State-averaged Complete Active Space Self-consistent Field Research Articles

Deciphering the Internal Conversion Processes Involved in the Photochemical Ring-Opening of 1,3-Cyclohexadiene by Symmetric sp2-Carbon Substitutions.

Chemical substituents hold the potential to markedly influence the photochemical behavior in molecular systems and assist in gaining a comprehensive understanding of nonadiabatic phenomena. In this study, we have conducted a comparative analysis of the influence of chemical substituents on the photochemical ring-opening of 1,3-cyclohexadiene (CHD), considering four systems: CHD, 2,3-dimethylcyclohexadiene (CHD-Me2-1), 1,4-dimethylcyclohexadiene (CHD-Me2-2), and 1,2,3,4-tetramethylcyclohexadiene (CHD-Me4), using electronic structure theory calculations and nonadiabatic molecular dynamics simulations. Employing extended multistate complete active space second-order perturbation (XMS-CASPT2) theory, we optimized reactants, S1 states, conical intersections (CIns), and products, revealing structural and energetic variations consistent with prior research. Nonadiabatic molecular dynamics simulation was used to gain insights into photochemical dynamics at state-averaged complete active space self-consistent field (SA-CASSCF) theory. CHD-Me4 exhibited reduced carbon-carbon single bond rupture rates, responsible for ring-opening, due to substituent proximity. Further, CHD-Me2-2 and CHD-Me4 displayed prolonged excited-state relaxation times, highlighting notable substituents' impact. Analysis of kinetic energy profiles of specific carbon atoms also revealed restrained atomic displacements, particularly in CHD-Me2-2 and CHD-Me4. These findings advance our understanding of how substituents modulate photochemical reactions in cyclohexadiene derivatives, guiding new molecular design and future research.

A Local Diabatisation Method for Two-State Adiabatic Conical Intersections.

A methodology to locally characterize conical intersections (CIs) between two adiabatic electronic states for which no nonadiabatic coupling (NAC) vectors are available is presented. Based on the Hessian and gradient at the CI, the branching space coordinates are identified. The potential energy surface around the CI in the branching space is expressed in the diabatic representation, from which the NAC vectors can be calculated in a wave-function-free, energy-based approach. To demonstrate the universality of the developed methodology, the minimum-energy CI (MECI) between the first (S1) and second (S2) singlet excited states of formamide is investigated at the state-averaged complete active space self-consistent field (SA-CASSCF) and extended multistate complete active space second-order perturbation theory (XMS-CASPT2) levels of theory. In addition, the asymmetrical MECI between the ground state (S0) and S1 of cyclopropanone is evaluated using SA-CASSCF, as well as (ME)CIs between the S1 and S2 states of benzene using SA-CASSCF and time-dependent density functional theory (TDDFT). Finally, a CI between the S1 and S2 excited states of thiophene was analyzed using TDDFT.

Study of electronic structure and optical transition properties of low-lying excited states of AuB molecules based on configuration interaction method

High-level configuration interaction method including the spin-orbit coupling is used to investigate the low-lying excited electronic states of AuB that is not reported experimentally. The electronic structure in our work is preformed through the three steps stated below. First of all, Hartree-Fock method is performed to compute the singlet-configuration wavefunction as the initial guess. Next, we generate a multi-reference wavefunction by using the state-averaged complete active space self-consistent field (SACASSCF). Finally, the wavefunctions from CASSCF are utilized as reference, the exact energy point values are calculated by the explicitly correlated dynamic multi-reference configuration interaction method (MRCI). The Davidson correction (+Q) is put forward to solve the size-consistence problem caused by the MRCI method. To ensure the accuracy, the spin-orbit effect and correlation for inner shell electrons and valence shell electrons are considered in our calculation. The potential energy curves of 12 Λ-S electronic states are obtained. According to the explicit potential energy curves, we calculate the spectroscopic constants through solving radial Schrödinger equation numerically. We analyze the influence of electronic state configuration on the dipole moment by using the variation of dipole moment with nuclear distance. The spin-orbit matrix elements for parts of low-lying exciting states are computed, and the relation between spin-orbit coupling and predissociation is discussed. The predissociation is analyzed by using the obtained spin-orbit matrix elements of the 4 Λ-S states which spilt into 12 Ω states. It indicates that due to the absence of the intersections between the curves of spin-orbit matrix elements related with the 4 low-lying Λ-S states, the predissociation for these low-lying exciting states will not occur. Finally, the properties of optical transition between the ground Ω state <inline-formula><tex-math id="M3">\begin{document}$ {\rm A}^{1}{{{\Pi}}}_{1} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231347_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231347_M3.png"/></alternatives></inline-formula> and first excited Ω state <inline-formula><tex-math id="M4">\begin{document}$ {{\mathrm{X}}}^{1}{{{\Sigma }}}_{{0}^{+}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231347_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231347_M4.png"/></alternatives></inline-formula> are discussed in laser-cooling filed by analyzing the Franck-Condon factors and radiative lifetime. And the transition dipole moment is also calculated. But our results reveal that the AuB is not an ideal candidate for laser-cooling. In conclusion, this work is helpful in deepening the understanding of AuB, especially the structures of electronic states, interaction between excited states, and optical transition properties. All the data presented in this paper are openly available at <ext-link ext-link-type="uri" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://www.doi.org/10.57760/sciencedb.j00213.00009">https://www.doi.org/10.57760/sciencedb.j00213.00009</ext-link>.

Quantification of the Ionic Character of Multiconfigurational Wave Functions: The Qat Diagnostic.

The complete active space self-consistent field (CASSCF) method is a cornerstone in modern excited-state quantum chemistry providing the starting point for most common multireference computations. However, CASSCF, when used with a minimal active space, can produce significant errors (>2 eV) even for the excitation energies of simple hydrocarbons if the states of interest possess ionic character. After illustrating this problem in some detail, we present a diagnostic for ionic character, denoted as Q at, that is readily computed from the transition density. A set of 11 molecules is considered to study errors in vertical excitation energies. State-averaged CASSCF obtains a mean absolute error (MAE) of 0.87 eV for the 34 singlet states considered. We highlight a strong correlation between the obtained errors and the Q at diagnostic, illustrating its power to predict problematic cases. Conversely, using multireference configuration interaction with single and double excitations and Pople's size extensivity correction (MR-CISD+P), excellent results are obtained with an MAE of 0.11 eV. Furthermore, correlations with the Q at diagnostic disappear. In summary, we hope that the presented diagnostic will facilitate reliable and user-friendly multireference computations on conjugated organic molecules.

Chemical Bonding in Isoelectronic NdO2and SmO22+

Neodymium dioxide (NdO2) and samarium dioxide cation (SmO22+) are isoelectronic molecules. Here we used calculations of the spin-orbit-free wave functions to study and compare their geometries, spin states, and bonding. We used Kohn-Sham density functional theory with the B97-1 exchange-correlation functional to optimize the geometries and found that the two molecules have different ground spin states and structures. NdO2 favors a linear ONdO triplet structure, and SmO22+ favors a linear SmOO2+ quintet structure. We then used state-averaged complete-active-space self-consistent-field (SA-CASSCF) calculations to investigate the bonding characteristics of NdO2 and SmO22+ in various geometries. We found that in NdOO, one electron is transferred from Nd to O, while in SmO22+, there is no electron transfer between Sm and O. The SA-CASSCF calculation also shows that ONdO has a stronger bonding orbital between a 4f orbital of Nd and a pz orbital of oxygen atoms. We compared three multireference methods, namely, extended multistate complete active space second-order perturbation theory (XMS-CASPT2), extended multistate pair-density functional theory (XMS-PDFT), and compressed multistate pair-density functional theory (CMS-PDFT), for calculating the spin-orbit-free energies of various isomers of both molecules. We found that although XMS-PDFT and CMS-PDFT are at the same cost level as SA-CASSCF, they give results with the same accuracy as given for the much more demanding XMS-CASPT2 calculation. Between the two multistate PDFT methods, CMS-PDFT is better at giving good degeneracies for states that should be degenerate.

State averaged CASSCF in AMOEBA polarizable water model for simulating nonadiabatic molecular dynamics with nonequilibrium solvation effects.

This paper presents a state-averaged complete active space self-consistent field (SA-CASSCF) in the atomic multipole optimized energetics for biomolecular application (AMOEBA) polarizable water model, which enables rigorous simulation of non-adiabatic molecular dynamics with nonequilibrium solvation effects. The molecular orbital and configuration interaction coefficients of the solute wavefunction, and the induced dipoles on solvent atoms, are solved by minimizing the state averaged energy variationally. In particular, by formulating AMOEBA water models and the polarizable continuum model (PCM) in a unified way, the algorithms developed for computing SA-CASSCF/PCM energies, analytical gradients, and non-adiabatic couplings in our previous work can be generalized to SA-CASSCF/AMOEBA by properly substituting a specific list of variables. Implementation of this method will be discussed with the emphasis on how the calculations of different terms are partitioned between the quantum chemistry and molecular mechanics codes. We will present and discuss results that demonstrate the accuracy and performance of the implementation. Next, we will discuss results that compare three solvent models that work with SA-CASSCF, i.e., PCM, fixed-charge force fields, and the newly implemented AMOEBA. Finally, the new SA-CASSCF/AMOEBA method has been interfaced with the ab initio multiple spawning method to carry out non-adiabatic molecular dynamics simulations. This method is demonstrated by simulating the photodynamics of the model retinal protonated Schiff base molecule in water.

Large-Scale Benchmarking of Multireference Vertical-Excitation Calculations via Automated Active-Space Selection.

We have calculated state-averaged complete-active-space self-consistent-field (SA-CASSCF), multiconfiguration pair-density functional theory (MC-PDFT), hybrid MC-PDFT (HMC-PDFT), and n-electron valence state second-order perturbation theory (NEVPT2) excitation energies with the approximate pair coefficient (APC) automated active-space selection scheme for the QUESTDB benchmark database of 542 vertical excitation energies. We eliminated poor active spaces (20–40% of calculations) by applying a threshold to the SA-CASSCF absolute error. With the remaining calculations, we find that NEVPT2 performance is significantly impacted by the size of the basis set the wave functions are converged in, regardless of the quality of their description, which is a problem absent in MC-PDFT. Additionally, we find that HMC-PDFT is a significant improvement over MC-PDFT with the translated PBE (tPBE) density functional and that it performs about as well as NEVPT2 and second-order coupled cluster on a set of 373 excitations in the QUESTDB database. We optimized the percentage of SA-CASSCF energy to include in HMC-PDFT when using the tPBE on-top functional, and we find the 25% value used in tPBE0 to be optimal. This work is by far the largest benchmarking of MC-PDFT and HMC-PDFT to date, and the data produced in this work are useful as a validation of HMC-PDFT and of the APC active-space selection scheme. We have made all the wave functions produced in this work (orbitals and CI vectors) available to the public and encourage the community to utilize this data as a tool in the development of further multireference model chemistries.

A trust-region augmented Hessian implementation for state-specific and state-averaged CASSCF wave functions.

In this work, we present a one-step second-order converger for state-specific (SS) and state-averaged (SA) complete active space self-consistent field (CASSCF) wave functions. Robust convergence is achieved through step restrictions using a trust-region augmented Hessian (TRAH) algorithm. To avoid numerical instabilities, an exponential parameterization of variational configuration parameters is employed, which works with a nonredundant orthogonal complement basis. This is a common approach for SS-CASSCF and is extended to SA-CASSCF wave functions in this work. Our implementation is integral direct and based on intermediates that are formulated in either the sparse atomic-orbital or small active molecular-orbital basis. Thus, it benefits from a combination with efficient integral decomposition techniques, such as the resolution-of-the-identity or the chain-of-spheres for exchange approximations. This facilitates calculations on large molecules, such as a Ni(II) complex with 231 atoms and 5154 basis functions. The runtime performance of TRAH-CASSCF is competitive with the other state-of-the-art implementations of approximate and full second-order algorithms. In comparison with a sophisticated first-order converger, TRAH-CASSCF calculations usually take more iterations to reach convergence and, thus, have longer runtimes. However, TRAH-CASSCF calculations still converge reliably to a true minimum even if the first-order algorithm fails.

Prediction of the excited-state reaction channels in photo-induced processes of nitrofurantoin using first-principle calculations and dynamics simulations

The understanding of the photochemistry of antibiotic compounds is important because it gives the direct information on the possible environmental pollution caused by them. Due to their large size, the theoretical studies of their excited-state reactions are rather challenging. In current work, we combined the on-the-fly trajectory surface-hopping dynamics, conical-intersection optimizations and excited-state pathway calculations to study the photochemistry of the trans-isomer of nitrofurantoin, a widely-used drug to treat the urinary tract infections. The dynamics-then-pathway approach was taken. First the trajectory surface hopping dynamics at the state-averaged complete-active-space self-consistent-field (SA-CASSCF) level with small active space and small basis sets were run. Second, the minimum-energy conical-intersection optimizations were performed. Finally the excited pathways from the Frank-Condon region to different reaction channels were built at the multi-state multi-reference second-order perturbation (MS-CASPT2) level with large active space and large basis set. Several possible channels responsible for the photo-induced reaction mechanism of the trans-nitrofurantoin were obtained, including the cleavage of the NO bond of the NO2 moiety, the photoisomerization at the central CN bond, and other internal conversion channels. Our findings give some preliminary explanations on available experimental observations. It is also demonstrates that the current theoretical approach is a powerful tool to explore the excited-state reactions in the photochemistry of media-sized or large-sized drug compounds.

Putting Photomechanical Switches to Work: An Ab Initio Multiple Spawning Study of Donor–Acceptor Stenhouse Adducts

Photomechanical switches are light sensitive molecules capable of transducing the energy of a photon into mechanical work via photodynamics. In this Letter, we present the first atomistic investigation of the photodynamics of a novel class of photochromes called donor-acceptor Stenhouse adducts (DASA) using state-of-the-art ab initio multiple spawning interfaced with state-averaged complete active-space self-consistent field theory. Understanding the Z/E photoisomerization mechanism in DASAs at the molecular level is crucial in designing new derivatives with improved photoswitching capabilities. Our dynamics simulations show that the actinic step consists of competing nonradiative relaxation pathways that collectively contribute to DASAs' low (21% in toluene) photoisomerization quantum yield. Furthermore, we highlight the important role the intramolecular hydrogen bond plays in the selectivity of photoisomerization in DASAs, identifying it as a possible structural element to tune DASA properties. Our fully ab initio simulations reveal the key degrees of freedom involved in the actinic step, paving the way for the rational design of new generations of DASAs with improved quantum yield and efficiency.

Analytic gradients for state-averaged multiconfiguration pair-density functional theory.

Analytic gradients are important for efficient calculations of stationary points on potential energy surfaces, for interpreting spectroscopic observations, and for efficient direct dynamics simulations. For excited electronic states, as are involved in UV-Vis spectroscopy and photochemistry, analytic gradients are readily available and often affordable for calculations using a state-averaged complete active space self-consistent-field (SA-CASSCF) wave function. However, in most cases, a post-SA-CASSCF step is necessary for quantitative accuracy, and such calculations are often too expensive if carried out by perturbation theory or configuration interaction. In this work, we present the analytic gradients for multiconfiguration pair-density functional theory based on SA-CASSCF wave functions, which is a more affordable alternative. A test set of molecules has been studied with this method, and the stationary geometries and energetics are compared to values in the literature as obtained by other methods. Excited-state geometries computed with state-averaged pair-density functional theory have similar accuracy to those from complete active space perturbation theory at the second-order.

The relativistic all-electron ab initio calculations on the multiplet electronic structure of U3+ ion

The relativistic all-electron ab initio calculations have been performed on 5f3 manifold of free U3+ ion to explore the electronic structure and spectra. The spin-orbit-free low lying electronic states have been calculated at the level of theories of State-Averaged Complete Active Space Self-Consistent Field (SA-CASSCF) and Multi-State Complete Active Space Second-Order Perturbation (MS-CASPT2) using different sets of active orbitals. The corresponding spin-orbit states and the energy levels have been computed using Douglas-Kroll type of atomic mean-field integral (AMFI) approach. The ground state is 4I9/2 and the electron correlation has been found to be small in case of the excited 4I states. The low-lying energy levels obtained with the core-valence correlation effects in the treatment are in very good agreement with the experimental values.

Remote Functionalization through Symmetric or Asymmetric Substitutions Control the Pathway of Intermolecular Singlet Fission.

Singlet fission (SF) produces two coupled triplet excitons from a high energy singlet excitation. The mechanism of SF in a variety of phenyl (-Ph) substituted pentacene is systematically studied through both ab initio and density functional theory calculations. Two classes of substitution to pentacene are considered, namely, symmetric configuration with four Ph groups (TPP) and an asymmetric configuration with two Ph groups (DPP). The positions of the singlet and triplet states are determined by calibrating the active space through state averaged complete active space self-consistent field (SA-CASSCF) calculations. The SF rates are computed based on restricted active space with single and double spin flip wave functions (RAS-SF and RAS-2SF), which are analyzed based on different intermolecular π-stacking patterns of TPP and DPP. The contribution of charge transfer (CT) state near the multiexciton (ME) state plays a significant role for SF efficiency. The role of excimer formation is supportive for ME generation [J. Am. Chem. Soc. 2016, 138, 617], and hence it is critically studied. The ME generation in TPP is a slower process and occurs through an excimer-mediated path with a large coupling between the first singlet excited state and ME state. On the other hand, DPP exhibits a relatively faster SF rate through the formation of a ME state via low-lying CT state, especially the slip-stacked dimers. The present computation elegantly demonstrates the crucial role of functional group substitution in the structure of SF active molecules in determining the efficiency of fission dynamics.

Benchmarks for Electronically Excited States with CASSCF Methods.

The accuracy of three different complete active space (CAS) self-consistent field (CASSCF) methods is investigated for the electronically excited-state benchmark set of SchreiberM.; et al. J. Chem. Phys.2008, 128, 13411018397056. Comparison of the CASSCF linear response (LR) methods MC-RPA and MC-TDA and the state-averaged (SA) CASSCF method is made for 122 singlet excitation energies and 69 oscillator strengths. Of all CASSCF methods, when considering the complete test set, MC-RPA performs best for both excitation energies and oscillator strengths with a mean absolute error (MAE) of 0.74 eV and 51%, respectively. MC-TDA and SA-CASSCF show a similar accuracy for the excitation energies with a MAE of ∼1 eV with respect to more accurate coupled cluster (CC3) excitation energies. The opposite trend is observed for the subset of n → π* excitation energies for which SA-CASSCF exhibits the least deviations (MAE 0.65 eV). By looking at s-tetrazine in more detail, we conclude that better performance for the n → π* SA-CASSCF excitation energies can be attributed to a fortunate error compensation. For oscillator strengths, SA-CASSCF performs worst for the complete test set (MAE 100%) as well as for the subsets of n → π* (MAE 192%) and π → π* excitations (MAE 84.9%). In general, CASSCF gives the worst performance for excitation energies of all excited-state ab initio methods considered so far due to lacking the major part of dynamic electron correlation, though MC-RPA and TD-DFT (BP86) show similar performance. Among all LR-type methods, LR-CASSCF oscillator strengths are the ones with the least accuracy for the same reason. As state-specific orbital relaxation effects are accounted for in LR-CASSCF, oscillator strengths are significantly more accurate than those of MS-CASPT2. Our findings should encourage further developments of response theory-based multireference methods with higher accuracy and feasibility.

CASSCF linear response calculations for large open-shell molecules

The complete active space self-consistent-field (CASSCF) linear response method for the simulation of ultraviolet-visible (UV/Vis) absorption and electronic circular dichroism (ECD) spectra of large open-shell molecules is presented. By using a one-index transformed Hamiltonian, the computation of the most time-consuming intermediates can be pursued in an integral-direct fashion, which allows us to employ the efficient resolution-of-the-identity and overlap-fitted chain-of-spheres approximation. For the iterative diagonalization, pairs of Hermitian and anti-Hermitian trial vectors are used which facilitate, on the one hand, an efficient solution of the pair-structured generalized eigenvalue problem in the reduced space, and on the other hand, make the full multiconfigurational random phase approximation as efficient as the corresponding Tamm-Dancoff approximation. Electronic transitions are analyzed and characterized in the particle-hole picture by natural transition orbitals that are introduced for CASSCF linear response theory. For a small organic radical, we can show that the accuracy of simulated UV/Vis absorption spectra with the CASSCF linear response approach is significantly improved compared to the popular state-averaged CASSCF method. To demonstrate the efficiency of the implementation, the 50 lowest roots of a large Ni triazole complex with 231 atoms are computed for the simulated UV/Vis and ECD spectra.

Ab initio surface hopping molecular dynamics on the dissociative recombination of CH3+

Ab initio molecular dynamics (AIMD) simulations were carried out to investigate dynamics in the dissociative recombination of CH3+ at the state-averaged complete active space self-consistent field (SA-CASSCF) level. Nonadiabatic transitions between adiabatic electronic states were taken into account by the Tully's fewest switches algorithm. The direct process was examined by trajectories starting from the crossing points of the potential energy surfaces of the CH3+ ground state and CH3 dissociative state, while the indirect process was investigated by trajectories starting from the approximate crossing points of the CH3 Rydberg state and dissociative states. It is shown that, in the direct process, the dominant products, CH2 + H, are generated in 96% of trajectories, while in the indirect process, the ratio of the other products, CH + 2H, CH + H2, C + H2 + H, increases extensively due to the intramolecular energy redistribution while descending through multiple potential energy surfaces, which is more consistent with the experimental observation.

On the accuracy of retinal protonated Schiff base models

ABSTRACTWe investigate the molecular geometries of the ground state and the minimal energy conical intersections between the ground and first excited states of the models for the retinal protonated Schiff base in the gas phase using the extended multistate complete active space second-order perturbation theory (XMS-CASPT2). The biggest model in this work is the rhodopsin chromophore truncated between the ε and δ carbon atoms, which consists of 54 atoms and 12-orbital π conjugation. The results are compared with those obtained by the state-averaged complete active space self-consistent field (SA-CASSCF). The XMS-CASPT2 results suggest that the minimum energy conical intersection associated with the so-called 13–14 isomerisation is thermally inaccessible, which is in contrast to the SA-CASSCF results. The differences between the geometries of the conical intersections computed by SA-CASSCF and XMS-CASPT2 are ascribed to the fact that the charge transfer states are more stabilised by dynamical electron correlation than the diradicaloid states. The impact of the various choices of active spaces, basis sets and state-averaging schemes is also examined.

α-CASSCF: An Efficient, Empirical Correction for SA-CASSCF To Closely Approximate MS-CASPT2 Potential Energy Surfaces.

Because of its computational efficiency, the state-averaged complete active-space self-consistent field (SA-CASSCF) method is commonly employed in nonadiabatic ab initio molecular dynamics. However, SA-CASSCF does not effectively recover dynamical correlation. As a result, there can be qualitative differences between SA-CASSCF potential energy surfaces (PESs) and more accurate reference surfaces computed using multistate complete active space second-order perturbation theory (MS-CASPT2). Here we introduce an empirical correction to SA-CASSCF that scales the splitting between individual states and the state-averaged energy. We call this the α-CASSCF method, and we show here that it significantly improves the accuracy of relative energies and PESs compared with MS-CASPT2 for the chromophores of green fluorescent and photoactive yellow proteins. As such, this method may prove to be quite valuable for nonadiabatic dynamics.

Electronic g Tensors in UV Complexes-A Computational Study.

The theory and computation of EPR parameters from first principles has seen a great deal of development over the past two decades. In particular, various techniques for the computation of the electronic g tensor have been implemented in many quantum chemistry packages. These methods have been successfully applied to paramagnetic organic species and transition metal systems. The situation is less well-understood and established in the case of actinide-containing molecules and there is a dearth of experimental data available for validation of computations. In this study quantum chemical techniques have been used to evaluate the g tensor for UV complexes, for which experimental data are available for comparison. The g tensors were calculated using relatively simple, state-averaged complete active space self-consistent field (SA-CASSCF) calculations. This approach is shown to be capable of providing useful accuracy. Aspects of the computations that should be refined to provide a more quantitative approach are discussed. The key features of the underlying electronic structure that influence the computed g values are delineated, providing a simple physical picture of these subtle molecular properties.

Color in Bridge-Substituted Cyanines

Theories of color in cyanine dyes have evolved around the idea of a "resonance" of structures with distinct bonding and charge localization. Understanding the emergence of resonance models from the underlying many-electron problem remains a central issue for these systems. Here, the issue is addressed using a maximum-entropy approach to valence-bond representations of state-averaged complete-active space self-consistent field models. The approach allows calculation of energies and couplings of high-energy valence-bond structures that mediate superexchange couplings and chemical bonding. A series of valence-bond Hamiltonians for a series of bridge-substituted derivatives of Michler's hydrol blue (a monomethine cyanine) is presented. The Hamiltonians are approximated with a simple linear model parametrized by the Brown-Okamoto σp+ parameter of the bridge substituent. A quantitative lower bound on σp+, beyond which a resonant cyanine-like ground state will not exist, is presented. The large effective coupling in two-state resonance models emerges from superexchange associated with either covalent bonding or charge-carrier delocalization, with the former contribution significantly the stronger. The results provide ab initio justification for empirical diabatic-state models of methine optical response. They are of general interest for understanding the optoelectronic response in cyanines.