Accurate Scaling Functions of the Scaled Schrödinger Equation. II. Variational Examination of the Correct Scaling Functions with the Free Complement Theory Applied to the Helium Atom.

In a previous paper [. 030403.], one of the authors introduced the scaled Schrödinger equation (SSE), ( - )ψ = 0 for atoms and molecules, where the scaling function is the positive function of the electron-nuclear (e-n) and electron-electron (e-e) distances.

Potential Energy Curves of the Low-Lying Five Σ and Π States of a CH Molecule Based on the Free Complement - Local Schrödinger Equation Theory and the Chemical Formula Theory.

The potential energy curves (PECs) of the low-lying five Σ and Π states (XΣ, CΣ, 3Σ, AΠ, and DΠ states) of a CH molecule, an important interstellar molecule, were calculated by the free complement (FC) - local Schrödinger equation (LSE) theory with the direct local sampling scheme. The FC wave functions were constructed based on the chemical formula theory (CFT), whose local characters correspond to the covalent dissociations: C(P°(sp))) + H(S) of the XΣ and AΠ states and the ionic dissociations: C(D(sp)) + H of the CΣ and DΠ states. All the calculated PECs were obtained with satisfying the chemical accuracy, i.

Potential curves of the lower nine states of Li molecule: Accurate calculations with the free complement theory and the comparisons with the SAC/SAC-CI results.

The free-complement (FC) theory proposed for solving the Schrödinger equation of atoms and molecules highly accurately was applied to the calculations of the potential curves of the lower nine states of the Li molecule. The results were compared with the accurate experimental Rydberg-Klein-Rees potential curves available. They overlap completely with each other without any shift everywhere for all the states of Li.

Accurate scaling functions of the scaled Schrödinger equation.

The scaling function g of the scaled Schrödinger equation (SSE) is generalized to obtain accurate solutions of the Schrödinger equation (SE) with the free complement (FC) theory. The electron-nuclear and electron-electron scaling functions, g and g, respectively, are generalized. From the relations between SE and SSE at the inter-particle distances being zero and infinity, the scaling function must satisfy the collisional (or coalescent) condition and the asymptotic condition, respectively.

Light-Driven Proton, Sodium Ion, and Chloride Ion Transfer Mechanisms in Rhodopsins: SAC-CI Study.

Bacteriorhodopsin (BR) and halorhodopsin (HR) are well-known light-driven ion-pumping rhodopsins. BR transfers a proton from the intracellular medium to the extracellular medium. HR takes in chloride ion from the extracellular medium.

Solving the Schrödinger equation with the free-complement chemical-formula theory: Variational study of the ground and excited states of Be and Li atoms.

The chemical formula theory (CFT) proposed in Paper I of this series [H. Nakatsuji et al., J.

Solving the Schrödinger equation of hydrogen molecule with the free complement-local Schrödinger equation method: Potential energy curves of the ground and singly excited singlet and triplet states, Σ, Π, Δ, and Φ.

The free-complement (FC) theory for solving the Schrödinger equation (SE) was applied to calculate the potential energy curves of the ground and excited states of the hydrogen molecule (H) with the Σ , Σ , Σ , Σ , Π, Π, Π, Π, Δ, Δ, Δ, Δ, Φ, Φ, Φ, and Φ symmetries (in total, 54 states). The initial functions of the FC theory were formulated based on the atomic states of the hydrogen atom and its positive and negative ions at the dissociation limits. The local Schrödinger equation (LSE) method, which is a simple sampling-type integral-free methodology, was employed instead of the ordinary variational method and highly accurate results were obtained stably and smoothly along the potential energy curves.

Solving the Schrödinger equation of hydrogen molecules with the free-complement variational theory: essentially exact potential curves and vibrational levels of the ground and excited states of the Σ symmetry.

The Schrödinger equation of hydrogen molecules was solved essentially exactly and systematically for calculating the potential energy curves of the electronic ground and excited states of the Σ, Σ, Σ, and Σ symmetries. The basic theory is the variational free complement theory, which is an exact general theory for solving the Schrödinger equation of atoms and molecules. The results are essentially exact with the absolute energies being correct beyond μ-hartree digits.

Solving the Schrödinger equation of atoms and molecules: Chemical-formula theory, free-complement chemical-formula theory, and intermediate variational theory.

Chemistry is governed by the principle of quantum mechanics as expressed by the Schrödinger equation (SE) and Dirac equation (DE). The exact general theory for solving these fundamental equations is therefore a key for formulating accurately predictive theory in chemical science. The free-complement (FC) theory for solving the SE of atoms and molecules proposed by one of the authors is such a general theory.

Accuracy of Td-DFT in the Ultraviolet and Circular Dichroism Spectra of Deoxyguanosine and Uridine.

Accuracy of the time-dependent density functional theory (Td-DFT) was examined for the ultraviolet (UV) and circular dichroism (CD) spectra of deoxyguanosine (dG) and uridine, using 11 different DFT functionals and two different basis sets. The Td-DFT results of the UV and CD spectra were strongly dependent on the functionals used. The basis-set dependence was observed only for the CD spectral calculations.