The finite-element discrete variable representation is proposed to express the nonequilibrium Green's function for strongly inhomogeneous quantum systems. This method is highly favorable against a general basis approach with regard to numerical complexity, memory resources, and computation time. Its flexibility also allows for an accurate representation of spatially extended Hamiltonians and thus opens the way toward a direct solution of the two-time Schwinger-Keldysh-Kadanoff-Baym equations on spatial grids, including, for example, the description of highly excited states in atoms. As benchmarks, we compute and characterize, in Hartree-Fock and second Born approximations, the ground states of the He atom, the ${\mathrm{H}}_{2}$ molecule, and the LiH molecule in one spatial dimension. Thereby, the ground-state and binding energies, densities, and bond lengths are compared with the direct solution of the time-dependent Schr\"odinger equation.The finite-element discrete variable representation is proposed to express the nonequilibrium Green's function for strongly inhomogeneous quantum systems. This method is highly favorable against a general basis approach with regard to numerical complexity, memory resources, and computation time. Its flexibility also allows for an accurate representation of spatially extended Hamiltonians and thus opens the way toward a direct solution of the two-time Schwinger-Keldysh-Kadanoff-Baym equations on spatial grids, including, for example, the description of highly excited states in atoms. As benchmarks, we compute and characterize, in Hartree-Fock and second Born approximations, the ground states of the He atom, the ${\mathrm{H}}_{2}$ molecule, and the LiH molecule in one spatial dimension. Thereby, the ground-state and binding energies, densities, and bond lengths are compared with the direct solution of the time-dependent Schr\"odinger equation.

arXiv:0910.5458Physical Review AFeb 25, 201074 citations

The Weak Li2 ? He Interaction Revisited: a Combined Ab-initio and Empirical Modelling.

Enrico Bodo, Francesco Antonio Gianturco, Ersin Yurtsever

Journal of Low Temperature PhysicsJan 1, 200522 citations

Binding of small number of He4 atoms

Stefan Sunarić, Srećko Kilić

Physica B+CAug 1, 19811 citation

A supersonic beam of cold lithium hydride molecules

S. K. Tokunaga, J. O. Stack, J. J. Hudson +3 more

We have developed a source of cold LiH molecules for Stark deceleration and trapping experiments. Lithium metal is ablated from a solid target into a supersonically expanding carrier gas. The translational, rotational, and vibrational temperatures are 0.9+/-0.1, 5.9+/-0.5, and 468+/-17 K, respectively. Although they have not reached thermal equilibrium with the carrier gas, we estimate that 90% of the LiH molecules are in the ground state, X (1)Sigma(+)(v=0,J=0). With a single 7 ns ablation pulse, the number of molecules in the ground state is 4.5+/-1.8 x 10(7) molecules/sr. A second, delayed, ablation pulse produces another LiH beam in a different part of the same gas pulse, thereby almost doubling the signal. A long pulse, lasting 150 micros, can make the beam up to 15 times more intense.We have developed a source of cold LiH molecules for Stark deceleration and trapping experiments. Lithium metal is ablated from a solid target into a supersonically expanding carrier gas. The translational, rotational, and vibrational temperatures are 0.9+/-0.1, 5.9+/-0.5, and 468+/-17 K, respectively. Although they have not reached thermal equilibrium with the carrier gas, we estimate that 90% of the LiH molecules are in the ground state, X (1)Sigma(+)(v=0,J=0). With a single 7 ns ablation pulse, the number of molecules in the ground state is 4.5+/-1.8 x 10(7) molecules/sr. A second, delayed, ablation pulse produces another LiH beam in a different part of the same gas pulse, thereby almost doubling the signal. A long pulse, lasting 150 micros, can make the beam up to 15 times more intense.

arXiv:physics/0612163The Journal of Chemical PhysicsMar 28, 200718 citations

Structurally Sparse Molecular Hamiltonians for Near-Term Quantum Simulation

Josh Loutey

We present a library of qubit Hamiltonians for molecular quantum simulation that are structurally sparser than conventional Gaussian-basis alternatives by one to three orders of magnitude. The Hamiltonians are constructed from a spectral graph theory framework (GeoVac) that exploits natural coordinate separations in molecular electronic structure, producing block-diagonal electron repulsion integrals and Gaunt-enforced selection rules that persist through Jordan-Wigner encoding. For the composed architecture (PK-partitioned), the composed LiH Hamiltonian is near parity with minimal-basis STO-3G on Pauli count (334 vs. STO-3G's 276 reduced / 907 raw) while using more qubits; the decisive resource advantages are the $O(Q^{2.5})$ Pauli scaling and a 190 $×$ reduction versus cc-pVDZ. The balanced coupled architecture (PK-free) binds LiH with an FCI minimum at a computed $R_{\mathrm{eq}} = 3.227$ bohr (7.0% above the experimental 3.015 bohr) at $n_{\max}=2$ (878 Pauli terms, 30 qubits); a single-point evaluation at the experimental geometry reaches 0.20% energy error at $n_{\max}=3$ (84 qubits) when solved exactly. Chemistry-accuracy scope at $n_{\max}=2$ is row-conditional: first-row hydrides (LiH, BeH $_2$ , H $_2$ O, $\ldots$ ) bind with documented potential-energy-surface (PES) topology, while second-row hydrides (NaH and below) exhibit monotone overattraction under every tested configuration — frozen-core balanced, multi-zeta valence, screened cross-center, explicit-core Hartree–Fock — with no interior PES minimum at the qubit-Hamiltonian level. We document this scope boundary empirically in \S(ref); the framework's primary value proposition is structural sparsity with quantitative truncation-convergence rates (Paper 38 state-space GH convergence), not energy-accuracy parity with CCSD(T) on second-row systems. The hamiltonian() registry covers 37 systems (35 composed molecules spanning $Z=1$ –56, H through Ba, plus the He and H $_2$ reference atoms), including multi-center systems (CO, N $_2$ , F $_2$ ), mixed frozen-core molecules (NaCl), and the full first transition series as hydrides (ScH through ZnH), with Pauli scaling $O(Q^{2.5})$ confirmed universal across all three rows, compared to $O(Q^{3.9–4.3})$ for Gaussian baselines. The composed Pauli count is exactly linear in qubit count (coefficient $11.10$ , exact, for main-group molecules; $9.23$ for $d$ -orbital blocks under the pair-diagonal ERI approximation (Sec. (ref))—the exact global- $M_L$ rule makes the $d$ -block coefficient higher, not lower), so adding atoms to a molecule increases quantum cost linearly. Second- and third-row molecules use analytical frozen cores ([Ne], [Ar], [Ar]3 $d^{10}$ ); the frozen-core energy enters only through the identity operator and does not affect quantum measurement cost. Isostructural molecules with frozen cores produce identical Pauli counts across periodic table rows. The Hamiltonians are available as a Python library with Qiskit, OpenFermion, and PennyLane export. GeoVac Paper 20. Part of the GeoVac research corpus (quantum computing group). Code, tests, and the full paper series: https://github.com/jloutey-hash/geovac. Corpus archive DOI: 10.5281/zenodo.20482394. Corpus version at deposit: v4.75.0.We present a library of qubit Hamiltonians for molecular quantum simulation that are structurally sparser than conventional Gaussian-basis alternatives by one to three orders of magnitude. The Hamiltonians are constructed from a spectral graph theory framework (GeoVac) that exploits natural coordinate separations in molecular electronic structure, producing block-diagonal electron repulsion integrals and Gaunt-enforced selection rules that persist through Jordan-Wigner encoding. For the composed architecture (PK-partitioned), the composed LiH Hamiltonian is near parity with minimal-basis STO-3G on Pauli count (334 vs. STO-3G's 276 reduced / 907 raw) while using more qubits; the decisive resource advantages are the $O(Q^{2.5})$ Pauli scaling and a 190$×$ reduction versus cc-pVDZ. The balanced coupled architecture (PK-free) binds LiH with an FCI minimum at a computed $R_{\mathrm{eq}} = 3.227$ bohr (7.0% above the experimental 3.015 bohr) at $n_{\max}=2$ (878 Pauli terms, 30 qubits); a single-point evaluation at the experimental geometry reaches 0.20% energy error at $n_{\max}=3$ (84 qubits) when solved exactly. Chemistry-accuracy scope at $n_{\max}=2$ is row-conditional: first-row hydrides (LiH, BeH$_2$, H$_2$O, $\ldots$) bind with documented potential-energy-surface (PES) topology, while second-row hydrides (NaH and below) exhibit monotone overattraction under every tested configuration — frozen-core balanced, multi-zeta valence, screened cross-center, explicit-core Hartree–Fock — with no interior PES minimum at the qubit-Hamiltonian level. We document this scope boundary empirically in \S(ref); the framework's primary value proposition is structural sparsity with quantitative truncation-convergence rates (Paper 38 state-space GH convergence), not energy-accuracy parity with CCSD(T) on second-row systems. The hamiltonian() registry covers 37 systems (35 composed molecules spanning $Z=1$–56, H through Ba, plus the He and H$_2$ reference atoms), including multi-center systems (CO, N$_2$, F$_2$), mixed frozen-core molecules (NaCl), and the full first transition series as hydrides (ScH through ZnH), with Pauli scaling $O(Q^{2.5})$ confirmed universal across all three rows, compared to $O(Q^{3.9–4.3})$ for Gaussian baselines. The composed Pauli count is exactly linear in qubit count (coefficient $11.10$, exact, for main-group molecules; $9.23$ for $d$-orbital blocks under the pair-diagonal ERI approximation (Sec. (ref))—the exact global-$M_L$ rule makes the $d$-block coefficient higher, not lower), so adding atoms to a molecule increases quantum cost linearly. Second- and third-row molecules use analytical frozen cores ([Ne], [Ar], [Ar]3$d^{10}$); the frozen-core energy enters only through the identity operator and does not affect quantum measurement cost. Isostructural molecules with frozen cores produce identical Pauli counts across periodic table rows. The Hamiltonians are available as a Python library with Qiskit, OpenFermion, and PennyLane export. GeoVac Paper 20. Part of the GeoVac research corpus (quantum computing group). Code, tests, and the full paper series: https://github.com/jloutey-hash/geovac. Corpus archive DOI: 10.5281/zenodo.20482394. Corpus version at deposit: v4.75.0.

Jul 9, 20260 citations

Spectroscopic Detection of the Lithium Helium (LiHe) van der Waals Molecule

Al Taisan, Nada Ahmed

Jan 1, 20130 citations

{\mathrm{H}}_{2}

molecule, and the LiH molecule in one spatial dimension. Thereby, the ground-state and binding energies, densities, and bond lengths are compared with the direct solution of the time-dependent Schr\"odinger equation.

O(Q^{2.5})

Pauli scaling and a 190

×

reduction versus cc-pVDZ. The balanced coupled architecture (PK-free) binds LiH with an FCI minimum at a computed

R_{\mathrm{eq}} = 3.227

bohr (7.0% above the experimental 3.015 bohr) at

n_{\max}=2

(878 Pauli terms, 30 qubits); a single-point evaluation at the experimental geometry reaches 0.20% energy error at

n_{\max}=3

(84 qubits) when solved exactly. Chemistry-accuracy scope at

n_{\max}=2

is row-conditional: first-row hydrides (LiH, BeH

_2

, H

_2

\ldots

) bind with documented potential-energy-surface (PES) topology, while second-row hydrides (NaH and below) exhibit monotone overattraction under every tested configuration — frozen-core balanced, multi-zeta valence, screened cross-center, explicit-core Hartree–Fock — with no interior PES minimum at the qubit-Hamiltonian level. We document this scope boundary empirically in \S(ref); the framework's primary value proposition is structural sparsity with quantitative truncation-convergence rates (Paper 38 state-space GH convergence), not energy-accuracy parity with CCSD(T) on second-row systems. The hamiltonian() registry covers 37 systems (35 composed molecules spanning

Z=1

–56, H through Ba, plus the He and H

_2

reference atoms), including multi-center systems (CO, N

_2

, F

_2

), mixed frozen-core molecules (NaCl), and the full first transition series as hydrides (ScH through ZnH), with Pauli scaling

O(Q^{2.5})

confirmed universal across all three rows, compared to

O(Q^{3.9–4.3})

for Gaussian baselines. The composed Pauli count is exactly linear in qubit count (coefficient

11.10

, exact, for main-group molecules;

9.23

for

d

-orbital blocks under the pair-diagonal ERI approximation (Sec. (ref))—the exact global-

M_L

rule makes the

d

-block coefficient higher, not lower), so adding atoms to a molecule increases quantum cost linearly. Second- and third-row molecules use analytical frozen cores ([Ne], [Ar], [Ar]3

d^{10}

); the frozen-core energy enters only through the identity operator and does not affect quantum measurement cost. Isostructural molecules with frozen cores produce identical Pauli counts across periodic table rows. The Hamiltonians are available as a Python library with Qiskit, OpenFermion, and PennyLane export. GeoVac Paper 20. Part of the GeoVac research corpus (quantum computing group). Code, tests, and the full paper series: https://github.com/jloutey-hash/geovac. Corpus archive DOI: 10.5281/zenodo.20482394. Corpus version at deposit: v4.75.0.