Notes on quantum chemistry, teaching, and the occasional photograph.https://yhliang.com/https://yhliang.com/notes/periodic-systems/periodic-conditional-convergence/https://yhliang.com/notes/periodic-systems/periodic-conditional-convergence/The Coulomb energy of a crystal is a sum whose value depends on the order you add it up. Resolving the paradox and Ewald summation.Wed, 05 Aug 2026 00:00:00 GMThttps://yhliang.com/notes/machine-learning/mob-ml/https://yhliang.com/notes/machine-learning/mob-ml/Reading notes on molecular-orbital-based machine learning, which predicts post-Hartree-Fock correlation energies from Hartree-Fock orbital features.Tue, 07 Apr 2026 00:00:00 GMThttps://yhliang.com/notes/machine-learning/unke-2021/https://yhliang.com/notes/machine-learning/unke-2021/Reading notes mapping the machine learning force field toolkit of Unke et al. onto familiar quantum chemistry concepts.Tue, 07 Apr 2026 00:00:00 GMThttps://yhliang.com/notes/machine-learning/reading-club-kernel-trick/https://yhliang.com/notes/machine-learning/reading-club-kernel-trick/From nonlinear features to kernels, and the trick that makes an infinite-dimensional feature space cost almost nothing.Thu, 02 Apr 2026 00:00:00 GMThttps://yhliang.com/notes/machine-learning/reading-club-linear-regression/https://yhliang.com/notes/machine-learning/reading-club-linear-regression/Linear regression in primal and dual form, and least squares as the maximum likelihood answer.Thu, 19 Mar 2026 00:00:00 GMThttps://yhliang.com/writing/dream-vault-i-climbing-down/https://yhliang.com/writing/dream-vault-i-climbing-down/Short story based on a memorable dream.Sun, 16 Apr 2023 00:00:00 GMThttps://yhliang.com/notes/graduate-quantum/ising-cluster-monte-carlo/https://yhliang.com/notes/graduate-quantum/ising-cluster-monte-carlo/The Wolff single-cluster algorithm for the 2D Ising model, and the statistics trouble near the critical point.Wed, 26 Oct 2022 00:00:00 GMThttps://yhliang.com/notes/periodic-systems/fcc-graphene-bands/https://yhliang.com/notes/periodic-systems/fcc-graphene-bands/One orbital and one hopping parameter go a long way. Band structures for the FCC lattice and graphene, and the counting rule that makes most zigzag nanotubes semiconductors.Tue, 09 Aug 2022 00:00:00 GMThttps://yhliang.com/notes/periodic-systems/honeycomb-tight-binding/https://yhliang.com/notes/periodic-systems/honeycomb-tight-binding/Two ways to change graphene's band structure. Breaking the sublattice symmetry opens a gap, and stacking a second layer flattens the Dirac cones.Sat, 09 Apr 2022 00:00:00 GMThttps://yhliang.com/notes/general-chemistry/genchem-quiz-3/https://yhliang.com/notes/general-chemistry/genchem-quiz-3/A trip around the PV graph. Heat, internal energy, and entropy along three paths, with a microstates bonus. For CHEM UN1604.Fri, 01 Apr 2022 00:00:00 GMThttps://yhliang.com/notes/general-chemistry/genchem-quiz-2/https://yhliang.com/notes/general-chemistry/genchem-quiz-2/Phosphorus equilibrium, the pH of morphine, and a midterm question revisited. A take-home quiz for CHEM UN1604.Tue, 01 Mar 2022 00:00:00 GMThttps://yhliang.com/notes/general-chemistry/genchem-quiz-1/https://yhliang.com/notes/general-chemistry/genchem-quiz-1/Particle in a well, isotopes on springs, and five multiple-choice questions. A take-home quiz for CHEM UN1604.Tue, 01 Feb 2022 00:00:00 GMThttps://yhliang.com/notes/general-chemistry/genchem-intro-to-intro-qm/https://yhliang.com/notes/general-chemistry/genchem-intro-to-intro-qm/Blackbody radiation, Planck's quanta, and an intuition for where the Schrödinger equation comes from. Notes for CHEM UN1604.Sat, 15 Jan 2022 00:00:00 GMThttps://yhliang.com/notes/periodic-systems/periodic-equation-of-state/https://yhliang.com/notes/periodic-systems/periodic-equation-of-state/Fitting diamond's energy-volume curve to the Birch-Murnaghan form, and the effect of the HF reference quality on MP2.Mon, 03 Jan 2022 00:00:00 GMThttps://yhliang.com/notes/periodic-systems/periodic-thermodynamic-limit/https://yhliang.com/notes/periodic-systems/periodic-thermodynamic-limit/Supercells and k-point sampling are the same limit approached two ways. Extrapolating diamond to infinite size, and the Ewald correction's effect on convergence.Sun, 02 Jan 2022 00:00:00 GMThttps://yhliang.com/notes/periodic-systems/periodic-density-fitting/https://yhliang.com/notes/periodic-systems/periodic-density-fitting/The four-index integral is too expensive for crystals. Density fitting, its four flavors in PySCF, and a first benchmark on diamond.Sat, 01 Jan 2022 00:00:00 GMThttps://yhliang.com/notes/graduate-quantum/qm1-midterm-solutions/https://yhliang.com/notes/graduate-quantum/qm1-midterm-solutions/Exponential operators, Gram-Schmidt on degenerate eigenfunctions, the classical limit of the commutator, and density matrices for polarized light.Fri, 15 Oct 2021 00:00:00 GMThttps://yhliang.com/notes/graduate-quantum/tddft-charge-transfer/https://yhliang.com/notes/graduate-quantum/tddft-charge-transfer/Local functionals place charge-transfer states several electron volts too low, and the failure traces to a single missing exchange term in the response equations.Sun, 18 Apr 2021 00:00:00 GMThttps://yhliang.com/notes/quantum-mechanics/quantum-tunneling/https://yhliang.com/notes/quantum-mechanics/quantum-tunneling/Animating a Gaussian wavepacket hitting a barrier it classically cannot cross.Fri, 12 Feb 2021 00:00:00 GMThttps://yhliang.com/notes/quantum-mechanics/bras-kets-and-operators/https://yhliang.com/notes/quantum-mechanics/bras-kets-and-operators/The Dirac notation and the postulates of quantum mechanics.Mon, 18 Jan 2021 00:00:00 GMThttps://yhliang.com/notes/quantum-mechanics/angular-momentum-matrix-elements/https://yhliang.com/notes/quantum-mechanics/angular-momentum-matrix-elements/Building the matrix representation of angular momentum operators.Mon, 16 Nov 2020 00:00:00 GMThttps://yhliang.com/notes/quantum-mechanics/variational-principle/https://yhliang.com/notes/quantum-mechanics/variational-principle/Notes on the variational principle, the workhorse behind approximate quantum chemistry.Mon, 16 Nov 2020 00:00:00 GMThttps://yhliang.com/notes/quantum-mechanics/quantum-harmonic-oscillator/https://yhliang.com/notes/quantum-mechanics/quantum-harmonic-oscillator/Solving the quantum harmonic oscillator with the ladder-operator trick.Tue, 29 Sep 2020 00:00:00 GMThttps://yhliang.com/notes/quantum-mechanics/measurements-and-projection-operators/https://yhliang.com/notes/quantum-mechanics/measurements-and-projection-operators/What a measurement does to a quantum state, and the operators that describe it.Thu, 10 Sep 2020 00:00:00 GMThttps://yhliang.com/notes/quantum-mechanics/stern-gerlach-experiment/https://yhliang.com/notes/quantum-mechanics/stern-gerlach-experiment/An introduction to quantum mechanics through one of the most well known physical experiments.Sat, 01 Aug 2020 00:00:00 GMThttps://yhliang.com/notes/graduate-quantum/configuration-interaction-singles/https://yhliang.com/notes/graduate-quantum/configuration-interaction-singles/The simplest post Hartree-Fock route to excited states, and the properties that keep it in use.Sun, 10 May 2020 00:00:00 GMThttps://yhliang.com/writing/a-collection-of-thoughts/https://yhliang.com/writing/a-collection-of-thoughts/Randomly defining words.Tue, 19 Nov 2019 00:00:00 GMT