From 9cc988a09b7780f6831524a00566b1abf305624d Mon Sep 17 00:00:00 2001 From: Shuhei Ohno Date: Fri, 14 Aug 2026 11:27:12 +0900 Subject: [PATCH 1/5] Add charmonium example --- docs/src/Rayleigh-Ritz.md | 43 +++++++++++++++++++++++++++++++++++++++ test/Rayleigh-Ritz.jl | 29 ++++++++++++++++++++++++++ 2 files changed, 72 insertions(+) diff --git a/docs/src/Rayleigh-Ritz.md b/docs/src/Rayleigh-Ritz.md index dd70dbb..d8f2d1f 100644 --- a/docs/src/Rayleigh-Ritz.md +++ b/docs/src/Rayleigh-Ritz.md @@ -254,6 +254,49 @@ save("assets/RR_SO.svg", fig) # hide ``` ![](assets/RR_SO.svg) +## Example of Charmonium + +This ``\eta_c`` calculation uses the Cornell potential and parameters of [Meng, Wang, and Oka (2024)](https://doi.org/10.48550/arXiv.2404.01238). Natural units are used, so the result is in GeV. + +```@example charmonium +using TwoBody + +masses = (1.836, 1.836) +spin = -3 +Λ = 0.8321 +λ = 0.1653 +κ = 0.5069 +κ′ = 1.8609 +A = 1.6553 +B = 0.2204 +μ = inv(inv(masses[1]) + inv(masses[2])) +r₀ = A * (2masses[1] * masses[2] / sum(masses))^(-B) + +H = Hamiltonian( + RestEnergy(m=masses[1]), + RestEnergy(m=masses[2]), + Kinetic(hbar=1, m=μ), + Coulomb(coefficient=-κ), + Linear(coefficient=λ), + Constant(constant=-Λ), + Gaussian( + coefficient=2π * κ′ * spin / + (3masses[1] * masses[2] * (sqrt(π) * r₀)^3), + exponent=inv(r₀^2), + ), +) + +BS = BasisSet( + SimpleGaussianBasis(13.00773), + SimpleGaussianBasis(1.962079), + SimpleGaussianBasis(0.444529), + SimpleGaussianBasis(0.1219492), +) + +result = solve(H, BS; info=0) +round(result.E[1]; digits=6) +``` + ## STO-3G This example reproduces the STO-3G calculation for hydrogen reported by [Pérez-Torres (2019)](https://doi.org/10.1021/acs.jchemed.8b00959). In the contracted calculation, the published coefficients are held fixed, and the resulting contracted function is supplied to the solver. In the uncontracted calculation, the three primitive functions are supplied separately, allowing the Rayleigh–Ritz solver to optimize their linear coefficients. diff --git a/test/Rayleigh-Ritz.jl b/test/Rayleigh-Ritz.jl index 6839826..9212d12 100644 --- a/test/Rayleigh-Ritz.jl +++ b/test/Rayleigh-Ritz.jl @@ -57,6 +57,35 @@ @printf("%3d\t%.9f\t%.9f\t%s\n", 1, numerical, analytical, acceptance ? "✔" : "✗") @test acceptance + @testset "charmonium" begin + masses = (1.836, 1.836) + spin = -3 + Λ = 0.8321 + λ = 0.1653 + κ = 0.5069 + κ′ = 1.8609 + A = 1.6553 + B = 0.2204 + μ = inv(inv(masses[1]) + inv(masses[2])) + r₀ = A * (2masses[1] * masses[2] / sum(masses))^(-B) + charmonium = Hamiltonian( + RestEnergy(m=masses[1]), + RestEnergy(m=masses[2]), + Kinetic(hbar=1, m=μ), + Coulomb(coefficient=-κ), + Linear(coefficient=λ), + Constant(constant=-Λ), + Gaussian( + coefficient=2π * κ′ * spin / + (3masses[1] * masses[2] * (sqrt(π) * r₀)^3), + exponent=inv(r₀^2), + ), + ) + + result = solve(charmonium, BS; info=0) + @test result.E[1] ≈ 3.006976036203 atol=1e-12 + end + @testset "Pérez-Torres STO-3G contraction" begin exponents = (0.109818, 0.405771, 2.227660) contraction = (0.444635, 0.535328, 0.154329) From bae293aa4946165a0e48209e105ce7567a0a2cba Mon Sep 17 00:00:00 2001 From: Shuhei Ohno Date: Thu, 20 Aug 2026 08:44:38 +0900 Subject: [PATCH 2/5] Update hadron spectroscopy examples --- docs/src/Rayleigh-Ritz.md | 98 +++++++++++++++++++++++++++++---------- test/Rayleigh-Ritz.jl | 67 +++++++++++++++++++------- 2 files changed, 123 insertions(+), 42 deletions(-) diff --git a/docs/src/Rayleigh-Ritz.md b/docs/src/Rayleigh-Ritz.md index d8f2d1f..500c41c 100644 --- a/docs/src/Rayleigh-Ritz.md +++ b/docs/src/Rayleigh-Ritz.md @@ -254,47 +254,97 @@ save("assets/RR_SO.svg", fig) # hide ``` ![](assets/RR_SO.svg) -## Example of Charmonium +## Examples of Hadron Spectroscopy -This ``\eta_c`` calculation uses the Cornell potential and parameters of [Meng, Wang, and Oka (2024)](https://doi.org/10.48550/arXiv.2404.01238). Natural units are used, so the result is in GeV. +Natural units are used below; masses are displayed in MeV. -```@example charmonium +### ``\Lambda_c(1/2^+)`` + +Parameters follow [Kim, Hiyama, Oka, and Suzuki (2020)](https://doi.org/10.1103/PhysRevD.102.014004). + +```@example lambda_c using TwoBody -masses = (1.836, 1.836) -spin = -3 -Λ = 0.8321 -λ = 0.1653 +Mqq = 0.725 +Mc = 1.750 +μ = inv(inv(Mqq) + inv(Mc)) +α = 0.06 / μ + +H = Hamiltonian( + RestEnergy(m=Mqq), + RestEnergy(m=Mc), + Kinetic(hbar=1, m=μ), + Coulomb(coefficient=-α), + Linear(coefficient=0.165), + Constant(constant=-0.83116597), +) +BS = GeometricBasisSet(GaussianBasis, 0.01, 9.0, 40) + +round(1000 * solve(H, BS; info=0).E[1]; digits=3) +``` + +### ``\eta_c(1S)``: Meng, Wang, and Oka + +Parameters follow [Meng, Wang, and Oka (2024)](https://doi.org/10.48550/arXiv.2404.01238). + +```@example meng_charmonium +using TwoBody + +m₁ = 1.836 +m₂ = 1.836 κ = 0.5069 κ′ = 1.8609 -A = 1.6553 -B = 0.2204 -μ = inv(inv(masses[1]) + inv(masses[2])) -r₀ = A * (2masses[1] * masses[2] / sum(masses))^(-B) +spin = -3 +μ = inv(inv(m₁) + inv(m₂)) +r₀ = 1.6553 * (2m₁ * m₂ / (m₁ + m₂))^(-0.2204) H = Hamiltonian( - RestEnergy(m=masses[1]), - RestEnergy(m=masses[2]), + RestEnergy(m=m₁), + RestEnergy(m=m₂), Kinetic(hbar=1, m=μ), Coulomb(coefficient=-κ), - Linear(coefficient=λ), - Constant(constant=-Λ), + Linear(coefficient=0.1653), + Constant(constant=-0.8321), Gaussian( - coefficient=2π * κ′ * spin / - (3masses[1] * masses[2] * (sqrt(π) * r₀)^3), + coefficient=2π * κ′ * spin / (3m₁ * m₂ * (sqrt(π) * r₀)^3), exponent=inv(r₀^2), ), ) +BS = GeometricBasisSet(GaussianBasis, 0.1, 80.0, 20) -BS = BasisSet( - SimpleGaussianBasis(13.00773), - SimpleGaussianBasis(1.962079), - SimpleGaussianBasis(0.444529), - SimpleGaussianBasis(0.1219492), +round(1000 * solve(H, BS; info=0).E[1]; digits=3) +``` + +### ``\eta_c(1S)``: Arifi, Happ, Ohno, and Oka + +Parameters follow [Arifi, Happ, Ohno, and Oka (2024)](https://arxiv.org/abs/2401.07933). + +```@example arifi_charmonium +using TwoBody + +m₁ = 1.515 +m₂ = 1.515 +αs = 0.285 +spin = -3/4 +μ = inv(inv(m₁) + inv(m₂)) +λ = 1.437 * sqrt(μ) + +H = Hamiltonian( + RestEnergy(m=m₁), + RestEnergy(m=m₂), + RelativisticKinetic(m=m₁), + RelativisticKinetic(m=m₂), + Constant(constant=-0.189), + Linear(coefficient=0.092), + Coulomb(coefficient=-4αs/3), + Gaussian( + coefficient=32π * αs * (λ / sqrt(π))^3 * spin / (9m₁ * m₂), + exponent=λ^2, + ), ) +BS = GeometricBasisSet(GaussianBasis, 0.358, 2.720, 10) -result = solve(H, BS; info=0) -round(result.E[1]; digits=6) +round(1000 * solve(H, BS; info=0).E[1]; digits=3) ``` ## STO-3G diff --git a/test/Rayleigh-Ritz.jl b/test/Rayleigh-Ritz.jl index 9212d12..c59f08e 100644 --- a/test/Rayleigh-Ritz.jl +++ b/test/Rayleigh-Ritz.jl @@ -57,33 +57,64 @@ @printf("%3d\t%.9f\t%.9f\t%s\n", 1, numerical, analytical, acceptance ? "✔" : "✗") @test acceptance - @testset "charmonium" begin - masses = (1.836, 1.836) - spin = -3 - Λ = 0.8321 - λ = 0.1653 + @testset "hadron spectroscopy" begin + Mqq = 0.725 + Mc = 1.750 + μ = inv(inv(Mqq) + inv(Mc)) + lambda_c = Hamiltonian( + RestEnergy(m=Mqq), + RestEnergy(m=Mc), + Kinetic(hbar=1, m=μ), + Coulomb(coefficient=-0.06 / μ), + Linear(coefficient=0.165), + Constant(constant=-0.83116597), + ) + lambda_c_basis = GeometricBasisSet(GaussianBasis, 0.01, 9.0, 40) + @test solve(lambda_c, lambda_c_basis; info=0).E[1] ≈ 2.286 atol=1e-6 + + m₁ = 1.836 + m₂ = 1.836 κ = 0.5069 κ′ = 1.8609 - A = 1.6553 - B = 0.2204 - μ = inv(inv(masses[1]) + inv(masses[2])) - r₀ = A * (2masses[1] * masses[2] / sum(masses))^(-B) - charmonium = Hamiltonian( - RestEnergy(m=masses[1]), - RestEnergy(m=masses[2]), + spin = -3 + μ = inv(inv(m₁) + inv(m₂)) + r₀ = 1.6553 * (2m₁ * m₂ / (m₁ + m₂))^(-0.2204) + meng = Hamiltonian( + RestEnergy(m=m₁), + RestEnergy(m=m₂), Kinetic(hbar=1, m=μ), Coulomb(coefficient=-κ), - Linear(coefficient=λ), - Constant(constant=-Λ), + Linear(coefficient=0.1653), + Constant(constant=-0.8321), Gaussian( - coefficient=2π * κ′ * spin / - (3masses[1] * masses[2] * (sqrt(π) * r₀)^3), + coefficient=2π * κ′ * spin / (3m₁ * m₂ * (sqrt(π) * r₀)^3), exponent=inv(r₀^2), ), ) + meng_basis = GeometricBasisSet(GaussianBasis, 0.1, 80.0, 20) + @test solve(meng, meng_basis; info=0).E[1] ≈ 3.005 atol=1e-3 - result = solve(charmonium, BS; info=0) - @test result.E[1] ≈ 3.006976036203 atol=1e-12 + m₁ = 1.515 + m₂ = 1.515 + αs = 0.285 + spin = -3/4 + μ = inv(inv(m₁) + inv(m₂)) + λ = 1.437 * sqrt(μ) + arifi = Hamiltonian( + RestEnergy(m=m₁), + RestEnergy(m=m₂), + RelativisticKinetic(m=m₁), + RelativisticKinetic(m=m₂), + Constant(constant=-0.189), + Linear(coefficient=0.092), + Coulomb(coefficient=-4αs/3), + Gaussian( + coefficient=32π * αs * (λ / sqrt(π))^3 * spin / (9m₁ * m₂), + exponent=λ^2, + ), + ) + arifi_basis = GeometricBasisSet(GaussianBasis, 0.358, 2.720, 10) + @test solve(arifi, arifi_basis; info=0).E[1] ≈ 3.019 atol=2e-3 end @testset "Pérez-Torres STO-3G contraction" begin From c2df55349850989f620d7fac0560195e5878c6c3 Mon Sep 17 00:00:00 2001 From: Shuhei OHNO Date: Wed, 16 Sep 2026 12:31:00 +0900 Subject: [PATCH 3/5] Document issue #39 hadron spectroscopy examples in GEM --- docs/src/GEM.md | 149 ++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 149 insertions(+) diff --git a/docs/src/GEM.md b/docs/src/GEM.md index 6b9580d..2a5a0c6 100644 --- a/docs/src/GEM.md +++ b/docs/src/GEM.md @@ -143,6 +143,154 @@ round(eta_c.E[1] * 1000; digits=6) The 1.18 MeV difference from the paper table is consistent with using the rounded parameters and rounded variational exponent shown above. +## Examples of Hadron Spectroscopy + +The following three examples use the parameters and basis ranges specified in +[Issue #39](https://github.com/JuliaFewBody/TwoBody.jl/issues/39#issuecomment-5349154437). +Natural units (``\hbar=c=1``) are used: energies and masses are in GeV, +and Gaussian ranges are in GeV``^{-1}``. The displayed ground-state masses +are converted to MeV. All three examples use ``l=0`` Gaussian basis functions. + +### ``\Lambda_c(1/2^+)`` + +Parameters follow [Kim, Hiyama, Oka, and Suzuki (2020)](https://doi.org/10.1103/PhysRevD.102.014004). + +The charm quark and scalar diquark are treated as a two-body system, with +``\mu=M_{qq}M_c/(M_{qq}+M_c)`` and + +```math +\hat H = \frac{\boldsymbol p^2}{2\mu} + M_{qq} + M_c +- \frac{\alpha}{r} + \lambda r + C. +``` + +```@example lambda_c +using TwoBody + +Mqq = 0.725 +Mc = 1.750 +μ = inv(inv(Mqq) + inv(Mc)) +α = 0.06 / μ + +H = Hamiltonian( + RestEnergy(m=Mqq), + RestEnergy(m=Mc), + Kinetic(hbar=1, m=μ), + Coulomb(coefficient=-α), + Linear(coefficient=0.165), + Constant(constant=-0.83116597), +) +BS = GeometricBasisSet(GaussianBasis, 0.01, 9.0, 40) + +round(1000 * solve(H, BS; info=0).E[1]; digits=3) +``` + +### ``\eta_c(1S)``: Meng, Wang, and Oka + +Parameters follow [Meng, Wang, and Oka (2024)](https://doi.org/10.48550/arXiv.2404.01238). + +The AL1 Hamiltonian is + +```math +\hat H = \frac{\boldsymbol p^2}{2\mu} + m_1 + m_2 +- \frac{\kappa}{r} + \lambda r - \Lambda ++ \frac{2\pi\kappa'}{3m_1m_2} + \frac{e^{-r^2/r_0^2}}{\pi^{3/2}r_0^3} + \boldsymbol\sigma_1\cdot\boldsymbol\sigma_2. +``` + +Here ``r_0=A(2\mu)^{-B}`` and +``\langle\boldsymbol\sigma_1\cdot\boldsymbol\sigma_2\rangle=-3`` +for the spin-singlet state. + +```@example meng_charmonium +using TwoBody + +m₁ = 1.836 +m₂ = 1.836 +κ = 0.5069 +κ′ = 1.8609 +spin = -3 +μ = inv(inv(m₁) + inv(m₂)) +r₀ = 1.6553 * (2m₁ * m₂ / (m₁ + m₂))^(-0.2204) + +H = Hamiltonian( + RestEnergy(m=m₁), + RestEnergy(m=m₂), + Kinetic(hbar=1, m=μ), + Coulomb(coefficient=-κ), + Linear(coefficient=0.1653), + Constant(constant=-0.8321), + Gaussian( + coefficient=2π * κ′ * spin / (3m₁ * m₂ * (sqrt(π) * r₀)^3), + exponent=inv(r₀^2), + ), +) +BS = GeometricBasisSet(GaussianBasis, 0.1, 80.0, 20) + +round(1000 * solve(H, BS; info=0).E[1]; digits=3) +``` + +### ``\eta_c(1S)``: Arifi, Happ, Ohno, and Oka + +Parameters follow [Arifi, Happ, Ohno, and Oka (2024)](https://arxiv.org/abs/2401.07933). + +The semirelativistic Hamiltonian is + +```math +\hat H = \sqrt{m_1^2+\boldsymbol p^2}+\sqrt{m_2^2+\boldsymbol p^2} ++ a + br - \frac{4\alpha_s}{3r} ++ \frac{32\pi\alpha_s}{9m_1m_2} + \left(\frac{\lambda}{\sqrt{\pi}}\right)^3 e^{-\lambda^2r^2} + \boldsymbol S_1\cdot\boldsymbol S_2. +``` + +Here ``\lambda=\Lambda\sqrt{\mu}`` and +``\langle\boldsymbol S_1\cdot\boldsymbol S_2\rangle=-3/4``. +`RelativisticKinetic` represents ``\sqrt{m^2+\boldsymbol p^2}-m``, +so each constituent also needs a `RestEnergy` term. + +```@example arifi_charmonium +using TwoBody + +m₁ = 1.515 +m₂ = 1.515 +αs = 0.285 +spin = -3/4 +μ = inv(inv(m₁) + inv(m₂)) +λ = 1.437 * sqrt(μ) + +H = Hamiltonian( + RestEnergy(m=m₁), + RestEnergy(m=m₂), + RelativisticKinetic(m=m₁), + RelativisticKinetic(m=m₂), + Constant(constant=-0.189), + Linear(coefficient=0.092), + Coulomb(coefficient=-4αs/3), + Gaussian( + coefficient=32π * αs * (λ / sqrt(π))^3 * spin / (9m₁ * m₂), + exponent=λ^2, + ), +) +BS = GeometricBasisSet(GaussianBasis, 0.358, 2.720, 10) + +round(1000 * solve(H, BS; info=0).E[1]; digits=3) +``` + +### Comparison with the reference masses + +| Example | TwoBody.jl (MeV) | Reference quoted in Issue #39 (MeV) | +|:--|--:|--:| +| Kim, Hiyama, Oka, and Suzuki | 2286.000 | 2286 | +| Meng, Wang, and Oka | 3005.252 | 3005 | +| Arifi, Happ, Ohno, and Oka | 3020.148 | 3019 | + +The last example differs from the quoted reference by about 1.15 MeV with +the supplied parameters and basis ranges; it does not reproduce 3019 MeV +to the displayed precision. The regression tests allow 1 MeV for the Meng +example and 2 MeV for the Arifi example. These tolerances compare with the +quoted reference masses and are not estimates of numerical convergence. + ## API reference ```@docs; canonical=false @@ -152,3 +300,4 @@ TwoBody.ComplexGaussianBasisSet TwoBody.φp TwoBody.ψp ``` + From 4e2274c30761276bf7018e7ad9ac91c33b85d9d1 Mon Sep 17 00:00:00 2001 From: Shuhei OHNO Date: Wed, 16 Sep 2026 12:31:23 +0900 Subject: [PATCH 4/5] Remove hadron examples duplicated by the GEM documentation --- docs/src/Rayleigh-Ritz.md | 94 +-------------------------------------- 1 file changed, 1 insertion(+), 93 deletions(-) diff --git a/docs/src/Rayleigh-Ritz.md b/docs/src/Rayleigh-Ritz.md index 500c41c..5d75fdb 100644 --- a/docs/src/Rayleigh-Ritz.md +++ b/docs/src/Rayleigh-Ritz.md @@ -254,99 +254,6 @@ save("assets/RR_SO.svg", fig) # hide ``` ![](assets/RR_SO.svg) -## Examples of Hadron Spectroscopy - -Natural units are used below; masses are displayed in MeV. - -### ``\Lambda_c(1/2^+)`` - -Parameters follow [Kim, Hiyama, Oka, and Suzuki (2020)](https://doi.org/10.1103/PhysRevD.102.014004). - -```@example lambda_c -using TwoBody - -Mqq = 0.725 -Mc = 1.750 -μ = inv(inv(Mqq) + inv(Mc)) -α = 0.06 / μ - -H = Hamiltonian( - RestEnergy(m=Mqq), - RestEnergy(m=Mc), - Kinetic(hbar=1, m=μ), - Coulomb(coefficient=-α), - Linear(coefficient=0.165), - Constant(constant=-0.83116597), -) -BS = GeometricBasisSet(GaussianBasis, 0.01, 9.0, 40) - -round(1000 * solve(H, BS; info=0).E[1]; digits=3) -``` - -### ``\eta_c(1S)``: Meng, Wang, and Oka - -Parameters follow [Meng, Wang, and Oka (2024)](https://doi.org/10.48550/arXiv.2404.01238). - -```@example meng_charmonium -using TwoBody - -m₁ = 1.836 -m₂ = 1.836 -κ = 0.5069 -κ′ = 1.8609 -spin = -3 -μ = inv(inv(m₁) + inv(m₂)) -r₀ = 1.6553 * (2m₁ * m₂ / (m₁ + m₂))^(-0.2204) - -H = Hamiltonian( - RestEnergy(m=m₁), - RestEnergy(m=m₂), - Kinetic(hbar=1, m=μ), - Coulomb(coefficient=-κ), - Linear(coefficient=0.1653), - Constant(constant=-0.8321), - Gaussian( - coefficient=2π * κ′ * spin / (3m₁ * m₂ * (sqrt(π) * r₀)^3), - exponent=inv(r₀^2), - ), -) -BS = GeometricBasisSet(GaussianBasis, 0.1, 80.0, 20) - -round(1000 * solve(H, BS; info=0).E[1]; digits=3) -``` - -### ``\eta_c(1S)``: Arifi, Happ, Ohno, and Oka - -Parameters follow [Arifi, Happ, Ohno, and Oka (2024)](https://arxiv.org/abs/2401.07933). - -```@example arifi_charmonium -using TwoBody - -m₁ = 1.515 -m₂ = 1.515 -αs = 0.285 -spin = -3/4 -μ = inv(inv(m₁) + inv(m₂)) -λ = 1.437 * sqrt(μ) - -H = Hamiltonian( - RestEnergy(m=m₁), - RestEnergy(m=m₂), - RelativisticKinetic(m=m₁), - RelativisticKinetic(m=m₂), - Constant(constant=-0.189), - Linear(coefficient=0.092), - Coulomb(coefficient=-4αs/3), - Gaussian( - coefficient=32π * αs * (λ / sqrt(π))^3 * spin / (9m₁ * m₂), - exponent=λ^2, - ), -) -BS = GeometricBasisSet(GaussianBasis, 0.358, 2.720, 10) - -round(1000 * solve(H, BS; info=0).E[1]; digits=3) -``` - ## STO-3G This example reproduces the STO-3G calculation for hydrogen reported by [Pérez-Torres (2019)](https://doi.org/10.1021/acs.jchemed.8b00959). In the contracted calculation, the published coefficients are held fixed, and the resulting contracted function is supplied to the solver. In the uncontracted calculation, the three primitive functions are supplied separately, allowing the Rayleigh–Ritz solver to optimize their linear coefficients. @@ -436,3 +343,4 @@ element(o::PowerLaw, SGB1::SimpleGaussianBasis, SGB2::SimpleGaussianBasis) element(o::Gaussian, SGB1::SimpleGaussianBasis, SGB2::SimpleGaussianBasis) element(o::Custom, SGB1::SimpleGaussianBasis, SGB2::SimpleGaussianBasis) ``` + From e5b1d92fdc15c787e16d62d4cd0febc98182da83 Mon Sep 17 00:00:00 2001 From: Shuhei OHNO Date: Wed, 16 Sep 2026 12:32:18 +0900 Subject: [PATCH 5/5] Keep the Rayleigh-Ritz page unchanged from main --- docs/src/Rayleigh-Ritz.md | 1 - 1 file changed, 1 deletion(-) diff --git a/docs/src/Rayleigh-Ritz.md b/docs/src/Rayleigh-Ritz.md index 5d75fdb..dd70dbb 100644 --- a/docs/src/Rayleigh-Ritz.md +++ b/docs/src/Rayleigh-Ritz.md @@ -343,4 +343,3 @@ element(o::PowerLaw, SGB1::SimpleGaussianBasis, SGB2::SimpleGaussianBasis) element(o::Gaussian, SGB1::SimpleGaussianBasis, SGB2::SimpleGaussianBasis) element(o::Custom, SGB1::SimpleGaussianBasis, SGB2::SimpleGaussianBasis) ``` -