Ab initio optical spectroscopy made simple with VIKING

Optical spectroscopy has long been a cornerstone of experimental science, allowing researchers to probe the structure and dynamics of molecules and nanoscale systems through their interaction with light. In recent decades, first-principles computational methods have become indispensable companions to laboratory measurements, particularly when experiments involve complex systems or regimes of strong light-matter coupling. Yet a persistent gap has separated the theoretical power of these methods from their practical accessibility. Setting up the underlying calculations, interfacing multiple programs, and processing the results often demand technical skills far beyond the scientific questions being asked. A team of researchers from Germany and Italy now reports a solution designed to close that gap: a user-friendly online tool that brings ab initio optical spectroscopy directly into the web browser.

The new tool, called the Optical spectroscopy task, is the latest addition to VIKING, a free, browser-based platform for nanoscale modeling developed at Carl von Ossietzky Universität Oldenburg and its partner institutions. VIKING does not perform calculations on its own. Instead, it offers ready-to-use simulation workflows, referred to as tasks, that rely on well-established scientific software running on external high-performance computational facilities. Input and validation of task parameters, along with visualization of results, are handled in the web-browser interface, while everything else—preparation of input files, execution of specialized codes, and display of outputs—is managed automatically by the platform. If an error occurs during execution, VIKING displays a message describing the underlying issue and suggesting how to fix it, sparing users from deciphering raw log files.

At the heart of the new task lies time-dependent density-functional theory, or TDDFT, the theoretical framework that underpins most modern ab initio simulations of optical properties. TDDFT generalizes the widely used density functional theory, which maps an interacting electron system onto a fictitious non-interacting one with the same ground-state density through the Kohn-Sham approach. Central to this mapping is the exchange-correlation potential, a functional of the electron density that accounts for many-body correlation effects and whose exact form is unknown, so it must be approximated. Even simple approximations, such as the adiabatic local-density approximation, prove valuable for studying optical spectra and other time-dependent properties of molecules.

In practice, TDDFT solutions are obtained in two distinct ways, both of which the Optical spectroscopy task supports. The first is linear-response TDDFT, limited to first-order expansions, which comes in two widespread formulations originally developed by Casida and by Sternheimer. The Casida scheme solves a generalized eigenvalue problem to extract optical excitation frequencies and oscillator strengths, from which the absorption cross-section is evaluated. Beyond its relatively low computational cost, it provides information on the nature of single-particle transitions, making it the method of choice for studying low-lying singlet excitations. The Sternheimer scheme, by contrast, solves a self-consistent system of equations for the response of the Kohn-Sham system to a perturbation at each frequency. It does not directly yield excitation energies, which are instead extracted from peaks of the calculated absorption cross-section, but its main advantages are excellent scalability, since it requires only occupied states, and straightforward parallelizability, because the response to each frequency can be computed independently.

The second approach is real-time TDDFT, in which the response of the system to a time-dependent excitation is explicitly recorded as the Kohn-Sham equations are numerically integrated forward in time. The absorption cross-section is then calculated from the Fourier transforms of the system’s dipole moment and of the excitation electric field. Excitations can take the form of a finite laser pulse or of an instantaneous pulse, commonly known as a delta-kick, which supplies the Kohn-Sham wavefunctions with a momentum kick and thereby triggers their time propagation, providing an efficient way to study the response across an infinitely broad range of frequencies. Real-time TDDFT scales very well with system size, can be applied to excitations of any intensity, unlike the linear-response case, and allows nuclear dynamics to be included through the semiclassical Ehrenfest scheme. By applying multiple pulses at varying time delays, it can even be used to explore the dynamics of excited electrons, though care must be taken in choosing the integration time step to ensure both efficiency and numerical stability.

The developers chose Octopus, an open-source package for performing density-functional theory calculations on a real-space grid in the pseudopotential formalism, as the computational engine for the task. Octopus supports both real-time and linear-response TDDFT, implemented in both the Casida and Sternheimer schemes, and its free availability and parallelization capabilities made it a natural fit. For transparency and practicality, the Optical spectroscopy task is divided into three sequential stages: numerical grid optimization, geometry optimization, and, most importantly, the optical response calculation itself. The current implementation is applicable to finite systems, meaning molecules and clusters, rather than periodic solids.

The first stage optimizes the real-space grid used by Octopus, a step the developers recommend including when studying a system for the first time to balance computational cost against accuracy. The optimization proceeds by performing a series of ground-state energy calculations across a user-provided set of grid parameters, successively comparing energies until the absolute difference exceeds a specified threshold. The second stage implements the standard geometry optimization procedure, in which users can choose the minimization method, set limits on the number of steps, and specify criteria in terms of minimal allowed atomic displacement and maximal allowed force on atoms. The third and central stage computes the optical response using either linear-response or real-time TDDFT, with users supplying the relevant parameters through the browser interface.

One particularly thoughtful feature addresses a common pitfall of real-time simulations. During propagation, the task constantly monitors for numerical instabilities that manifest as diverging total energy, typically caused by large integration time steps. Users can supply multiple candidate time-step values, and VIKING proceeds automatically: it starts the simulations with the largest value, and if instabilities are detected, it terminates and restarts them with the next smaller value, continuing until a stable value is found or the list is exhausted. In the demonstration calculations, the largest candidate time step of 0.080 atomic units proved unstable, and the platform automatically restarted the simulations with 0.010 atomic units, for which no stability issues arose—all without any user intervention. The task can also be repeatedly executed with varying setups without overwriting previous results, a feature called task extension that makes it easy to compare results obtained with different methods or parameters.

To demonstrate the tool’s capabilities, the team calculated the absorption spectra of pyrene, a polycyclic aromatic hydrocarbon with important applications in photochemistry, and of a small silver cluster known to show strong absorption in the ultraviolet-visible range. All available methods—Casida and Sternheimer linear response, and real-time propagation with both laser and delta-kick excitations—were applied, using the adiabatic local-density approximation throughout. The optimized average carbon-carbon bond length in pyrene came out at 1.399 angstroms, and the average distance between neighboring silver atoms in the cluster at 2.650 angstroms, both slightly smaller than reported experimental and calculated values of 1.410 and 2.700 angstroms respectively, a discrepancy consistent with the well-known tendency of the local-density approximation to overbind. Crucially, all methods yielded spectra in good mutual agreement, and the calculated absorption edge of pyrene, located around 3.5 electronvolts, agreed reasonably well with the experimental value of 3.8 electronvolts, while the cluster’s first calculated peak near 2.5 electronvolts and main absorption near 3.4 electronvolts matched experimental values of 2.86 and 3.45 electronvolts.

The advantages of the automated workflow become immediately apparent when one considers the manual alternative. Reproducing the demonstration results by hand would require at least thirteen Octopus calculations per system, carried out in a particular order and interfaced so that optimization results feed into subsequent calculations, along with substantial effort in preparing and checking input files, post-processing outputs, and monitoring real-time simulations for instabilities. Setting up the corresponding tasks in VIKING, by contrast, required specifying only a handful of parameters, with everything else—including result visualization and post-processing—handled automatically. All graphs in the demonstration were generated directly from the VIKING user interface without any additional plotting software. Looking ahead, the developers plan to remove the current limitation to non-periodic systems and to introduce support for multipulse excitations, needed for the theoretical description of transient-absorption and two-dimensional spectroscopies. They hope the tool will serve a broad scientific community, from theoreticians to experimentalists of all skill levels, freeing researchers to focus on the scientific rather than technical aspects of their work.

Subject of Research: A browser-based workflow tool for ab initio TDDFT optical spectroscopy of nanoscale systems

Article Title: Ab initio optical spectroscopy made simple with VIKING

Article References: Bačić, V., Guerrini, M., Krumland, J., Oliveira, A. F., Cocchi, C., & Solov’yov, I. A. (2026). Ab initio optical spectroscopy made simple with VIKING. Frontiers in Physics, 14, Article 1926459. https://doi.org/10.3389/fphy.2026.1926459

Image Credits: AI Generated

DOI: 10.3389/fphy.2026.1926459

Keywords: ab initio methods, optical spectroscopy, TDDFT, VIKING web app, Octopus, simulation pipelines, density functional theory, nanoscale systems, absorption spectra, linear response, real-time propagation, computational physics