Circular Dichroism

Q-Chem contains an ever-growing suite of many-body methods for describing open-shell molecules and excited states.¹⁷² The EOM-CC^224–226 (link) and ADC^227,241 (link) formalisms are two powerful approaches for describing multiconfigurational wave functions within a black-box single-reference formalism. Target states |Ψ_ex⟩ are described as excitations from a reference state |Ψ₀⟩, $$|{\mathrm{\Psi }}_{\text{ex}}〉=\widehat{R}|{\mathrm{\Psi }}_0〉,$$ where $\widehat{R}$ is an excitation operator parameterized via amplitudes that are determined by solving an eigenvalue problem. In EOM-CC, these amplitudes are eigenvectors of the effective Hamiltonian $$\overline{H}=e^{-\widehat{T}}\widehat{H}{e}^{\widehat{T}},$$ in which $\widehat{T}$ is either the CC or the MP2 operator for the reference state. Currently, EOM-CCSD and EOM-MP2 models are available. In ADC, an effective shifted Hamiltonian is constructed using perturbation theory and the intermediate state representation (ISR) formalism,^227,241 (link) similar to Eq. (10), to afford $$\mathbf{M}=⟨{\mathrm{\Psi }}_{\text{ex}}|\widehat{H}-E_0|{\mathrm{\Psi }}_{\text{ex}}⟩,$$ where E₀ is the energy of the MPn reference state. Diagonalization of the Hermitian matrix M yields excitation energies, and the ADC eigenvectors give access to the excited-state wave function. Second-order standard ADC(2), extended ADC(2)-x, and ADC(3) are available.²⁴¹ For the second-order ADC schemes, spin-opposite-scaled (SOS) variants are also implemented.²⁴² (link)
Various EOM-CC and ADC models are defined by the choice of reference state |Ψ₀⟩ and excitation operator $\widehat{R}$ , as illustrated in Fig. 10. The following models are available:^224,227,241 (link) EE (excitation energies), IP (ionization potentials), EA (electron affinities), SF (spin–flip, for triplet and quartet references), 2SF (double SF, for quintet references); DIP (double IP), and DEA (double EA). At present, the 2SF, DIP, and DEA variants are only available in combination with an EOM treatment.²⁴³ (link)
Analytic gradients^244,245 (link) and properties^246–248 (link) are available for most of these models, including transition properties between different target states (e.g., transition dipoles, angular momentum, and electronic circular dichroism rotatory strengths),²⁴⁹ (link) nonadiabatic couplings,²⁵⁰ (link) spin–orbit couplings,^220,251,252 (link) and nonlinear optical properties, including two-photon transition moments and (hyper)polarizabilities for both ground and excited states.^253–256 (link) Extensions of these theories to metastable states²⁵⁷ (link) (resonances) and to core-level excitations^258–260 (link) are also available and are highlighted in Sec. V.
The IP and EA variants of these models afford spin-pure descriptions of ground and excited doublet states and are useful for modeling charge-transfer processes. EOM-SF and SF-ADC methods are suitable for treating diradicals, triradicals, and conical intersections. The DEA and DIP ansätze further expand the scope of applicability.²⁴³ (link) Spin–flip methods can be used to treat strongly correlated systems within an effective Hamiltonian formalism,^221,261,262 (link) with applications to single-molecule magnets and even infinite spin chains.²²² (link)
For visualization purposes, both Dyson orbitals²⁶⁴ (link) and natural transition orbitals²⁶⁵ (link) (NTOs) are available,^{15,88,220,266–269} (link) including NTOs of the response density matrices for analyzing two-photon absorption²⁷⁰ (link) and resonant inelastic x-ray scattering.²⁷¹ (link)
Figure 11 highlights the application of these tools to model magnetic properties and spin-forbidden chemistry. Exciton analyses,^{267,268,272–274} (link) bridging the gap between the quasiparticle and MO pictures of excited states, enable the calculation and visualization of electron–hole correlation.^{89,267,268,272,273} (link)

Materials used for the experiments done in the current work were employed in the experiments without further purifications. From Merck, 2-hydroxybenzaldehyde, N-methyl propane 1,3-diamine, imidazole, methanol, CuCl₂·2H₂O, Ni(ClO₄)₂·6H₂O etc. were procured. BSA and DNA was purchased from Sigma-Aldrich Chemicals (USA) and was prepared in 10 mM Phosphate Buffer (pH 7.4). For steady-state and time-resolved experiments, the concentration of BSA was kept as 5 μM, whereas 2 μM BSA was used for Circular Dichroism (CD) spectroscopic studies.

Recombinant mouse RBP4 with 6XHis Tag was expressed E.coli expression system and extracted in Tris buffer with composition of 50 mM Tris-HCl, 1 M L-Arginine, 10% Glycerol, pH 8.0. The lysate was purified by nickel NTA column. The msRBP4 protein quality was monitored by western blot using anti His-tag antibody. The structural quality of the recombinant RBP4 protein was confirmed with Circular dichroism (CD) spectroscopy (Jasco 815 circular dichroism, Spectramax Gemini) (Micsonai et al., 2015 (link)). The mean residue ellipticity (θ), was calculated using the following formula. $\left[\mathrm{\theta }\right]=\left(\mathrm{S}\times \mathrm{m}\mathrm{R}\mathrm{w}\right)/\left(10\mathrm{c}\mathrm{l}\right)$ where S represents the CD signal in mθ, mRw represents the mean residue mass, c represents the concentration of the protein in mg/mL, and l represents the path length in cm. The percent change in molecules structure were calculated using BeStSel Secondary Structure Analysis to Protein Fold Prediction by CD Spectroscopy (https://bestsel.elte.hu), (see Supplementary Information Supplementary Materials S1–S5). The initial interaction quality of the recombinant RBP4 with msSTRA6, msRBPR2, and control peptides were checked with intrinsic tryptophan fluorescence assay. The peptides were diluted in various micromolar concentrations and the incubated with 3 μg RBP4 in room temperature for 5 min and excited at 290 nm and the emission was scanned from 300 nm to 400 nm wavelength. The data were normalized with the blank and peptide only conditions and plotted in GraphPad prism version 9.3. San Diego, CA, United States. (Supplementary Figure S5).