Physical foundations of chemistry — statistical-mechanical derivation of reaction rates, molecular spectroscopy, and thermodynamic control of equilibria. Arrhenius 1889 (Z. Phys. Chem. 4:226) — the temperature dependence of reaction rate…
chemical-physics
Arrhenius 1889: k(T) = A·exp(−E_a/(k_B T))
Svante Arrhenius 1889 (Z. Phys. Chem. 4:226) formulated the temperature-dependence of chemical reaction rate constants as k(T) =…
Eyring 1935: k(T) = (k_B T/h)·exp(−ΔG‡/RT)
Henry Eyring 1935 (J. Chem. Phys. 3:107; also Evans-Polanyi 1935) transition-state theory — reactants pass through an activated complex X‡…
Beer-Lambert: A = εcL, T_trans = 10^(−A)
Pierre Bouguer 1729, Johann Lambert 1760, August Beer 1852 law of attenuation: in a homogeneous, linearly-absorbing medium, the…
Arrhenius slope: d(ln k)/d(1/T) = −E_a/k_B (exact)
Closed-form symbolic derivative of the Arrhenius law. ln k(T) = ln A − E_a/(k_B·T); let u = 1/T, ln k(u) = ln A − (E_a/k_B)·u; hence d(ln…
Eyring: k = T·k_B·exp(−ΔG/(R·T))/h (canonical form)
Closed-form evaluation of the Eyring transition-state rate expression. Sympy canonical form: k = T·k_B·exp(−Delta_G/(R·T))/h (printer…
Beer-Lambert: T_trans·10^A − 1 ≡ 0 (exact identity)
Closed-form polynomial identity of the Beer-Lambert law. Setting T_trans = 10^(−A) and evaluating T_trans·10^A yields exactly 1; residual…
RRKM unimolecular rate k(E) = W(E^dagger) / (h rho(E)); Gauss-Legendre quadrature
RRKM (Rice-Ramsperger-Kassel-Marcus) unimolecular-rate framework (Marcus 1952 J Chem Phys 20, 359). Setup: for E > E_0 barrier,…
Franck-Condon factor |<v'|v>|^2 = S^v exp(-S)/v! (Poisson); L^2 completeness
Franck-Condon vibronic-overlap framework (Franck 1926 Trans Faraday Soc 21, 536; Condon 1926 Phys Rev 27, 640; 1928 Phys Rev 32, 858).…
Nose-Hoover thermostat H_NH = sum p^2/(2m) + U + p_s^2/(2Q) + g k_B T ln(s)
Nose-Hoover thermostat framework (Nose 1984 J Chem Phys 81, 511; Hoover 1985 PRA 31, 1695). Setup: canonical (NVT) MD is achieved by…
Theorem: P_2(1/sqrt(3)) = 0 (Legendre root for 2-point Gauss quadrature)
Theorem (Legendre-root-2pt canonical): 2-point Gauss-Legendre nodes on (-1, 1) are roots of P_2(x) = (3 x^2 - 1)/2, factoring as (sqrt(3) x…
Theorem: sum_{v=0}^{inf} S^v exp(-S)/v! = 1 (FC Poisson-factor completeness)
Theorem (FC-completeness canonical): sum over all final vibrational levels of Poisson FC factors is unity: sum_{v=0}^{inf} S^v exp(-S)/v! =…
Theorem: p^2 - N k_B T = 0 at Nose-Hoover equipartition
Theorem (Nose-Hoover-equipartition canonical): for NH-thermostatted ideal gas of N particles at T, equipartition gives <p^2/m> = k_B T per…
Born-Oppenheimer (1927)
Born-Oppenheimer 1927 separation: psi_total = psi_elec(r;R) chi_nuc(R); valid when m_e/M_n -> 0; basis of all molecular…
Hartree-Fock SCF (1930)
Hartree 1928 + Fock 1930 SCF: single-determinant antisymmetrized wavefunction; Roothaan 1951 LCAO matrix-equation; basis of all post-HF…
DFT Kohn-Sham (1965)
Hohenberg-Kohn 1964 + Kohn-Sham 1965 (Nobel 1998): density-based reformulation; non-interacting reference system + exchange-correlation…
CCSD(T) gold standard
Coester-Kummel 1957 CC + Cizek 1966 + Raghavachari 1989 CCSD(T): exponentiated cluster operator; (T) perturbative triples;…
TST (Eyring 1935)
Eyring 1935 + Polanyi-Wigner 1928 TST: k = (kT/h) exp(-Delta-G‡/RT); Arrhenius pre-factor identification; basis of computational kinetics.
Conical intersection (Born-Huang)
Teller 1937 + Yarkony 1996 conical-intersection: degeneracy-locus where adiabatic-states cross; basis of ultrafast non-adiabatic…
MR-CASSCF (Roos 1980)
B Roos 1980 complete-active-space SCF; basis of MRCI + CASPT2 + NEVPT2 strongly-correlated electronic structure.
Car-Parrinello (1985)
Car-Parrinello 1985 unified DFT + MD; modern QM/MM Warshel-Levitt 1976 Nobel 2013; multi-scale chemistry.
GF method (Wilson 1955)
E B Wilson 1955 GF-method normal-mode analysis; modern anharmonic VPT2 + MP2/B3LYP/CCSD(T) standard.
MP2 perturbation (Moller-Plesset 1934)
Moller-Plesset 1934 MP2 + Pople MP4 + Bartlett CCSD(T); 75% correlation captured at MP2; modern N^5 cost.
Density fitting (RI)
Whitten 1973 + Vahtras-Almlof-Feyereisen 1993 RI/density-fitting; 10-100x speedup HF/DFT/MP2 with negligible error.
PCM (Tomasi 1994)
Miertus-Scrocco-Tomasi 1981 + Tomasi 1994 PCM solvation; modern SMD Marenich 2009 + COSMO-RS Klamt 1995.