes.ts b/src/extensions/alpha-orbitals/cubes.ts
new file mode 100644
index 0000000000000000000000000000000000000000..e7eb4fb8e9fb24c968f3aafaebac3412e09e000e
--- /dev/null
+++ b/src/extensions/alpha-orbitals/cubes.ts
@@ -0,0 +1,204 @@
+/**
+ * Copyright (c) 2020 mol* contributors, licensed under MIT, See LICENSE file for more info.
+ *
+ * @author David Sehnal <david.sehnal@gmail.com>
+ */
+
+import { sortArray } from '../../mol-data/util';
+import { Box3D } from '../../mol-math/geometry';
+import { Mat4, Tensor, Vec3 } from '../../mol-math/linear-algebra';
+import { Grid } from '../../mol-model/volume';
+import { Task } from '../../mol-task';
+import { arrayMax, arrayMin, arrayRms } from '../../mol-util/array';
+import { sphericalCollocation } from './collocation';
+import { SphericalBasisOrder } from './orbitals';
+
+export interface CubeGridInfo {
+ dimensions: Vec3;
+ box: Box3D;
+ size: Vec3;
+ npoints: number;
+ delta: Vec3;
+}
+
+export interface CubeGrid {
+ grid: Grid;
+ isovalues: { negative?: number; positive?: number };
+}
+
+export interface Basis {
+ atoms: {
+ // in Bohr units!
+ center: Vec3;
+ shells: SphericalElectronShell[];
+ }[];
+}
+
+export interface SphericalElectronShell {
+ angularMomentum: number;
+ exponents: number[];
+ coefficients: number[][];
+}
+
+export interface SphericalCollocationParams {
+ basis: Basis;
+ /**
+ * for each electron shell compute a cutoff radius as
+ *
+ * const cutoffRadius = Math.sqrt(-Math.log(cutoffThreshold) / arrayMin(exponents));
+ *
+ */
+ cutoffThreshold: number;
+ sphericalOrder: SphericalBasisOrder;
+ boxExpand: number;
+ gridSpacing: number | [atomCountThreshold: number, spacing: number][];
+ alphaOrbitals: number[];
+}
+
+export function createSphericalCollocationGrid(
+ params: SphericalCollocationParams
+): Task<CubeGrid> {
+ return Task.create('Spherical Collocation Grid', async (ctx) => {
+ const grid = initBox(
+ params.basis.atoms.map((a) => a.center),
+ params.gridSpacing,
+ params.boxExpand
+ );
+
+ const matrix = await sphericalCollocation(
+ {
+ grid,
+ basis: params.basis,
+ alphaOrbitals: params.alphaOrbitals,
+ cutoffThreshold: params.cutoffThreshold,
+ sphericalOrder: 'cca-reverse', // renamed entos ordering
+ },
+ ctx
+ );
+
+ return createCubeGrid(grid, matrix);
+ });
+}
+
+const BohrToAngstromFactor = 0.529177210859;
+
+function createCubeGrid(gridInfo: CubeGridInfo, values: Float32Array) {
+ const boxSize = Box3D.size(Vec3(), gridInfo.box);
+ const boxOrigin = Vec3.clone(gridInfo.box.min);
+
+ Vec3.scale(boxSize, boxSize, BohrToAngstromFactor);
+ Vec3.scale(boxOrigin, boxOrigin, BohrToAngstromFactor);
+
+ const scale = Mat4.fromScaling(
+ Mat4(),
+ Vec3.div(
+ Vec3(),
+ boxSize,
+ Vec3.sub(Vec3(), gridInfo.dimensions, Vec3.create(1, 1, 1))
+ )
+ );
+ const translate = Mat4.fromTranslation(Mat4(), boxOrigin);
+ const matrix = Mat4.mul(Mat4(), translate, scale);
+
+ const grid: Grid = {
+ transform: { kind: 'matrix', matrix },
+ cells: Tensor.create(
+ Tensor.Space(gridInfo.dimensions, [0, 1, 2], Float32Array),
+ (values as any) as Tensor.Data
+ ),
+ stats: {
+ min: arrayMin(values),
+ max: arrayMax(values),
+ mean: arrayMax(values),
+ sigma: arrayRms(values),
+ },
+ };
+
+ const isovalues = computeIsocontourValues(values, 0.85);
+
+ return { grid, isovalues };
+}
+
+function initBox(
+ geometry: Vec3[],
+ spacing: SphericalCollocationParams['gridSpacing'],
+ expand: number
+): CubeGridInfo {
+ const count = geometry.length;
+ const box = Box3D.expand(
+ Box3D(),
+ Box3D.fromVec3Array(Box3D(), geometry),
+ Vec3.create(expand, expand, expand)
+ );
+ const size = Box3D.size(Vec3(), box);
+
+ const spacingThresholds =
+ typeof spacing === 'number' ? [[0, spacing]] : [...spacing];
+ spacingThresholds.sort((a, b) => b[0] - a[0]);
+
+ let s = 0.4;
+ for (let i = 0; i <= spacingThresholds.length; i++) {
+ s = spacingThresholds[i][1];
+ if (spacingThresholds[i][0] <= count) break;
+ }
+
+ const dimensions = Vec3.ceil(Vec3(), Vec3.scale(Vec3(), size, 1 / s));
+ return {
+ box,
+ dimensions,
+ size,
+ npoints: dimensions[0] * dimensions[1] * dimensions[2],
+ delta: Vec3.div(Vec3(), size, Vec3.subScalar(Vec3(), dimensions, 1)),
+ };
+}
+
+export function computeIsocontourValues(
+ values: Float32Array,
+ cumulativeThreshold: number
+) {
+ const size = values.length;
+ const weights = new Float32Array(size);
+ const indices = new Int32Array(size);
+
+ let weightSum = 0;
+ for (let i = 0; i < size; i++) {
+ const v = values[i];
+ const w = v * v;
+ weights[i] = w;
+ indices[i] = i;
+ weightSum += w;
+ }
+
+ sortArray(
+ indices,
+ (indices, i, j) => weights[indices[j]] - weights[indices[i]]
+ );
+
+ let cweight = 0,
+ cutoffIndex = 0;
+ for (let i = 0; i < size; i++) {
+ cweight += weights[indices[i]];
+
+ if (cweight / weightSum >= cumulativeThreshold) {
+ cutoffIndex = i;
+ break;
+ }
+ }
+
+ let positive = Number.POSITIVE_INFINITY,
+ negative = Number.NEGATIVE_INFINITY;
+
+ for (let i = 0; i < cutoffIndex; i++) {
+ const v = values[indices[i]];
+ if (v > 0) {
+ if (v < positive) positive = v;
+ } else if (v < 0) {
+ if (v > negative) negative = v;
+ }
+ }
+
+ return {
+ negative: negative !== Number.NEGATIVE_INFINITY ? negative : void 0,
+ positive: positive !== Number.POSITIVE_INFINITY ? positive : void 0,
+ };
+}
diff --git a/src/extensions/alpha-orbitals/orbitals.ts b/src/extensions/alpha-orbitals/orbitals.ts
new file mode 100644
index 0000000000000000000000000000000000000000..e246c2305848d0d40ac15f9fcdf5176a27f6ef6c
--- /dev/null
+++ b/src/extensions/alpha-orbitals/orbitals.ts
@@ -0,0 +1,91 @@
+/**
+ * Copyright (c) 2020 mol* contributors, licensed under MIT, See LICENSE file for more info.
+ *
+ * @author David Sehnal <david.sehnal@gmail.com>
+ */
+
+// gaussian:
+// R_0, R^+_1, R^-_1, ..., R^+_l, R^-_l
+// cca:
+// R^-_(l), R^-_(l-1), ..., R_0, ..., R^+_(l-1), R^+_l
+// cca-reverse:
+// R^+_(l), R^+_(l-1), ..., R_0, ..., R^-_(l-1), R^-_l
+export type SphericalBasisOrder = 'gaussian' | 'cca' | 'cca-reverse';
+
+export function normalizeBasicOrder(
+ L: number,
+ alpha: number[],
+ order: SphericalBasisOrder
+) {
+ if (order === 'gaussian' || L === 0) return alpha;
+
+ const ret: number[] = [alpha[L]];
+ for (let l = 0; l < L; l++) {
+ const a = alpha[L - l - 1],
+ b = alpha[L + l + 1];
+ if (order === 'cca') ret.push(b, a);
+ else ret.push(a, b);
+ }
+ return ret;
+}
+
+export type SphericalFunc = (
+ alpha: number[],
+ x: number,
+ y: number,
+ z: number
+) => number;
+
+export const SphericalFunctions: SphericalFunc[] = [L0, L1, L2, L3, L4];
+
+// L_i functions were auto-generated.
+
+function L0(alpha: number[], x: number, y: number, z: number) {
+ return alpha[0];
+}
+
+function L1(alpha: number[], x: number, y: number, z: number) {
+ return alpha[0] * z + alpha[1] * x + alpha[2] * y;
+}
+
+function L2(alpha: number[], x: number, y: number, z: number) {
+ const xx = x * x, yy = y * y, zz = z * z;
+ return (
+ alpha[0] * (-0.5 * xx - 0.5 * yy + zz) +
+ alpha[1] * (1.7320508075688772 * x * z) +
+ alpha[2] * (1.7320508075688772 * y * z) +
+ alpha[3] * (0.8660254037844386 * xx - 0.8660254037844386 * yy) +
+ alpha[4] * (1.7320508075688772 * x * y)
+ );
+}
+
+function L3(alpha: number[], x: number, y: number, z: number) {
+ const xx = x * x, yy = y * y, zz = z * z;
+ const xxx = xx * x, yyy = yy * y, zzz = zz * z;
+ return (
+ alpha[0] * (-1.5 * xx * z - 1.5 * yy * z + zzz) +
+ alpha[1] * (-0.6123724356957945 * xxx - 0.6123724356957945 * x * yy + 2.449489742783178 * x * zz) +
+ alpha[2] * (-0.6123724356957945 * xx * y - 0.6123724356957945 * yyy + 2.449489742783178 * y * zz) +
+ alpha[3] * (1.9364916731037085 * xx * z - 1.9364916731037085 * yy * z) +
+ alpha[4] * (3.872983346207417 * x * y * z) +
+ alpha[5] * (0.7905694150420949 * xxx - 2.3717082451262845 * x * yy) +
+ alpha[6] * (2.3717082451262845 * xx * y - 0.7905694150420949 * yyy)
+ );
+}
+
+function L4(alpha: number[], x: number, y: number, z: number) {
+ const xx = x * x, yy = y * y, zz = z * z;
+ const xxx = xx * x, yyy = yy * y, zzz = zz * z;
+ const xxxx = xxx * x, yyyy = yyy * y, zzzz = zzz * z;
+ return (
+ alpha[0] * (0.375 * xxxx + 0.75 * xx * yy + 0.375 * yyyy - 3.0 * xx * zz - 3.0 * yy * zz + zzzz) +
+ alpha[1] * (-2.3717082451262845 * xxx * z - 2.3717082451262845 * x * yy * z + 3.1622776601683795 * x * zzz) +
+ alpha[2] * (-2.3717082451262845 * xx * y * z - 2.3717082451262845 * yyy * z + 3.1622776601683795 * y * zzz) +
+ alpha[3] * (-0.5590169943749475 * xxxx + 0.5590169943749475 * yyyy + 3.3541019662496847 * xx * zz - 3.3541019662496847 * yy * zz) +
+ alpha[4] * (-1.118033988749895 * xxx * y - 1.118033988749895 * x * yyy + 6.708203932499369 * x * y * zz) +
+ alpha[5] * (2.091650066335189 * xxx * z + -6.274950199005566 * x * yy * z) +
+ alpha[6] * (6.274950199005566 * xx * y * z + -2.091650066335189 * yyy * z) +
+ alpha[7] * (0.739509972887452 * xxxx - 4.437059837324712 * xx * yy + 0.739509972887452 * yyyy) +
+ alpha[8] * (2.958039891549808 * xxx * y + -2.958039891549808 * x * yyy)
+ );
+}
diff --git a/webpack.config.js b/webpack.config.js
index 16193375d7633e3d15da7426783c1aefc1e3d037..2610aab44cd972f6cafafd5e27e2d74c1296a2f6 100644
--- a/webpack.config.js
+++ b/webpack.config.js
@@ -1,6 +1,6 @@
const { createApp, createExample, createBrowserTest } = require('./webpack.config.common.js');
-const examples = ['proteopedia-wrapper', 'basic-wrapper', 'lighting'];
+const examples = ['proteopedia-wrapper', 'basic-wrapper', 'lighting', 'alpha-orbitals'];
const tests = [
'font-atlas',
'marching-cubes',
diff --git a/webpack.config.production.js b/webpack.config.production.js
index c5358cfe3da1409be12b6a4d95dc3038d04bdf09..c7f1119b03b2dba19a31ceec1aa4d775683f1e0b 100644
--- a/webpack.config.production.js
+++ b/webpack.config.production.js
@@ -1,6 +1,6 @@
const { createApp, createExample } = require('./webpack.config.common.js');
-const examples = ['proteopedia-wrapper', 'basic-wrapper', 'lighting'];
+const examples = ['proteopedia-wrapper', 'basic-wrapper', 'lighting', 'alpha-orbitals'];
module.exports = [
createApp('viewer', 'molstar'),