Exact Theory Applied to the Lithium Atom.

The free complement (FC) theory for solving the scaled Schrödinger equation (SSE) was applied to the Li atom for calculating the exact wave functions, the energies, and the various properties of the ground doublet S and excited P states. The SSE is equivalent to the Schrödinger equation (SE) but does not have the divergence difficulty of the variational equation of the SE. Because the Li atom is a three-electron system, the variational exact FC calculations for solving the SSE are possible using the function = 1 - exp(-γ) as the "correct" scaling function of the SSE.

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.

Gaussian functions with odd power of r produced by the free complement theory.

We investigate, in this paper, the Gaussian (G) function with odd powers of r, rxaybzc exp(-αr2), called the r-Gaussian or simply the rG function. The reason we investigate this function here is that it is generated as the elements of the complement functions (cf's) when we apply the free complement (FC) theory for solving the Schrödinger equation to the initial functions composed of the Gaussian functions. This means that without the rG functions, the Gaussian set of functions cannot produce the exact solutions of the Schrödinger equation, showing the absolute importance of the rG functions in quantum chemistry.

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.

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

Following a previous study of the Σ states (Phys. Chem. Chem.

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.

Photoelectron spectrum of NO : SAC-CI gradient study of vibrational-rotational structures.

Three-dimensional accurate potential energy surfaces around the local minima of NO and NO were calculated with the SAC/SAC-CI analytical energy gradient method. Therefrom, the ionization photoelectron spectra of NO , the equilibrium geometries and adiabatic electron affinity of NO , and the vibrational frequencies including harmonicity and anharmonicity of NO and NO were obtained. The calculated electron affinity was in reasonable agreement with the experimental value.

Solving the Schrödinger equation of atoms and molecules with the free-complement chemical-formula theory: First-row atoms and small molecules.

The free-complement chemical-formula theory (FC-CFT) for solving the Schrödinger equation (SE) was applied to the first-row atoms and several small molecules, limiting only to the ground state of a spin symmetry. Highly accurate results, satisfying chemical accuracy (kcal/mol accuracy for the absolute total energy), were obtained for all the cases. The local Schrödinger equation (LSE) method was applied for obtaining the solutions accurately and stably.

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.

Similarities and Differences between RNA and DNA Double-Helical Structures in Circular Dichroism Spectroscopy: A SAC-CI Study.

The helical structures of DNA and RNA are investigated experimentally using circular dichroism (CD) spectroscopy. The signs and the shapes of the CD spectra are much different between the right- and left-handed structures as well as between DNA and RNA. The main difference lies in the sign at around 295 nm of the CD spectra: it is positive for the right-handed B-DNA and the left-handed Z-RNA but is negative for the left-handed Z-DNA and the right-handed A-RNA.

Electronic Transitions in Conformationally Controlled Peralkylated Hexasilanes.

The photophysical properties of oligosilanes show unique conformational dependence due to σ-electron delocalization. The excited states of the SAS, AAS, and AEA conformations of peralkylated n-hexasilanes, in which the SiSiSiSi dihedral angles are controlled into a syn (S), anti (A), or eclipsed (E) conformation, were investigated by using UV absorption, magnetic circular dichroism (MCD), and linear dichroism spectroscopy. Simultaneous Gaussian fitting of all three spectra identified a minimal set of transitions and the wavenumbers, oscillator strengths, and MCD B terms in all three compounds.

Indicator of the Stacking Interaction in the DNA Double-Helical Structure: ChiraSac Study.

The double-helical structures of DNA are experimentally distinguished by the circular dichroism (CD) spectra. The CD spectra are quite different between the left- and right-handed double-helical structures of DNA. The lowest peak is negative for the left-handed Z-DNA but positive for the right-handed B-DNA.

Solving the Schrödinger equation of molecules by relaxing the antisymmetry rule: Inter-exchange theory.

The Schrödinger equation (SE) and the antisymmetry principle constitute the governing principle of chemistry. A general method of solving the SE was presented before as the free complement (FC) theory, which gave highly accurate solutions for small atoms and molecules. We assume here to use the FC theory starting from the local valence bond wave function.

Free-complement local-Schrödinger-equation method for solving the Schrödinger equation of atoms and molecules: basic theories and features.

The free-complement (FC) method is a general method for solving the Schrödinger equation (SE): The produced wave function has the potentially exact structure as the solution of the Schrödinger equation. The variables included are determined either by using the variational principle (FC-VP) or by imposing the local Schrödinger equations (FC-LSE) at the chosen set of the sampling points. The latter method, referred to as the local Schrödinger equation (LSE) method, is integral-free and therefore applicable to any atom and molecule.

Electronic transitions in conformationally controlled tetrasilanes with a wide range of SiSiSiSi dihedral angles.

Unlike π-electron chromophores, the peralkylated n-tetrasilane σ-electron chromophore resembles a chameleon in that its electronic spectrum changes dramatically as its silicon backbone is twisted almost effortlessly from the syn to the anti conformation (changing the SiSiSiSi dihedral angle ω from 0 to 180°). A combination of UV absorption, magnetic circular dichroism (MCD), and linear dichroism (LD) spectroscopy on conformationally controlled tetrasilanes 1-9, which cover fairly evenly the full range of angles ω, permitted a construction of an experimental correlation diagram for three to four lowest valence electronic states. The free chain tetrasilane n-Si4 Me10 (10), normally present as a mixture of three enantiomeric conformer pairs of widely different angles ω, has also been included in our study.

General coalescence conditions for the exact wave functions. II. Higher-order relations for many-particle systems.

We derived the necessary conditions that must be satisfied by the non-relativistic time-independent exact wave functions for many-particle systems at a two-particle coalescence (or cusp) point. Some simple conditions are known to be Kato's cusp condition (CC) and Rassolov and Chipman's CC. In a previous study, we derived an infinite number of necessary conditions that two-particle wave functions must satisfy at a coalescence point.

Circular dichroism spectra of uridine derivatives: ChiraSac study.

The experimental circular dichroism (CD) spectra of uridine and NH2-uridine that were different in the intensity and shape were studied in the light of the ChiraSac method. The theoretical CD spectra at several different conformations using the symmetry-adapted-cluster configuration-interaction (SAC-CI) theory largely depended on the conformational angle, but those of the anti-conformers and the Boltzmann average reproduced the experimentally obtained CD spectra of both uridine and NH2-uridine. The differences in the CD spectra between the two uridine derivatives were analyzed by using the angle θ between the electric transition dipole moment (ETDM) and the magnetic transition dipole moment (MTDM).

Conformational dependence of the circular dichroism spectrum of α-hydroxyphenylacetic acid: a ChiraSac study.

The conformational dependence of the circular dichroism (CD) spectrum of a chiral molecule, α-hydroxyphenylacetic acid (HPAA) containing phenyl, COOH, OH and H groups around a chiral carbon atom, has been studied theoretically by using the SAC-CI (symmetry adapted cluster-configuration interaction) theory. The results showed that the CD spectrum of HPAA depends largely on the rotations (conformations) of the phenyl and COOH groups around the single bonds. The first band is due to the excitation of electrons belonging to the phenyl region and therefore sensitive to the phenyl rotation.