""" 01-jacobs-ladder.py =================== Jacob's ladder of density functional approximations (Perdew 2001). A small figure climbs five ascending rungs -- LDA, GGA, meta-GGA, hybrid, RPA -- while accuracy and cost bar charts grow on the right at every rung reached. Run from the repo root: manim -qm dft_notes/animations/chapter_05/01-jacobs-ladder.py JacobsLadder Writes to: dft_notes/animations/chapter_05/videos/ """ import numpy as np from manim import ( Scene, MathTex, Tex, Text, VGroup, VMobject, Write, Create, FadeIn, FadeOut, GrowFromEdge, MoveAlongPath, Indicate, Rectangle, Line, Circle, Triangle, UP, DOWN, RIGHT, ORIGIN, PI, YELLOW, ) CORAL = "#cc785c" TEALC = "#5db8a6" INK = "#e8e4de" DIM = "#9a958c" NAMES = ["LDA", "GGA", "meta-GGA", "hybrid", "RPA"] INGS = [ r"\rho", r"\rho,\ \nabla\rho", r"\rho,\ \nabla\rho,\ \tau", r"+\ E_x^{\mathrm{HF}}", ] ING_TEX = [ MathTex(INGS[0], color=DIM, font_size=26), MathTex(INGS[1], color=DIM, font_size=26), MathTex(INGS[2], color=DIM, font_size=26), MathTex(INGS[3], color=DIM, font_size=26), Tex("+ unoccupied orbitals", color=DIM, font_size=24), ] COST_REL = [1, 3, 6, 20, 100] def cost_height(v): return 0.60 + 0.78 * np.log10(v) class JacobsLadder(Scene): def construct(self): # ------------------------------------------------ 1. title card title = Tex( "Jacob's ladder of density functional approximations", color=INK, font_size=38, ).to_edge(UP, buff=0.40) sub = Tex("five rungs, five physical ingredients", color=DIM, font_size=26).next_to(title, DOWN, buff=0.18) self.play(Write(title), run_time=1.8) self.play(FadeIn(sub), run_time=0.8) self.wait(3.6) self.play(FadeOut(sub), run_time=0.6) # ------------------------------------------------ 2. staircase dx, dy, t, w, g = 1.7, 1.2, 0.14, 1.48, 0.22 xs = np.array([-6.7 + dx * i for i in range(5)]) ys = np.array([-2.8 + dy * i for i in range(5)]) steps = [] names = [] ings = [] for i in range(5): tread = ( Rectangle(width=w, height=t) .set_fill(CORAL, 1.0) .set_stroke(INK, 1.0) .move_to(np.array([xs[i] + w / 2, ys[i], 0.0])) ) step = VGroup(tread) if i > 0: riser = ( Rectangle(width=g, height=dy) .set_fill(CORAL, 1.0) .set_stroke(INK, 1.0) .move_to(np.array([xs[i] - g / 2, ys[i] + t - dy / 2, 0.0])) ) step.add(riser) name = Text( NAMES[i], font_size=30, color=INK, weight="BOLD" ).move_to(np.array([xs[i] + 0.95, ys[i] - 0.42, 0.0])) ing = ING_TEX[i].move_to(np.array([xs[i] + 1.15, ys[i] - 0.85, 0.0])) steps.append(step) names.append(name) ings.append(ing) self.play(Create(step), FadeIn(name), FadeIn(ing), run_time=1.1) self.wait(1.5) # ------------------------------------------------ 3. right panel cx = np.array([4.05 + 0.62 * i for i in range(5)]) axis = Line( np.array([3.5, -3.0, 0.0]), np.array([7.0, -3.0, 0.0]), color=DIM, stroke_width=2, ) ticks = VGroup(*[ Text(str(i + 1), font_size=18, color=DIM).move_to( np.array([cx[i], -3.32, 0.0]) ) for i in range(5) ]) chip_a = Rectangle(width=0.16, height=0.16).set_fill(TEALC, 1.0) tex_a = Tex("accuracy $\\uparrow$", color=DIM, font_size=22) leg_a = VGroup(chip_a, tex_a).arrange(RIGHT, buff=0.12).move_to( np.array([4.45, 0.12, 0.0]) ) chip_b = Rectangle(width=0.16, height=0.16).set_fill(CORAL, 1.0) tex_b = Tex("cost (rel.)", color=DIM, font_size=22) leg_b = VGroup(chip_b, tex_b).arrange(RIGHT, buff=0.12).move_to( np.array([6.35, 0.12, 0.0]) ) self.play( Create(axis), FadeIn(ticks), FadeIn(leg_a), FadeIn(leg_b), run_time=1.0, ) self.wait(0.8) # ------------------------------------------------ 4. the climber dot = ( Circle(radius=0.14) .set_fill(TEALC, 1.0) .set_stroke(INK, 1.5) .move_to(np.array([xs[0] + w / 2, ys[0] + t / 2 + 0.14, 0.0])) ) self.play(FadeIn(dot), run_time=0.7) self.wait(0.8) bars_acc = [] bars_cost = [] cost_lbls = [] def arrive(i, hold): ha = 0.50 * (i + 1) hc = cost_height(COST_REL[i]) bar_a = ( Rectangle(width=0.24, height=ha) .set_fill(TEALC, 1.0) .move_to(np.array([cx[i] - 0.19, -3.0 + ha / 2, 0.0])) ) bar_c = ( Rectangle(width=0.24, height=hc) .set_fill(CORAL, 1.0) .move_to(np.array([cx[i] + 0.19, -3.0 + hc / 2, 0.0])) ) lbl = MathTex( r"\times\," + str(COST_REL[i]), color=DIM, font_size=20 ).move_to(np.array([cx[i], -3.0 + max(ha, hc) + 0.22, 0.0])) bars_acc.append(bar_a) bars_cost.append(bar_c) cost_lbls.append(lbl) self.play( GrowFromEdge(bar_a, DOWN), GrowFromEdge(bar_c, DOWN), FadeIn(lbl), run_time=0.8, ) self.play(names[i].animate.set_color(TEALC), run_time=0.4) self.play(Indicate(ings[i]), run_time=1.0) self.wait(hold) arrive(0, 1.8) # ------------------------------------------------ 5. climb for i in range(4): p0 = np.array([xs[i] + w / 2, ys[i] + t / 2 + 0.14, 0.0]) p1 = np.array([xs[i + 1] + w / 2, ys[i + 1] + t / 2 + 0.14, 0.0]) apex_y = min(max(p0[1], p1[1]) + 1.2, 2.8) path = VMobject().set_points_smoothly( [p0, np.array([(p0[0] + p1[0]) / 2, apex_y, 0.0]), p1] ) self.play(MoveAlongPath(dot, path), run_time=1.35) arrive(i + 1, 2.4 if i + 1 >= 3 else 1.8) # ------------------------------------------------ 6. summit flag pole = Line( np.array([xs[4] + w, ys[4] + t, 0.0]), np.array([xs[4] + w, ys[4] + 0.68, 0.0]), color=DIM, stroke_width=2.5, ) flag = ( Triangle(radius=0.15) .rotate(-PI / 2) .set_fill(YELLOW, 1.0) .set_stroke(width=0) .move_to(np.array([xs[4] + w + 0.16, ys[4] + 0.68, 0.0])) ) self.play(Create(pole), Create(flag), run_time=0.8) self.play(Indicate(dot, scale_factor=1.6), run_time=0.8) self.wait(2.6) # ------------------------------------------------ 7. end card everything = VGroup( title, *steps, *names, *ings, dot, axis, ticks, leg_a, leg_b, *bars_acc, *bars_cost, *cost_lbls, pole, flag, ) self.wait(1.0) self.play(FadeOut(everything), run_time=0.9) line1 = Tex( "every rung adds one physical ingredient", color=INK, font_size=34, ) line2 = Tex( r"heaven = chemical accuracy ($1\ \mathrm{kcal/mol}$)", color=YELLOW, font_size=42, ) card = VGroup(line1, line2).arrange(DOWN, buff=0.55).move_to( np.array([0.0, 0.3, 0.0]) ) src = Tex( "Perdew, Schmidt, AIP Conf. Proc. 577, 1 (2001)", color=DIM, font_size=24, ).next_to(card, DOWN, buff=0.7) self.play(Write(line1), run_time=1.5) self.wait(1.0) self.play(Write(line2), run_time=1.5) self.play(FadeIn(src), run_time=0.8) self.wait(3.6)