Multistate density functional theory (MSDFT) generalizes Kohn-Sham density functional theory to a finite subspace of interacting states through a Hamiltonian matrix functional of the matrix density D(r). A central challenge is to construct matrix functionals that preserve subspace unitary invariance while encoding nontrivial state coupling. Here we show that any local, unitary-covariant matrix functional of D(r) must be codiagonalizable with D(r), and is therefore completely specified by a scalar generator acting on its eigenvalues. This establishes a one-to-all mapping from a scalar generator to the full matrix functional. As a consequence, the construction of N2 matrix elements is reduced to a single scalar mapping evaluated on the eigenvalue spectrum at each spatial grid point. The formalism is illustrated using a four-state Hubbard model, where exact reconstruction is achieved with a known scalar function, and deviations from this mapping can be systematically corrected within the spectral framework. The results provide a rigorous foundation for constructing local matrix exchange-correlation functionals with computational complexity comparable to Kohn-Sham DFT, and offer a practical route toward scalable MSDFT approximations.

This study investigates the performance of Target State Optimization Density Functional Theory (TSO-DFT) in predicting molecular K-edge X-ray Absorption Spectra (XAS). In contrast to Time-Dependent Density Functional Theory (TDDFT), which systematically underestimates core excitation energies by more than 10 eV, TSO-DFT optimizes wave function for every state to account for orbital relaxation effects and can achieve an accuracy of subelectronvolts. We apply TSO-DFT to predict the K-edge XAS for which is critical for accurate predictions of core excitations. TSO-DFT is applied to predict XAS for CO2, N2O, carbonyl compounds, and radicals. TSO-DFT succeeds in predicting both the main features and core excitation energies. TSO-DFT is also used to predict the angle-dependent XAS of porphyrin and polarized XAS of the uranyl ion. The calculated XAS agrees quite well with experiments and can give details of electronic structure change that cannot be obtained straightforwardly from experiments alone. TSO-DFT is a promising method for studying molecular XAS and is available in the software Qbics, which can be downloaded free of charge.

Multistate density functional theory (MSDFT) provides a rigorous variational framework for the simultaneous description of multiple electronic states through a matrix density, but practical implementations have relied on multiconfigurational many-body wavefunctions. Here, we introduce the Dyson field, ψ(r), an L×N matrix-valued function of the coordinate r that factorizes the matrix density as D(r) = ψ†(r)ψ(r). The elements of ψ(r) = {ψpA(r)} are shown to be Dyson orbitals connecting the n-electron states of interest to (n − 1)-electron ionization channels of size L, providing a direct physical interpretation of the matrix density in terms of electron removal amplitudes. Variational minimization of the MSDFT subspace energy with respect to the Dyson field yields a matrix Fock equation, in which the kinetic and external potential operators act locally, while Hartree and exchange–correlation effects appear as N×N matrix potentials, VH[D](r) and Vxc[D](r), that couple electronic states within the subspace. This formulation defines a quasiparticle reference system for MSDFT that is analogous to the Kohn–Sham orbitals in Hohenberg-Kohn DFT. In appropriate limits, the formalism reduces exactly to Kohn-Sham DFT for N = 1 and to the Tamm-Dancoff approximation of time-dependent DFT within the single-excitation manifold. More generally, the Dyson-field construction transforms MSDFT from a formally exact but wavefunction-dependent framework into an orbital-based theory, opening a practical route to self-consistent, density-based treatments of strongly correlated and electronically coupled states.

A covariant local matrix density approximation (LMDA) is introduced within multistate density functional theory based on subspace invariance and the spectral decomposition of the matrix containing state and transition densities. The exchange correlation matrix functional is constructed through spectral reconstruction of this matrix density, whereby conventional local exchange-correlation functionals are incorporated as spectral-channel functionals within a covariant matrix-functional formalism. The resulting formulation preserves exact normalization of the exchange-correlation matrix hole, recovers Kohn-Sham density functional theory in the single-state limit, and preserves spin-multiplet degeneracy through covariance of the spin matrix functional under spin rotations. Combined with multistate self-consistent-field (MSSCF) optimization, the present framework enables fully variational calculations of interacting ground and excited states. Applications to atomic excitations, H2 dissociation, ethylene torsion and cyclobutadiene automerization reveals that the resulting MSDFT/LMDA approach captures essential multistate and strong-correlation physics, including static correlation and spin symmetry. The key insight is that the central obstacle in extending density functional theory to coupled electronic states is not necessarily the lack of appropriate scalar exchange-correlation approximations, but the lack of a covariant matrix-functional formalism in which such functionals can operate. The present MSDFT/LMDA provides a direct realization of this matrix-functional formalism.

The interaction between excited states of a closed-shell chromophore and a nearby free radical species gives rise to spin-coupled doublet states, namely singdoublet and tripdoublet, as well as a quartet state. This coupling facilitates transitions that are otherwise spin-forbidden, thereby enhancing intersystem crossing and influencing luminescence and non-radiative decay pathways. In this chapter, we explore these interactions using multistate density functional theory (MSDFT). By employing a minimal active space (MAS) comprising just ten determinant configurations, MSDFT effectively captures local and charge-transfer excitations with inclusion of correlation effects. MSDFT extends the Hohenberg-Kohn density functional theory from the ground state to encompass all electronic states, underscoring the potential for developing computationally efficient methods to study excited states. Numerical results demonstrate that MSDFT accurately reproduces both qualitative trends and quantitative excited-state energies, in accord with previous studies using extended multistate complete-active-space second-order perturbation theory (XMS-CASPT2). The work explores energy changes along a reaction path from the D_0/D_1 minimum energy crossing intersection to the D_2/D_3 crossing in the exciplex formed by 10-methylphenothiazine and a dicarboximide electron acceptor linked to the stable free radical 2,2,6,6-tetramethylpiperidin-1-oxyl (TEMPO).

A quantum theory of density functionals and its applications is presented. By introducing a matrix density D ( r ) of rank N as the fundamental variable, a one-to-one correspondence has been established between D ( r ) and the Hamiltonian matrix representing N electronic states-that is, a matrix density functional ℋ [ D ] . Moreover, no more than N 2 Slater determinants are sufficient to represent D ( r ) exactly, giving rise to the concept of minimal active space (MAS). The use of a MAS naturally leads to the definition of correlation matrix functional ℰ c [ D ] , the multi-state extension of the exchange-correlation functional in Kohn-Sham DFT. Variational minimization of the multistate energy, which is defined as the trace of the Hamiltonian matrix functional, yields the exact energies and densities of the lowest N eigenstates. A nonorthogonal state interaction (NOSI) algorithm has been developed to optimize the orbitals associated with D ( r ) and to approximate the correlation matrix functional. The MSDFT-NOSI method is demonstrated across a range of applications, particularly in cases where KS-DFT and linear-response time-dependent DFT fail, with its accuracy validated through comparison with high-level multiconfigurational wave function theory.

On the basis of recent advancements in the Hamiltonian matrix density functional for multiple electronic eigenstates, this study delves into the mathematical foundation of the multistate density functional theory (MSDFT). We extend a number of physical concepts at the core of Kohn-Sham DFT, such as density representability, to the matrix density functional. In this work, we establish the existence of the universal matrix functional for many states as a proper generalization of the Lieb universal functional for the ground state. Consequently, the variation principle of MSDFT can be rigorously defined within an appropriate domain of matrix densities, thereby providing a solid framework for DFT of both the ground state and excited states. We further show that the analytical structure of the Hamiltonian matrix functional is considerably constrained by the subspace symmetry and invariance properties, requiring and ensuring that all elements of the Hamiltonian matrix functional are variationally optimized in a coherent manner until the Hamiltonian matrix within the subspace spanned by the lowest eigenstates is obtained. This work solidifies the theoretical foundation to treat multiple electronic states using density functional theory.

Tacrolimus (FK506) is an effective therapeutic for transplant rejection in clinical practice, primarily inhibiting rejection by suppressing the activation and proliferation of allogeneic T cells in the lymph nodes (LNs). However, conventional administration methods face challenges in directly delivering free FK506 to the LNs. In this study, we introduce a novel LN-targeted delivery system based on mesoporous silica nanoparticles (MSNs-FK506MECA79). These particles were designed to selectively target high endothelial venules in LNs; this was achieved through surface modification with MECA79 antibodies. Their mean size and zeta potential were 201.18 +/- 5.98 nm and - 16.12 +/- 0.36 mV, respectively. Our findings showed that MSNs-FK506-MECA79 could accumulate in LNs and increase the local concentration of FK506 from 28.02 +/- 7.71 ng/g to 123.81 +/- 76.76 ng/g compared with the free FK506 treatment group. Subsequently, the therapeutic efficacy of MSNs-FK506-MECA79 was evaluated in a skin transplantation model. The treatment with MSNs-FK506-MECA79 could lead to a decrease in the infiltration of T cells in the grafts, a reduction in the grade of rejection, and a significant prolongation of survival. Consequently, this study presents a promising strategy for the active LN-targeted delivery of FK506 and improving the immunotherapeutic effects on transplant rejection.

The activation of naive T cells by mature dendritic cells (DCs) presenting allograft antigens marks a pivotal stage in triggering transplant rejection. A critical intervention in this process involves the administration of rapamycin, which disrupts the mTOR signaling pathway, thereby impeding DC maturation. Nevertheless, systemic administration of rapamycin faces challenges due to its limited bioavailability, non-specific targeting, and notable side effects. To address these limitations, LNP@rapa (liposome-encapsulated rapamycin) is developed, administered via subcutaneous injection. This formulation selectively targets lymph nodes, inhibiting DC maturation within these nodes and mitigating transplant rejection. This study validates the in vivo efficacy of LNP@rapa, demonstrating its ability to hinder DC maturation, reduce inflammatory cytokine secretion, and significantly prolong graft survival in two distinct mouse transplantation models. This study introduces an innovative strategy targeting lymph nodes to impede DC maturation, offering a promising approach to address transplant rejection. A kind of lipid nanoparticle containing rapamycin (LNP@rapa) is prepared. Following subcutaneous injection, LNP@rapa gains entry into lymph nodes via phagocytosis by immature dendritic cell (imDCs). Rapamycin's action involves the inhibition of imDC maturation by restraining the mammalian target of rapamycin (mTOR) pathway, culminating in costimulation blockade with T cells, and thus mitigating transplant rejection. image

Beyond the Hohenberg-Kohn density functional theory for the ground state, it has been established that the Hamiltonian matrix for a finite number (N) of lowest eigenstates is a matrix density functional. Its fundamental variable─the matrix density D(r)─can be represented by, or mapped to, a set of auxiliary, multiconfigurational wave functions expressed as a linear combination of no more than N2 determinant configurations. The latter defines a minimal active space (MAS), which naturally leads to the introduction of the correlation matrix functional, responsible for the electronic correlation effects outside the MAS. In this study, we report a set of rigorous conditions in the Hamiltonian matrix functional, derived by enforcing the symmetry of a Hilbert subspace, namely the subspace invariance property. We further establish a fundamental theorem on the correlation matrix functional. That is, given the correlation functional for a single state in the N-dimensional subspace, all elements of the correlation matrix functional for the entire subspace are uniquely determined. These findings reveal the intricate structure of electronic correlation within the Hilbert subspace of lowest eigenstates and suggest a promising direction for efficient simulation of excited states.

T cells serve a pivotal role in the rejection of transplants, both by directly attacking the graft and by recruiting other immune cells, which intensifies the rejection process. Therefore, monitoring T cells becomes crucial for early detection of transplant rejection, while targeted drug delivery specifically to T cells can significantly enhance the effectiveness of rejection therapy. However, regulating the activity of T cells within transplanted organs is challenging, and the prolonged use of immunosuppressive drugs is associated with notable side effects and complications. Functionalized nanoparticles offer a potential solution by targeting T cells within transplants or lymph nodes, thereby reducing the off-target effects and improving the long-term survival of the graft. In this review, we will provide an overview of recent advancements in T cell-targeted imaging molecular probes for diagnosing transplant rejection and the progress of T cell-regulating nanomedicines for treating transplant rejection. Additionally, we will discuss future directions and the challenges in clinical translation.

The performance of multistate density functional theory (MSDFT) with nonorthogonal state interaction (NOSI) is assessed for 100 vertical excitation energies against the theoretical best estimates extracted to the full configuration interaction accuracy on the database developed by Loos et al. in 2018 (Loos2018). Two optimization techniques, namely, block-localized excitation and target state optimization, are examined along with two ways of estimating the transition density functional (TDF) for the correlation energy of the Hamiltonian matrix density functional. The results from the two optimization methods are similar. It was found that MSDFT-NOSI using the spin-multiplet degeneracy constraint for the TDF of spin-coupling interaction, along with the M06-2X functional, yields a root-mean-square error (RMSE) of 0.22 eV, which performs noticeably better than time-dependent density functional theory (DFT) at an RMSE of 0.43 eV using the same functional and basis set on the Loos2018 database. In comparison with wave function theory, NOSI has smaller errors than CIS(D∞), LR-CC2, and ADC(3) all of which have an RMSE of 0.28 eV, but somewhat greater than STEOM-CCSD (RMSE of 0.14 eV) and LR-CCSD (RMSE of 0.11 eV) wave function methods. In comparison with Kohn-Sham (KS) DFT calculations, the multistate DFT approach has little double counting of correlation. Importantly, there is no noticeable difference in the performance of MSDFT-NOSI on the valence, Rydberg, singlet, triplet, and double-excitation states. Although the use of another hybrid functional PBE0 leads to a greater RMSE of 0.36 eV, the deviation is systematic with a linear regression slope of 0.994 against the results with M06-2X. The present benchmark reveals that density functional approximations developed for KS-DFT for the ground state with a noninteracting reference may be adopted in MSDFT calculations in which the state interaction is key.

A multistate energy decomposition analysis (MS-EDA) method is described to dissect the energy components in molecular complexes in excited states. In MS-EDA, the total binding energy of an excimer or an exciplex is partitioned into a ground-state term, called local interaction energy, and excited-state contributions that include exciton excitation energy, superexchange stabilization, and orbital and configuration-state delocalization. An important feature of MS-EDA is that key intermediate states associated with different energy terms can be variationally optimized, providing quantitative insights into widely used physical concepts such as exciton delocalization and superexchange charge-transfer effects in excited states. By introducing structure-weighted adiabatic excitation energy as the minimum photoexcitation energy needed to produce an excited-state complex, the binding energy of an exciplex and excimer can be defined. On the basis of the nature of intermolecular forces through MS-EDA analysis, it was found that molecular complexes in the excited states can be classified into three main categories, including (1) encounter excited-state complex, (2) charge-transfer exciplex, and (3) intimate excimer or exciplex. The illustrative examples in this Perspective highlight the interplay of local excitation polarization, exciton resonance, and superexchange effects in molecular excited states. It is hoped that MS-EDA can be a useful tool for understanding photochemical and photobiological processes.

FK506, a first-line immunosuppressant, is routinely administered orally and intravenously following heart transplantation. However, frequent administration can result in a substantial psychological burden to patients, resulting in non-adherence to medication. The purpose of our study is to overcome the disadvantages of systemic drug administration by developing a polymer-based delivery system that is tunable and biodegradable and that can release highly hydrophobic FK506 over extended periods to treat or prevent acute cardiac allograft rejection. Using an electrospinning method, long-acting microfibers were prepared, and FK506 appeared to be continuously released for up to 14 days based on the in vitro release profiles. After implanting the microfiber subcutaneously into the abdominals of transplanted rats, it was found that the infiltration of T cells and macrophages and the secretion of interleukin-2 (IL-2) and IL-1β were significantly reduced compared with those of the free FK506 groups. More importantly, the mean survival time (MST) of the PCL-FK506 group was significantly extended in comparison with that of untreated control recipients and free FK506 (MST of untreated control recipients, free FK506, and PCL-FK506 was 8, 26.1, and 37, respectively). In conclusion, we propose that this drug delivery approach would be suitable for developing long-lasting immunomodulatory agents that prolong cardiac graft survival safely and effectively.

Allograft rejection has always been a major obstacle in organ transplantation. The current clinical diagnostic gold standard for allograft rejection is an invasive biopsy. However, biopsy has some limitations, such as sampling errors, risk of serious complications, and high cost. In this study, we have rationally developed an activatable fluorescent probe CYGB for imaging of granzyme B, which is a biomarker released by CD8+T cells attacking the graft. Moreover, the ability of CYGB to detect rejection early in mouse heart and skin transplantation models was evaluated. The probe CYGB consists of a caged hemicyanine-based fluorophore and a GzmB-specifically cleaved peptide substrate linked via a self-immolating spacer, p-aminobenzyl alcohol. Endogenous GzmB in CD8+ T cells specifically activated the near-infrared fluorescence (NIRF) signal of CYGB. In vivo imaging in mice skin and heart graft models, showed that CYGB preferentially accumulates in grafts, enabling early diagnosis of rejection. Moreover, CYGB enables non-invasive assessment of the level of immunosuppression in allogeneic mice treated with FK506. This study provides an alternative method for monitoring the status of allografts without biopsy.

As macrophage infiltration is significantly related to the progression of inflammatory bowel disease (IBD), monitoring the macrophages is a valuable strategy for IBD diagnosis. However, owing to the harsh physiological environment of the gastrointestinal tract and enzymatic degradation, the development of orally administrable imaging probes for tracking macrophages remains a considerable challenge. Accordingly, herein, an orally administrable aggregation‐induced emission biomimetic probe (HBTTPIP/ β ‐glucan particles [GPs]) is developed for tracing macrophages; HBTTPIP/GPs can diagnose and alleviate dextran sulfate sodium (DSS)‐induced colonic inflammation and self‐report the treatment efficiency. The fluorophore HBTTPIP can effectively aggregate in GPs, restricting intramolecular rotation and activating the fluorescence of HBTTPIP. After being orally administrated, HBTTPIP/GPs are phagocytosed by intestinal macrophages, which then migrate to colonic lesions, enabling non‐invasive monitoring of the severity of IBD via in vivo fluorescence imaging. Notably, oral HBTTPIP/GPs ameliorate DSS‐induced IBD by inhibiting the expressions of pro‐inflammatory factors and improving colonic mucosal barrier function. Furthermore, these HBTTPIP/GPs realize self‐feedback of the therapeutic effects of GPs on DSS‐induced colitis. The oral biomimetic probe HBTTPIP/GPs reported herein provide a novel theranostic platform for IBD, integrating non‐invasive diagnosis of IBD in situ and the corresponding treatment.

Despite exquisite immune response modulation, the extensive application of microRNA therapy in treating heart transplant rejection is still impeded by poor stability and low target efficiency. Here we have developed a low-intensity pulsed ultrasound (LIPUS) cavitation-assisted genetic therapy after executing the heart transplantation (LIGHT) strategy, facilitating microRNA delivery to target tissues through the LIPUS cavitation of gas vesicles (GVs), a class of air-filled protein nanostructures. We prepared antagomir-155 encapsulated liposome nanoparticles to enhance the stability. Then the murine heterotopic transplantation model was established, and antagomir-155 was delivered to murine allografted hearts via the cavitation of GVs agitated by LIPUS, which reinforced the target efficiency while guaranteeing safety owing to the specific acoustic property of GVs. This LIGHT strategy significantly depleted miR-155, upregulating the suppressors of cytokine signaling 1 (SOCS1), leading to reparative polarization of macrophages, decrease of T lymphocytes and reduction of inflammatory factors. Thereby, rejection was attenuated and the allografted heart survival was markedly prolonged. The LIGHT strategy achieves targeted delivery of microRNA with minimal invasiveness and great efficiency, paving the way towards novel ultrasound cavitation-assisted strategies of targeted genetic therapy for heart transplantation rejection.

A flexible self-consistent field method, called target state optimization (TSO), is presented for exploring electronic excited configurations and localized diabatic states. The key idea is to partition molecular orbitals into different subspaces according to the excitation or localization pattern for a target state. Because of the orbital-subspace constraint, orbitals belonging to different subspaces do not mix. Furthermore, the determinant wave function for such excited or diabatic configurations can be variationally optimized as a ground state procedure, unlike conventional ΔSCF methods, without the possibility of collapsing back to the ground state or other lower-energy configurations. The TSO method can be applied both in Hartree-Fock theory and in Kohn-Sham density functional theory (DFT). The density projection procedure and the working equations for implementing the TSO method are described along with several illustrative applications. For valence excited states of organic compounds, it was found that the computed excitation energies from TSO-DFT and time-dependent density functional theory (TD-DFT) are of similar quality with average errors of 0.5 and 0.4 eV, respectively. For core excitation, doubly excited states and charge-transfer states, the performance of TSO-DFT is clearly superior to that from conventional TD-DFT calculations. It is shown that variationally optimized charge-localized diabatic states can be defined using TSO-DFT in energy decomposition analysis to gain both qualitative and quantitative insights on intermolecular interactions. Alternatively, the variational diabatic states may be used in molecular dynamics simulation of charge transfer processes. The TSO method can also be used to define basis states in multistate density functional theory for excited states through nonorthogonal state interaction calculations. The software implementing TSO-DFT can be accessed from the authors.