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Jiří Pittner

Publications and source records attributed to Jiří Pittner.

At least 19 recordsLinked to original sources
arXiv2026

Toward Machine Learning Enhancement of Accelerated Surface Hopping with Scaled Spin--Orbit Couplings

Surface hopping (SH) methods are typically employed to simulate ultrafast nonadiabatic processes, but long timescales often remain beyond their reach. To address this, accelerated SH scheme mitigate this limitation by scaling the driving forces of such process, either nonadiabatic couplings (NACs) in case of internal conversion or spin-orbit couplings (SOCs) for intersystem crossing. However, obtaining the actual time constant requires extrapolation from several ensembles of trajectories with different scaling factors. This introduces a significant computational demand, often restricting the number of trajectories per ensemble and, therefore, reducing the statistical confidence in the resulting time constant. In this work, we investigate the accelerated scheme using silaethylene (CH$_2$SiH$_2$) as a case study, evaluating various population fitting methods and extrapolation techniques. We trained machine learning models for potential energy surfaces (PESs) and NACs, and extended our rotate-predict-rotate approach to fit SOCs. These models demonstrate high performance, yielding populations within the confidence interval of the reference MR-CISD/SA-CASSCF(2,2) data; however, the extrapolation itself is highly sensitive to the fitted time constants, leading to discrepancies in the final time constant. Finally, we showcase and discuss how ML models can enhance the reliability of an accelerated SH scheme.

physics.chem-ph↗
arXiv2025

Flexible Framework for Surface Hopping: From Hybrid Schemes for Machine Learning to Benchmarkable Nonadiabatic Dynamics

Nonadiabatic molecular dynamics is a key technique for investigating a broad range of photochemical and photophysical processes. Among the established approaches, surface hopping schemes are widely used and can be easily integrated with various quantum chemistry programs or machine learning models. We present a flexible framework in MLatom that includes a newly implemented Tully's fewest-switches surface hopping algorithm and its time-dependent Baeck--An variant. The capabilities of this framework are demonstrated through three representative examples corresponding to typical stages of a surface hopping study. First, we focus on methods providing energy, energy gradients and nonadiabatic couplings. We show that the flexibility of user-defined custom models can save computational time and that it is useful for benchmarking machine learning models. Next, we compare curvature-driven surface hopping schemes and show that Landau--Zener approach outperforms the time-dependent Baeck--An scheme. Finally, we showcase easy-to-use analysis tools for both individual trajectories and trajectory ensembles. This framework enables accelerated development of machine learning models and provides deeper insight into nonadiabatic dynamics. It is available as a part of the open-source MLatom package.

physics.chem-ph↗
arXiv2025

A simple approach to rotationally invariant machine learning of avector quantity

Unlike with the energy, which is a scalar property, machine learning (ML) predictions of vector or tensor properties poses the additional challenge of achieving proper invariance (covariance) with respect to molecular rotation. If the properties cannot be obtained by differentiation, other appropriate methods should be applied to retain the covariance. There have been several approaches suggested to properly treat this issue. For nonadiabatic couplings and polarizabilities, for example, it was possible to construct virtual quantities from which the above tensorial properties are obtained by differentiation and thus guarantee the covariance. Here we propose a simpler alternative technique, which does not require construction of auxiliary properties or application of special equivariant ML techniques. We suggest a three-step approach, using the molecular tensor of inertia. In the first step, the molecule is rotated using the eigenvectors of this tensor to its principal axes. In the second step, the ML procedure predicts the vector property relative to this orientation, based on a training set where all vector properties were in this same coordinate system. As third step, it remains to transform the ML estimate of the vector property back to the original orientation. This rotate-predict-rotate (RPR) procedure should thus guarantee proper covariance of a vector property and is trivially extensible also to tensors such as polarizability. The PRP procedure has an advantage that the accurate models can be trained very fast for thousands of molecular configurations which might be beneficial where many trainings are required (e.g., in active learning). We have implemented the RPR technique, using the MLatom and Newton-X programs for ML and MD and performed its assessment on the dipole moment along MD trajectories of 1,2-dichloroethane.

physics.chem-ph↗
arXiv2025

A Descriptor Is All You Need: Accurate Machine Learning of Nonadiabatic Coupling Vectors

Nonadiabatic couplings (NACs) play a crucial role in modeling photochemical and photophysical processes with methods such as the widely used fewest-switches surface hopping (FSSH). There is therefore a strong incentive to machine learn NACs for accelerating simulations. However, this is challenging due to NACs' vectorial, double-valued character and the singularity near a conical intersection seam. For the first time, we design NAC-specific descriptors based on our domain expertise and show that they allow learning NACs with never-before-reported accuracy of $R^2$ exceeding 0.99. The key to success is also our new ML phase-correction procedure. We demonstrate the efficiency and robustness of our approach on a prototypical example of fully ML-driven FSSH simulations of fulvene targeting the SA-2-CASSCF(6,6) electronic structure level. This ML-FSSH dynamics leads to an accurate description of $S_1$ decay while reducing error bars by allowing the execution of a large ensemble of trajectories. Our implementations are available in open-source MLatom.

physics.comp-ph↗
arXiv2025

Quantum Chemical and Trajectory Surface Hopping Molecular Dynamics Study of Iodine-based BODIPY Photosensitizer

A computational study of I-BODIPY (2-ethyl-4,4-difluoro-6,7-diiodo-1,3-dimethyl-4-bora-3a,4a-diaza-s-indacene) was conducted to investigate its photophysical properties as a potential triplet photosensitizer for singlet oxygen generation. Multireference CASPT2 and CASSCF methods were used to calculate vertical excitation energies and spin-orbit couplings (SOCs) in a model monoiodinated BODIPY molecule to assess the applicability of the single-reference ADC(2) method. Time-dependent density functional theory (TD-DFT) with the Tamm-Dancoff approximation (TDA) was tested against ADC(2) using different exchange-correlation functionals, employing a two-component pseudopotential basis set for iodine. SOC magnitudes between excited states were discussed using the Slater-Condon rules. The geometry dependence of SOCs for the lowest states was also examined. TD-DFT/B3LYP and TD-DFT(TDA)/BHLYP were selected for subsequent absorption spectra and trajectory surface hopping (TSH) molecular dynamics (MD) simulations. Two bright states were identified in I-BODIPY's visible spectrum, showing a red shift due to iodine substitution. Excited-state MD simulations, including nonadiabatic effects and SOCs, were performed to investigate relaxation after photoexcitation to the S1 state. TSH MD simulations revealed that intersystem crossings occur on a similar timescale to internal conversions. After triplet population growth, a "saturation" phase was reached with a triplet-to-singlet ratio of about 4:1. The calculated triplet quantum yield of 0.85 agrees qualitatively with the experimental singlet oxygen generation yield of 0.99.

physics.chem-ph↗
arXiv2024

DMRG-tailored coupled cluster method in the 4c-relativistic domain: General implementation and application to the NUHFI and NUF$_3$ molecules

Heavy atom compounds represent a challenge for computational chemistry, due to the need for simultaneous treatment of relativistic and correlation effects. Often such systems exhibit also strong correlation which hampers the application of perturbation theory or single-reference coupled cluster (CC) methods. As a viable alternative, we have proposed to externally correct the CC method using the density matrix renormalization group (DMRG) wave functions, yielding the DMRG-tailored CC method. In a previous paper [J. Chem. Phys. {\bf 152}, 174107 (2020)] we have reported a first implementation of this method in the relativistic context, which was restricted to molecules with real double group symmetry. In this work we present a fully general implementation of the method, covering complex and quaternion double groups as well. The 4c-TCC method thus becomes applicable to polyatomic molecules including heavy atoms. For assessment of the method, we performed calculations of the chiral uranium compound NUHFI, which was previously studied in the context of the enhancement of parity violation effects. In particular, we performed calculations of a cut of the potential energy surface of this molecule along the dissociation of the N-U bond, where the system exhibits a strong multireference character. Since there are no experimental data for NUHFI, we have performed also an analogous study of the (more symmetric) NUF$_3$ molecule, where the vibrational frequency of the N-U bond can be compared with spectroscopic data.

physics.chem-ph↗
arXiv2020

Variational Quantum Eigensolver for Approximate Diagonalization of Downfolded Hamiltonians using Generalized Unitary Coupled Cluster Ansatz

In this paper we discuss the utilization of Variational Quantum Solver (VQE) and recently introduced Generalized Unitary Coupled Cluster (GUCC) formalism for the diagonalization of downfolded/effective Hamiltonians in active spaces. In addition to effective Hamiltonians defined by the downfolding of a subset of virtual orbitals we also consider their form defined by freezing core orbitals, which enables us to deal with larger systems. We also consider various solvers to identify solutions of the GUCC equations. We use N$_2$, H$_2$O, and C$_2$H$_4$, and benchmark systems to illustrate the performance of the combined framework.

quant-ph↗
arXiv2020

Ground State of the Fe(II)-porphyrin Model System Corresponds to the Quintet State: A DFT and DMRG-based Tailored CC Study

Fe(II)-porphyrins (FeP) play an important role in many reactions relevant to material science and biological processes, due to their closely lying spin states. However, this small energetic separation also makes it challenging to establish the correct spin state ordering. Although the prevalent opinion is that these systems posses the triplet ground state, the recent experiment on Fe(II)-phthalocyanine under conditions matching those of an isolated molecule points toward the quintet ground state. We present a thorough study of FeP model by means of the density functional theory and density matrix renormalization group based tailored coupled clusters, in which we address all previously discussed correlation effects. We examine the importance of geometrical parameters, the Fe-N distances in particular, and conclude that the system possesses the quintet ground state, which is in our calculations well-separated from the triplet state.

physics.chem-ph↗
arXiv2020

Towards DMRG-tailored coupled cluster method in the 4c-relativistic domain

There are three essential problems in computational relativistic chemistry: electrons moving at relativistic speeds, close lying states and dynamical correlation. Currently available quantum-chemical methods are capable of solving systems with one or two of these issues. However, there is a significant class of molecules, in which all the three effects are present. These are the heavier transition metal compounds, lanthanides and actinides with open d or f shells. For such systems, sufficiently accurate numerical methods are not available, which hinders the application of theoretical chemistry in this field. In this paper, we combine two numerical methods in order to address this challenging class of molecules. These are the relativistic versions of coupled cluster methods and density matrix renormalization group (DMRG) method. To the best of our knowledge, this is the first relativistic implementation of the coupled cluster method externally corrected by DMRG. The method brings a significant reduction of computational costs, as we demonstrate on the system of TlH, AsH and SbH.

physics.chem-ph↗
arXiv2020

Near-linear Scaling in DMRG-based Tailored Coupled Clusters: An Implementation of DLPNO-TCCSD and DLPNO-TCCSD(T)

We present a new implementation of DMRG-based tailored coupled clusters method (TCCSD), which employs the domain-based local pair natural orbital approach (DLPNO-TCCSD). Compared to the previous LPNO version of the method, the new implementation is more accurate, offers more favorable scaling and provides more consistent behavior across the variety of systems. On top of the singles and doubles, we include the perturbative triples correction (T), which is able to retrieve even more dynamic correlation. The methods were tested on three systems: tetramethyleneethane, oxo-Mn(Salen) and Iron(II)-porphyrin model. The first two were revisited to assess the performance with respect to LPNO-TCCSD. For oxo-Mn(Salen), we retrieved between 99.8-99.9% of the total canonical correlation energy which is the improvement of 0.2% over the LPNO version in less than 63% of the total LPNO runtime. Similar results were obtained for Iron(II)-porphyrin. When the perturbative triples correction was employed, irrespective of the active space size or system, the obtained energy differences between two spin states were within the chemical accuracy of 1 kcal/mol using the default DLPNO settings.

physics.chem-ph↗
arXiv2019

Towards the Efficient Local Tailored Coupled Cluster Approximation and the Peculiar Case of Oxo-Mn(Salen)

We introduce a new implementation of the coupled cluster method tailored by matrix product states wave functions (DMRG-TCCSD), which employs the local pair natural orbital approach (LPNO). By exploiting locality in the coupled cluster stage of the calculation, we were able to remove some of the limitations that hindered the application of the canonical version of the method to larger systems and/or with larger basis sets. We assessed the accuracy of the approximation using two systems: tetramethyleneethane (TME) and oxo-Mn(Salen). Using the default cut-off parameters, we were able to recover over 99.7% and 99.8% of canonical correlation energy for the triplet and singlet state of TME respectively. In case of oxo-Mn(Salen), we found out that the amount of retrieved canonical correlation energy depends on the size of the active space (CAS) - we retrieved over 99.6% for the larger 27 orbital CAS and over 99.8% for the smaller 22 orbital CAS. The use of LPNO-TCCSD allowed us to perform these calculations up to quadruple-$ζ$ basis set amounting to 1178 basis functions. Moreover, we examined dependance of the ground state of oxo-Mn(Salen) on CAS composition. We found out that the inclusion of 4d$_{xy}$ orbital plays an important role in stabilizing the singlet state at the DMRG-CASSCF level via double-shell effect. However, by including dynamic correlation the ground state was found to be triplet regardless of the size of the basis set or composition of CAS, which is in agreement with previous findings by canonical DMRG-TCCSD in smaller basis.

physics.chem-ph↗
arXiv2019

Quantum information-based analysis of electron-deficient bonds

Recently, the correlation theory of the chemical bond was developed, which applies concepts of quantum information theory for the characterization of chemical bonds, based on the multiorbital correlations within the molecule. Here for the first time, we extend the use of this mathematical toolbox for the description of electron-deficient bonds. We start by verifying the theory on the textbook example of a molecule with three-center two-electron bonds, namely the diborane(6). We then show that the correlation theory of the chemical bond is able to properly describe bonding situation in more exotic molecules which have been synthetized and characterized only recently, in particular the diborane molecule with four hydrogen atoms [diborane(4)] and neutral zerovalent s-block beryllium complex, whose surprising stability was attributed to a strong three-center two-electron $π$ bond stretching across the C-Be-C core. Our approach is of a high importance especially in the light of a constant chase after novel compounds with extraordinary properties where the bonding is expected to be unusual.

physics.chem-ph↗
arXiv2018

Numerical and Theoretical Aspects of the DMRG-TCC Method Exemplified by the Nitrogen Dimer

In this article, we investigate the numerical and theoretical aspects of the coupled-cluster method tailored by matrix-product states. We investigate chemical properties of the used method, such as energy size extensivity and the equivalence of linked and unlinked formulation. The existing mathematical analysis is here elaborated in a quantum chemical framework. In particular, we highlight the use of a so-called CAS-ext gap describing the basis splitting between the complete active space and the external part. Moreover, the behavior of the energy error as a function of the optimal basis splitting is discussed. We show numerical investigations on the robustness with respect to the bond dimensions of the single orbital entropy and the mutual information, which are quantities that are used to choose the complete active space. Furthermore, we extend the mathematical analysis with a numerical study on the complete active space dependence of the error.

physics.chem-ph↗
arXiv2018

Full configuration interaction quantum Monte Carlo benchmark and multireference coupled cluster studies of tetramethyleneethane diradical

We have performed a FCI-quality benchmark calculation for the tetramethyleneethane molecule in cc-pVTZ basis set employing a subset of CASPT2(6,6) natural orbitals for the FCIQMC calculation. The results are in an excellent agreement with the previous large scale diffusion Monte Carlo calculations by Pozun et al. and available experimental results. Our computations verified that there is a maximum on PES of the ground singlet state ($^1\text{A}$) $45^{\circ}$ torsional angle and the corresponding vertical singlet-triplet energy gap is $0.01$ eV. We have employed this benchmark for assessment of the accuracy of MkCCSDT and DMRG-tailored CCSD (TCCSD) methods. MR MkCCSDT with CAS(2,2) model space, though giving good values for the singlet-triplet energy gap, is not able to properly describe the shape of the multireference singlet PES. Similarly, DMRG(24,25) is not able to correctly capture the shape of the singlet surface, due to the missing dynamic correlation. On the other hand, the DMRG-tailored CCSD method describes the shape of the ground singlet state with an excellent accuracy, but for the correct ordering requires computation of the zero-spin-projection component of the triplet state ($^3\text{B}_1$).

physics.chem-ph↗
arXiv2016

Coupled cluster method with single and double excitations tailored by matrix product state wave functions

In the last decade, the quantum chemical version of the density matrix renormalization group (DMRG) method has established itself as the method of choice for calculations of strongly correlated molecular systems. Despite its favourable scaling, it is in practice not suitable for computations of dynamic correlation. We present a novel method for accurate "post-DMRG" treatment of dynamic correlation based on the tailored coupled cluster (CC) theory in which the DMRG method is responsible for the proper description of non-dynamic correlation, whereas dynamic correlation is incorporated through the framework of the CC theory. We illustrate the potential of this method on prominent multireference systems, in particular N$_2$, Cr$_2$ molecules and also oxo-Mn(Salen) for which we have performed the first "post-DMRG" computations in order to shed light on the energy ordering of the lowest spin states.

physics.chem-ph↗
arXiv2016

Quantum chemistry beyond Born-Oppenheimer approximation on a quantum computer: a simulated phase estimation study

We present an efficient quantum algorithm for beyond-Born-Oppenheimer molecular energy computations. Our approach combines the quantum full configuration interaction method with the nuclear orbital plus molecular orbital (NOMO) method. We give the details of the algorithm and demonstrate its performance by classical simulations. Two isotopomers of the hydrogen molecule (H$_2$, HT) were chosen as representative examples and calculations of the lowest rotationless vibrational transition energies were simulated.

quant-ph↗
arXiv2014

Adiabatic state preparation study of methylene

Quantum computers attract much attention as they promise to outperform their classical counterparts in solving certain type of problems. One of them with practical applications in quantum chemistry is simulation of complex quantum systems. An essential ingredient of efficient quantum simulation algorithms are initial guesses of the exact wave functions with high enough fidelity. As was proposed in [Aspuru-Guzik et al., Science 309, 1704 (2005)], the exact ground states can in principle be prepared by the adiabatic state preparation method. Here, we apply this approach to preparation of the lowest lying multireference singlet electronic state of methylene and numerically investigate preparation of this state at different molecular geometries. We then propose modifications that lead to speeding up the preparation process. Finally, we decompose the minimal adiabatic state preparation employing the direct mapping in terms of two-qubit interactions.

quant-ph↗