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DOE OSTI2022

Model predictive control of heating, ventilation, and air conditioning (HVAC) systems: A state-of-the-art review

Due to the fast advancement of communication and information technology, intelligent buildings have garnered great interest. These buildings can forecast weather, ambient temperature, and sun irradiation and can modify heating, ventilation, and air conditioning (HVAC) operations appropriately, based on current and previous data. This change is intended to reduce HVAC system energy usage while maintaining an appropriate degree of thermal comfort and indoor air quality. Since its inception, model predictive control (MPC) has been one of the prospective solutions for HVAC management systems to reduce both costs and energy usage. Additionally, MPC is becoming increasingly practical as the processing capacity of building automation systems increases and a large quantity of monitored building data becomes available. MPC also provides the potential to improve the energy efficiency of HVAC systems via its capacity to consider limitations, to predict disruptions, and to factor in multiple competing goals such as interior thermal comfort and building energy consumption. Although substantial research has been conducted on MPC in building HVAC systems, there is a shortage of critical reviews and a lack of a comprehensive framework that formulates and defines the applications. Here, this article provides a comprehensive state-of-the-art overview of MPC in HVAC systems. Detailed discussions of modeling approaches and optimization algorithms are included. Numerous design aspects such as prediction horizon, occupancy behavior, building type, and cost function, that impact MPC performance are discussed in detail. The technical characteristics, advantages, and disadvantages of various types of modeling software are discussed. The primary objective of this work is to highlight critical design characteristics for the MPC control scheme and to give improved suggestions for future research. Moreover, numerous prospective scenarios have been suggested that might provide future research direction.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2020

Least-Cost Pathways for India's Electric Power Sector

The Government of India has a target of deploying 175 GW from renewable energy by 2022 and 40% of electricity capacity from renewable energy by 2030 and has indicated that ambitions for 2030 could be higher. Rapid changes in technology costs and performance could drive further deployment of wind and solar capacity beyond these policy targets. Increased deployment of variable renewable energy (VRE) raises new questions for power system planning regarding the optimal siting of generation capacity, trade-offs between generation and transmission infrastructure, and system flexibility needs. This study aims to evaluate least-cost pathways for India's electric power system over the period 2017-2047. Uniquely, this work considers an expanded planning horizon and range of scenarios not previously analyzed in national planning studies in India. The data collection and model design processes undertaken for this study provides a framework for recurring planning studies. This study finds anticipated changes in electricity demand and component costs can drive a significant shift in India's future electricity supply and how this system will be operated. In the Base scenario, the share of generation from VRE reaches 54% by 2047. Reducing the capital cost of wind has a larger impact on VRE penetration than reducing the capital cost of solar PV or battery storage. In the lowest wind cost scenario (40% capital cost decline by 2047 relative to the Base scenario), the penetration of VRE in the generation mix reaches 722%, exceeding the penetration levels achieved when the cost of battery storage or solar PV are reduced by an even greater 50%. In a future system with high penetrations of RE, capacity additions are driven by the coincidence of demand and RE generation rather than peak demand alone. This study finds the system could have surplus capacity during the peak demand months of July–September because this period corresponds to periods with high wind speeds and more wind generation available to meet peak demand. By contrast, new capacity is needed to meet demand during moderate demand months of October–November when output from wind plants falls more than 75% nationally compared to the previous two months. Finally, the success for gas for electricity production may depend on cost competitiveness rather than fuel availability. Increasing the amount of gas available for electricity production had no significant impact on the capacity or generation mix by 2047, as determined from a scenario that significantly increases fuel availability throughout the planning horizon. In fact, over 80% of new gas fuel available for the power sector remains unused. This suggests the high cost of gas plant operations relative to other technologies may constrain the expansion of gas generation in India more than fuel availability.

14 SOLAR ENERGY↗

DOE OSTI2025

Decision-Dependent Uncertainty-Aware Distribution System Planning Under Wildfire Risk

The interaction between power systems and wildfires can be dangerous and costly. Distribution grids can be liable for the outbreak of wildfires during extreme weather. In wildfire-prone areas, investment planning should consider the impact of operational actions on wildfire-related uncertainties affecting line failure likelihood. Here, in this case, endogenous-based uncertainty modeling should comprise the backbone of the investment planning model viz-a-viz the inability of standard exogenous-based uncertainty modeling. Therefore, we propose a decision-dependent uncertainty (DDU) aware methodology to optimize investment portfolios for distribution systems, considering that high power-flow levels in high-threat areas can ignite wildfires and increase line failure probability. The methodology identifies the best combination of upgrades (new lines, hardening existing lines, and placing switching devices). Methodologically, we propose a two-stage distributionally robust planning optimization problem with DDU that considers the distribution system's multiperiod operation. The first stage determines optimal switching actions and line investments, and the second stage evaluates the worst-case expected operational cost under a DDU framework designed to account for the endogenous impact of power-flow levels and hardening investment decisions in the line failure probabilities. An iterative method is tailored to handle the problem and numerical experiments demonstrate a more prepared grid to deal with wildfire risk.

Power systems investment planning↗

DOE OSTI2020

A low temperature unitized regenerative fuel cell realizing 60% round trip efficiency and 10 000 cycles of durability for energy storage applications

Unitized regenerative fuel cells (URFC) convert electrical energy to and from chemical bonds in hydrogen. URFCs have the potential to provide economical means for efficient long-term, seasonal, energy storage and on-demand conversion back to electrical energy. We first optimize the catalyst layer for discrete electrolyzer and fuel cell and then configure the URFC. The goal is to identify a cost competitive configuration for URFCs, and demonstrate it in terms of upper limit of round trip efficiencies (RTEs). Two possible configurations of URFCs are compared via experiments and techno-economic analysis (TEA), which emphasize the advantages of the unconventional constant-electrode (CE) URFC over the traditional constant-gas (CG) configuration. We also study the stability via accelerated stress tests (ASTs) and demonstrate steady state operation in a daily cycle for day to night energy shifting. From the investigations, the optimum composition of the URFC anode catalyst layer is 90 at% Ir-black balanced by Pt-black for both CE and CG configurations. At 80 °C and 1 A cm -2 , the optimized CE URFC achieves 57% and 60% RTE with air and O 2 as the reductant gases, respectively. We then evaluated the differences in durability using an AST over 10k charge–discharge cycles; the results reveal that the wider potential window at the anode in CE (0.05–1.55 V) has minimal effect on catalyst layer stability compared to CG (0.55–1.55 V). Furthermore, there was no degradation up to the range of 2k–5k cycles; beyond that the fuel cell (discharge) performance degraded while the electrolyzer (charge) performance was still stable. Finally, the observations here indicate substantial potential to employ URFCs as efficient and cost-effective bidirectional energy-conversion devices within energy storage and utilization systems after appropriate technological and operational optimizations.

25 ENERGY STORAGE↗

DOE OSTI2022

Next-Cycle Optimal Dilute Combustion Control via Online Learning of Cycle-to-Cycle Variability Using Kernel Density Estimators

Dilute combustion using exhaust gas recirculation (EGR) presents a cost-effective method for increasing the efficiency of spark-ignition (SI) engines. However, the maximum amount of EGR that can be used at a given condition is limited by a rapid increment of cycle-to-cycle variability (CCV). This study describes a methodology to design a model-based stochastic optimal controller to adjust the cycle-to-cycle fuel injection quantity in order to reduce CCV and further extend the dilute limit. Given the complexity and chaotic nature of combustion events, the controller was enhanced with online learning in order to identify the statistical properties of combustion efficiency, which are needed to generate predictions for next-cycle events. This study showed that a kernel density estimator (KDE) can be used to learn the combustion properties in real time and can be incorporated into the feedback policy in order to calculate the optimal control command. Experimental results suggested that the dilute limit can be extended from 18.5% to 21% EGR fraction at an operating condition relevant for highway cruising. Additionally, the proposed controller can achieve a large CCV reduction with less fuel enrichment compared to previous methods, overall contributing to an increase in 0.2% indicated fuel conversion efficiency.

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2025

Carbonation reaction of recycled concrete aggregates (RCA): CO 2 mass consumption under various treatment conditions

Concrete is a key building material around the world due to its excellent strength and durability. Recycling demolished concrete for new construction materials may play a significant role in sustainable development. Producing recycled concrete aggregates (RCA) from waste concrete is one approach for such an initiative. However, using RCA may pose challenges, such as reduced density, lower elastic modulus and strength, and increased water absorption. Recently, the carbonation of RCA has emerged as a method to address those concerns. This study explores the carbon sequestration capacity of RCA through carbonation, examining various parametric conditions, including initial CO 2 pressure, relative humidity, temperature, and pre-treatment approach. Both lab-scale and large-scale carbonation tests were conducted. Additionally, a cost analysis and CO 2 footprint assessment were performed. The findings showed that applying higher initial CO 2 pressures (e.g., 40–60 psi) and optimal relative humidity (~55 %) could significantly enhance the carbonation efficiency of RCA. Elevating temperature also led to accelerated CO 2 consumption, being more effective on the lab scale. The economic analysis presented potential cost benefits when substituting natural aggregates with CO 2 -treated RCA. All in all, these results suggest that the carbonation of RCA may provide significant environmental benefits through carbon sequestration, promoting sustainable construction practices.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Optimization of catalyst-coated membranes for enhancing performance in proton exchange membrane electrolyzer cells

To achieve large-scale application of proton exchange membrane electrolyzer cells (PEMECs) for hydrogen production, it is highly desirable to reduce the manufacturing cost while enhancing cell performance. In the PEMPECs, a catalyst-coated membrane (CCM) is the vital component where electrochemical reactions and mass transport mainly occur. The fabrication methods and catalyst layer (CL) structure can significantly affect the cell performance. Herein, for the first time, a comparative study of CCM fabrications with decal transfer and direct spray deposition methods have been conducted by both ex-situ materials characterization and in-situ performance testing in PEMECs. It is found CCMs that are fabricated with a direct spray deposition method display enhanced cell performance compared to CCMs fabricated with a decal transfer method, mainly due to the largely reduced ohmic resistance and improved mass transport. More importantly, cell performance can be greatly enhanced by simply regulating the Nafion ionomer content at the anode CL. The optimal Nafion ionomer content of 10 wt% gives the best cell performance at 80 °C with a low cell voltage of 1.887 V at 2 A cm -2 , outperforming the commercial CCM and most other previous publications. Our study provides a valuable guidance for fabrication and optimization of CCMs with significantly enhanced performance and reduced cost for practical application of the PEMECs.

08 HYDROGEN↗

DOE OSTI2023

Capturing Travel Mode Adoption in Designing On-Demand Multimodal Transit Systems

This paper studies how to integrate rider mode preferences into the design of on-demand multimodal transit systems (ODMTSs). It is motivated by a common worry in transit agencies that an ODMTS may be poorly designed if the latent demand, that is, new riders adopting the system, is not captured. This paper proposes a bilevel optimization model to address this challenge, in which the leader problem determines the ODMTS design, and the follower problems identify the most cost efficient and convenient route for riders under the chosen design. The leader model contains a choice model for every potential rider that determines whether the rider adopts the ODMTS given her proposed route. To solve the bilevel optimization model, the paper proposes an exact decomposition method that includes Benders optimal cuts and no-good cuts to ensure the consistency of the rider choices in the leader and follower problems. Moreover, to improve computational efficiency, the paper proposes upper and lower bounds on trip durations for the follower problems, valid inequalities that strengthen the no-good cuts, and approaches to reduce the problem size with problem-specific preprocessing techniques. The proposed method is validated using an extensive computational study on a real data set from the Ann Arbor Area Transportation Authority, the transit agency for the broader Ann Arbor and Ypsilanti region in Michigan. The study considers the impact of a number of factors, including the price of on-demand shuttles, the number of hubs, and access to transit systems criteria. The designed ODMTSs feature high adoption rates and significantly shorter trip durations compared with the existing transit system and highlight the benefits of ensuring access for low-income riders. Finally, the computational study demonstrates the efficiency of the decomposition method for the case study and the benefits of computational enhancements that improve the baseline method by several orders of magnitude. Funding: This research was partly supported by National Science Foundation [Leap HI Proposal NSF-1854684] and the Department of Energy [Research Award 7F-30154].

Operations Research & Management Science↗

DOE OSTI2022

Optimization-based modeling and economic comparison of membrane distillation configurations for application in shale gas produced water treatment

Membrane distillation (MD) is an emerging membrane technology with great potential for treatment of hypersaline wastewater generated by unconventional (shale) oil and gas reservoirs. However, the low energy efficiency of this technology makes the operating cost of MD systems relatively high, especially in the absence of waste heat. There are several MD configurations with inherent advantages and disadvantages and varying performance. As such, there is a need for thermo-economic optimization of MD systems in a systematic manner to assess their economic performance. Here we present an optimization framework to model and compare the performance of six MD configurations (DCMD, AGMD, PGMD, CGMD, SGMD, and VMD) in continuous recirculation mode for treatment of hypersaline wastewater. The optimization results show that AGMD with small gap size operated at low stream Reynolds number outperforms all other configurations with treatment cost of 4.57 US $/m 3 of feed. However, restricting the system design to more practically relevant operating conditions, such as higher Reynolds number and larger gap size, diminishes the cost superiority of AGMD over other configurations. We also observed that treatment cost using PGMD configuration approaches those of CGMD and DCMD, particularly when modules with small gaps are used.

42 ENGINEERING↗

DOE OSTI2023

Disjunctive optimization model and algorithm for long-term capacity expansion planning of reliable power generation systems

This paper proposes a new optimization model and algorithm for long-term capacity expansion planning of reliable power generation systems. The model optimizes both investment decisions (e.g., size, location, and time to install, retire and decommission facilities) and operation decisions (e.g., on/off status, operating capacity, and expected power output). It is also able to optimize reserve systems (or backup systems), as well as the main systems, to improve power systems reliability. An impact of operational strategies of generators (i.e., participating in electricity production vs. remaining as idle units during operation) on power systems reliability is considered. Probability of equipment failures and capacity failure states are used to rigorously estimate the power systems reliability depending on design and operation strategies. The optimization model is formulated with Generalized Disjunctive Programming (GDP), which is reformulated as a mixed-integer linear programming (MILP) model using the Hull relaxation. Two reliability-related penalties, such as downtime penalty and unmet demand penalty, are included in the objective function to maximize reliability while minimizing the total net present cost. Furthermore, a bilevel decomposition with tailored cuts is developed to reduce computational times of the multi-scale optimization model. The effectiveness of the proposed model is shown by comparing the results with the results obtained from the expansion planning models that do not explicitly consider reliability. In conclusion, we also show that the proposed bilevel decomposition is computationally efficient for solving large scale problems through 5-years and 10-years planning case studies.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2021

Evaluation and Applications of Multi-Instrument Boundary-Layer Thermodynamic Retrievals

Recent reports have highlighted the need for improved observations of the atmosphere boundary layer. In this study, we explore the combination of ground-based active and passive remote sensors deployed for thermodynamic profiling to analyze various boundary-layer observation strategies. Optimal-estimation retrievals of thermodynamic profiles from Atmospheric Emitted Radiance Interferometer (AERI) observed spectral radiance are compared with and without the addition of active sensor observations from a May–June 2017 observation period at the Atmospheric Radiation Measurement Southern Great Plains site. In all, three separate thermodynamic retrievals are considered here: retrievals including AERI data only, retrievals including AERI data and Vaisala water vapour differential-absorption lidar data, and retrievals including AERI data and Raman lidar data. First, the three retrievals are compared to each other and to reference radiosonde data over the full observation period to obtain a bulk understanding of their differences and characterize the impact of clouds on these retrieved profiles. These analyses show that the most significant differences are in the water vapour field, where the active sensors are better able to represent the moisture gradient in the entrainment zone near the boundary-layer top. Furthermore, we also explore how differences in retrievals may affect results of applied analyses including land–atmosphere coupling, convection indices, and severe storm environmental characterization. Overall, adding active sensors to the optimal-estimation retrieval shows some added information, particularly in the moisture field. Given the costs of such platforms, the value of that added information must be weighed for the application at hand.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Efficient sensitivity analysis of the thermal profile in powder bed fusion of metals using hypercomplex automatic differentiation finite element method

Rapid cyclic temperature fluctuation occurring in powder bed fusion of metals using a laser beam (PBF-LB/M) influences the formation of flaws in printed parts. Consequently, there is a pressing need to enhance the quality of printed parts by developing innovative methodologies that can predict thermal histories and help uncover the intricate relationships between process parameters and thermal profiles. Sensitivity Analysis (SA) emerges as an essential tool for this, offering the potential for process optimization and enhanced quality control. Nonetheless, conventional SA methodologies often incur in excessive computational costs and potential numerical approximation errors. Here, to address this technical challenge, we present a novel method for SA that integrates the HYPercomplex-based Automatic Differentiation (HYPAD) technique with transient thermal simulations conducted via the finite element method (FEM). Leveraging this methodology, we efficiently and accurately perform SA for PBF-LB/M processes in a post-processing step. Compared to traditional methods like Finite Differences (FD), HYPAD-FEM required 96 % less computational time for obtaining sensitivities for 22 process parameters, under a comparative study conducted within the context of the 2018–02 AM benchmark of the National Institute of Standards and Technology. In summary, HYPAD-FEM offers superior efficiency and accuracy in SA over conventional methods, delivering the best sensitivity of a model without the need for step-size selection and problem or parameter-based implementations.

36 MATERIALS SCIENCE↗

DOE OSTI2025

A staged deep learning approach to spatial refinement in 3D temporal atmospheric transport

High-resolution spatiotemporal simulations effectively capture the complexities of atmospheric plume dispersion in complex terrain. However, their high computational cost makes them impractical for applications requiring rapid responses or iterative processes, such as optimization, uncertainty quantification, or inverse modeling. To address this challenge, this work introduces the Dual-Stage Temporal Three-dimensional UNet Super-resolution (DST3D-UNet-SR) model, a highly efficient deep learning model for plume dispersion predictions. DST3D-UNet-SR is composed of two sequential modules: the temporal module (TM), which predicts the transient evolution of a plume in complex terrain from low-resolution temporal data, and the spatial refinement module (SRM), which subsequently enhances the spatial resolution of the TM predictions. We train DST3D-UNet-SR using a comprehensive dataset derived from high-resolution large eddy simulations (LES) of plume transport. We propose the DST3D-UNet-SR model to significantly accelerate LES of three-dimensional (3D) plume dispersion by three orders of magnitude. Additionally, the model demonstrates the ability to dynamically adapt to evolving conditions through the incorporation of new observational data, substantially improving prediction accuracy in high-concentration regions near the source.

3D temporal sequences↗

DOE OSTI2023

Stochastic scheduling for commercial building cooling systems: considering uncertainty in zone temperature prediction

Here, this paper presents the first attempt to address the uncertainty in zone temperature prediction with stochastic optimization. The uncertain zone temperature is a process uncertainty and has not been considered in the existing stochastic optimization for building control. To fill this gap, we proposed a novel formulation of stochastic optimization to handle process uncertainty in building control. Specifically, we first examined the accuracy of a typical linear model for predicting zone temperature. We then formulated the scheduling of the building cooling system as a stochastic optimization problem over a 24-hour look-ahead period to minimize the electricity cost of the studied building cooling system. After that, we applied the proposed stochastic load scheduling (SLS) to a direct expansion (DX) cooling system that serves a medium office building. Through simulation with a detailed building energy simulation software, EnergyPlus, we evaluated the operational cost and the thermal comfort compared with a deterministic load scheduling. The operation cost of scheduling was found to vary with the level of zone temperature prediction uncertainty. The proposed SLS can mitigate the impacts of uncertain zone temperature predictions on both operational cost and thermal comfort. The evaluation results indicate that the proposed SLS works better when the uncertainty level is more significant.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2022

Numerical modeling of ion transport and adsorption in porous media: A pore-scale study for capacitive deionization desalination

In this report a pore-scale model is presented to simulate the dynamic ion transport and adsorption processes in porous electrodes used for capacitive deionization (CDI). The Stokes equation governing water flow is solved using the lattice Boltzmann method and Nernst-Planck equation describing ion transport is solved using the finite volume method. The ion adsorption process is considered at the surface of carbon electrodes. After validation against analytical solutions and published results, the model is used to study the coupled water flow, ion transport and adsorption in both two-dimensional and three-dimensional porous CDI electrodes at the pore scale. The effect of electrode microstructure, electrical potential and flow velocity on the adsorption processes is quantitatively investigated, and the relative importance of various parameters is determined. The presented model can be a powerful numerical tool to quantitatively analyze ion transport and adsorption in porous electrodes, and may provide useful information for the design and optimization of CDI electrodes and operating conditions for desired desalination efficiency, water throughput and cost.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2021

Thermal management of a high temperature sodium sulphur battery stack

The sodium sulfur battery is an advanced secondary battery with high potential for grid-level storage due to their high energy density, low cost of the reactants, and high open-circuit voltage. However, as the operating temperature of the battery is high (about 300 °C), effective thermal management is required to prevent thermal runaway under high current density operation. Here, to develop efficient thermal management strategies, a detailed, thermo-electrochemical, non-isothermal, distributed dynamic model of a sodium-sulfur battery stack is developed. Models of three thermal management strategies are developed and analyzed in this work: active cooling, passive cooling, and hybrid cooling. The active cooling strategy uses air as the cooling medium whereas, the passive cooling strategy uses a phase change material. In the hybrid cooling strategy, both active and passive cooling strategies are used. Due to the high operating temperature of the sodium sulfur batteries, the rejected heat can be utilized effectively and consequently a high variability in the heat rejection rate may not be acceptable. Performance of these strategies is analyzed under high current density operation by evaluating the variability in the cell temperature during charge/discharge cycles, temperature difference between the cells based on their locations, and variability in the heat rejection rate. The phase change-based hybrid thermal management strategy with an embedded controller maintained the temperature variation within ±/- 2.8 °C. Considering the tradeoff between the capital cost for PCM, fan power requirement, and variability in the heat rejection rate, the optimal quantity of the PCM and the maximum air velocity for the maximum current density of 260 mA/cm 2 (0.55 C-rate) were found be 0.74 g/Wh and 3 m/s, respectively.

25 ENERGY STORAGE↗

DOE OSTI2026

Optimization of well design and CO 2 injection strategy for risk reduction in Class VI geological carbon sequestration wells

The safety and durability of Class VI wells are critical for geological carbon sequestration (GCS). However, current GCS operations face unique challenges: unlike traditional Class II wells, Class VI CO 2 injection wells operate at rates up to 100 times higher, dramatically increasing the risk of wellbore leakage and structural compromise due to severe temperature drops and associated mechanical stresses. Despite existing guidelines on material selection, there remains a substantial gap in understanding how rapid CO 2 injection rates, low surface temperatures, and variable reservoir conditions interact to threaten long-term well integrity. This study presents a comprehensive, original workflow integrating advanced analytical and numerical models for both well flow and well integrity analysis. By systematically simulating a wide range of field-relevant scenarios—including variations in injection rate, CO 2 temperature, and reservoir pressure—this work provides the first cross-validated assessment of cooling effects on wellbore. The results reveal that extreme temperature drops, up to 60 °C, can occur under high injection rates, particularly in depleted reservoirs, significantly increasing the risk of cement failure. Building on these insights, the study proposes innovative, practical well design and operational strategies, including ductile cement formulations, pre-stressing techniques, advanced insulation coatings, and proactive management of injection rates. The safety of Class VI well extends beyond simply using CO 2 resistant materials. Cement materials should possess optimal thermo-hydraulic-mechanical-chemical properties for effective performance. This work provides a scientific basis for optimizing Class VI well designs, with direct benefits for minimizing environmental risk, lowering operational costs, and enhancing the long-term reliability of GCS.

25 ENERGY STORAGE↗

DOE OSTI2024

Site Suitability and Air Pollution Impacts of Composting Infrastructure for California’s Organic Waste Diversion Law

The emerging field of polaritonic chemistry explores the behavior of molecules under strong coupling with cavity modes. Despite recent developments in ab initio polaritonic methods for simulating polaritonic chemistry under electronic strong coupling, their capabilities are limited, especially in cases where the molecule also features strong electronic correlation. To bridge this gap, we have developed a novel method for cavity QED calculations utilizing the Density Matrix Renormalization Group (DMRG) algorithm in conjunction with the Pauli–Fierz Hamiltonian. Our approach is applied to investigate the effect of the cavity on the S0–S1 transition of n-oligoacenes, with n ranging from 2 to 5, encompassing 22 fully correlated π orbitals in the largest pentacene molecule. Our findings indicate that the influence of the cavity intensifies with larger acenes. Additionally, we demonstrate that, unlike the full determinantal representation, DMRG efficiently optimizes and eliminates excess photonic degrees of freedom, resulting in an asymptotically constant computational cost as the photonic basis increases.

54 ENVIRONMENTAL SCIENCES↗