Molecular Wave Functions Research Articles

Quantum information reveals that orbital-wise correlation is essentially classical in natural orbitals.

The intersection of quantum chemistry and quantum computing has led to significant advancements in understanding the potential of using quantum devices for the efficient calculation of molecular energies. Simultaneously, this intersection enhances the comprehension of quantum chemical properties through the use of quantum computing and quantum information tools. This paper tackles a key question in this relationship: Is the nature of the orbital-wise electron correlations in wavefunctions of realistic prototypical cases classical or quantum? We address this question with a detailed investigation of molecular wavefunctions in terms of Shannon and von Neumann entropies, common tools of classical and quantum information theory. Our analysis reveals a notable distinction between classical and quantum mutual information in molecular systems when analyzed with Hartree-Fock canonical orbitals. However, this difference decreases dramatically, by ∼100-fold, when natural orbitals are used as reference. This finding suggests that orbital correlations, when viewed through the appropriate basis, are predominantly classical. Consequently, our study underscores the importance of using natural orbitals to accurately assess molecular orbital correlations and to avoid their overestimation.

Tailoring masses to artificial molecules based on the shape of their wavefunctions

Abstract In this short paper, we examine artificial molecules composed of coupled artificial atoms such as quantum dots. Similar to artificial atoms, which have position-dependent effective masses for electrons, artificial molecules exhibit this characteristic while comprising more than one artificial atom. While in the literature, such artificial molecules are focused on the kinetic term of the electrons in such a setup, we consider the full description that includes the kinetic and potential terms that involve the nuclei. The proposed artificial molecules consist of nuclei and electrons coupled through Coulomb potentials and kinetic energy influenced by electronic position-dependent effective masses that also depend on the positions of the nuclei and the other electrons in the system. We demonstrate how the Schrödinger equation for such systems can be solved by assuming the entire shape of the molecular wavefunction, guided by a tailored non-parabolic energy-momentum relation for at least one electron within the molecular structure. Additionally, we show that instead of pre-specifying the entire form of the molecular wavefunction, we can consider the coupling between the electrons and nuclei to obtain the wavefunction of the system.

Positron interactions with vinyl acetate from 0.1 eV to 5 keV

Abstract Scattering cross sections from positron impact on vinyl acetate are explored in the energy region 0.1 eV to a 5 keV, employing a cc-pVTZ basis set. The optimized molecular wavefunction of the target was obtained through a multi-center expansion of Gaussian-type orbitals in the Hartree–Fock self-consistent field framework. The elastic cross sections are computed using the single-centre-expansion formalism. Two distinct models were employed to address the long-range effects associated with the target's polar nature and yielded almost identical corrections. The Born-corrected elastic cross sections align more strongly with the existing experimental corrected data than the results reported from the independent-atom-model approximation. The differential and momentum transfer cross sections after applying Born-correction are also reported. The direct ionization cross sections are obtained using the binary-encounter-Bethe model for positrons. The cross sections obtained by summing elastic and ionization cross sections align closely with ‘forward angle corrected’ experimental total cross sections across a significant energy range. The agreement significantly improves beyond 30 eV, suggesting that the omission of excitation and positronium formation cross sections becomes less significant. A brief analysis of the electron interaction with the target is also made.

Chemical information from XPS: Theory and experiment for Ni(OH)2.

The features and the electronic character of the states for the Ni 2p x-ray photoelectron spectroscopy (XPS) of Ni(OH)2 were analyzed. This detailed analysis is based on abinitio molecular orbital wavefunctions for a cluster model of Ni(OH)2. The theory is validated by comparison with experiment. Then, advanced methods are used to explain and contrast the properties of different groups of ionic states. An important conclusion is that in most cases, the ionic states cannot be described with a single configuration or determinant. Despite this essential many-body character of the XPS, we demonstrate that it is possible to understand the origin of the main and satellite XPS features in terms of their orbital character.

Net emission coefficient of magnesium oxide crystal arc plasma with different Mg particle concentrations

The aim of the present study was to construct a molecular spectral database of magnesium oxide crystal arc plasma, thereby allowing for the net emission coefficient of arc to be calculated at different temperatures, pressures and Mg ratios. First, Rydberg-Klein-Rees inversion method was adopted to reconstruct the potential-energy curves of diatomic molecules. Subsequently, the Schrödinger equation was solved to determine the molecular wave function. This solution combined with the electrical transition moment function facilitates the calculation of radiative transition probabilities between different energy levels and the development of this database. Second, calculation models of the bound-free and free-free radiative absorption cross-section were established and use to calculate the continuous radiation of atoms. Finally, the radiative capability of different particles was calculated separately, followed by calculation of the net emission coefficient of plasma through addition The experimental results reveal that the net emission coefficient of air plasma under atmospheric pressure is consistent with existing research in both its magnitude and trend. Given that Mg can be ionized at lower temperatures, the magnesium oxide crystal arc plasma exhibited a pronounced radiative capacity at these temperatures. Additionally, a larger optical transmission distance corresponded to a reduced net emission coefficient of the plasma.

Design and synthesis of thiahelicenes for molecular electronics.

The conductance of a tunneling electron through a π-conjugated molecule may be affected by the presence of different pathways in the orbital structure of the molecule, resulting in the constructive or destructive interference of the molecular wave function. This quantum interference (QI) directly translates into enhancement or suppression of conductance and offers the possibility of controlling this phenomenon through tailored synthesis. Hence, we set up synthetic methodologies to access a series of thiophene-fused helicenes with a well-defined positioning of the sulfur atoms, which control the occurrence of conducting, linearly conjugated as well as disrupted, cross-conjugated pathways. We describe these synthetic strategies and relate the expected electronic transport through our molecules to three key variables: a) the exo-/endo-topology of the S atom within the ring; b) the parity (odd/even) of the overall number of rings conforming to the helicene; and c) the size of the circuit. This series ranks from [7] to [11] fused rings, having both exo-, endo-, or mixed exo-endo-topology. Comparison of homologous dithiahelicenes with size-tunable highest occupied molecular orbital (HOMO)/lowest unoccupied molecular orbital (LUMO) energies allows us to isolate the key variable of the bond topology from other electronic properties and face the study of QI in helically conjugated molecules. Understanding and tuning the conductance in such molecular solenoids is the main purpose of this work.

Emergence of the Molecular Geometric Phase from Exact Electron-Nuclear Dynamics.

Geometric phases play a crucial role in diverse fields. In molecules, they appear when a reaction path encircles an intersection between adiabatic potential energy surfaces and the molecular wave function experiences quantum-mechanical interference effects. This intriguing effect, closely resembling the magnetic Aharonov-Bohm effect, crucially relies on the adiabatic description of the dynamics, and it is an open issue whether and how it persists in an exact quantum dynamical framework. Recent works suggest that the molecular geometric phase is an artifact of the adiabatic approximation, thereby challenging the entire concept. Here, building upon a recent investigation (Martinazzo, R.; Burghardt, I. Phys. Rev. Lett. 2024, 132, 243002), we address this issue using the exact factorization of the total wave function. We introduce instantaneous gauge-invariant phases separately for the electrons and nuclei and use them to monitor the phase difference between the trailing edges of a wavepacket encircling a conical intersection between adiabatic surfaces. The transition from the time-dependent open-path phase differences to the closed-path limit is examined, revealing how the phase differences in the electronic and nuclear subspaces compensate for each other upon path closure. In this way, we unambiguously demonstrate the role of the geometric phase in the interference process and shed light on its persistence beyond the adiabatic approximation.

Electronic Vector Potential from the Exact Factorization of a Complex Wavefunction.

We generalize the definitions of local scalar potentials named and , which are relevant to properly describe phenomena such as molecular dissociation with density-functional theory, to the case in which the electronic wavefunction corresponds to a complex current-carrying state. In such a case, an extra term in the form of a vector potential appears which cannot be gauged away. Both scalar and vector potentials are introduced via the exact factorization formalism which allows us to express the given Schrödinger equation as two coupled equations, one for the marginal and one for the conditional amplitude. The electronic vector potential is directly related to the paramagnetic current density carried by the total wavefunction and to the diamagnetic current density in the equation for the marginal amplitude. An explicit example of this vector potential in a triplet state of two non-interacting electrons is showcased together with its associated circulation, giving rise to a non-vanishing geometric phase. Some connections with the exact factorization for the full molecular wavefunction beyond the Born-Oppenheimer approximation are also discussed.

Time-dependent surface-enhanced Raman scattering: A theoretical approach.

A new procedure for computing the time-dependent Raman scattering of molecules in the proximity of plasmonic nanoparticles (NPs) is proposed, drawing inspiration from the pioneering Lee and Heller's theory. This strategy is based on a preliminary simulation of the molecular vibronic wavefunction in the presence of a plasmonic nanostructure and an incident light pulse. Subsequently, the Raman signal is evaluated through an inverse Fourier Transform of the coefficients' dynamics. Employing a multiscale approach, the system is treated by coupling the quantum mechanical description of the molecule with the polarizable continuum model for the NP. This method offers a unique advantage by providing insights into the time evolution of the plasmon-enhanced Raman signal, tracking the dynamics of the incident electric field. It not only provides for the total Raman signal at the process's conclusion but also gives transient information. Importantly, the flexibility of this approach allows for the simulation of various incident electric field profiles, enabling a closer alignment with experimental setups. This adaptability ensures that the method is relevant and applicable to diverse real-world scenarios.

Discontinuities of Kinetic Energy Densities within Finite and Complete Basis Sets.

Although electron densities are always continuous, other ingredients of density-functional approximations can be sharply discontinuous at isolated points. In particular, the positive-definite, Weizsäcker, and Pauli kinetic energy densities expressed in terms of Slater-type orbitals all have discontinuities at the positions of the atomic nuclei in molecules. The first two of those quantities are similarly discontinuous even in the basis-set limit. These striking features are not as widely recognized as they deserve to be. We show in detail how discontinuities of kinetic energy densities arise from asymmetric electron-nucleus cusps of molecular wave functions and point out instances of their significance in electronic structure theory.

"Core-Shell" Wave Function Modulation in Organic Narrowband Emitters.

Efficient red-green-blue primary luminescence with an extraordinarily narrow band and durability is crucial for advanced display applications. Recently, the emergence of multiple-resonance (MR) from short-range atomic interactions has been shown to induce extremely narrow spectral widths in pure organic emitters. However, achieving wide-range color tuning without compromising color purity remains a persistent challenge for MR emitters. Herein, the concept of electronic donor/acceptor "core-shell" modulation is proposed within a boron/nitrogen (B/N) MR skeleton, enabling the rational utilization of intramolecular charge transfer to facilitate wavelength shift. The dense B atoms localized at the center of the molecule effectively compress the electron density and stabilize the lowest unoccupied molecular orbital wave function. This electron-withdrawing core is embedded with peripheral electron-donating atoms. Consequently, doping a single B atom into a deep-blue MR framework led to a profound bathochromic shift from 447 to 624 nm (∼0.8 eV) while maintaining a narrow spectral width of 0.10 eV in this pure-red emitter. Notably, organic light-emitting diodes assisted by thermally activated delayed fluorescence molecules achieved superb electroluminescent stability, with an LT99 (99% of the initial luminance) exceeding 400 h at an initial luminance of 1000 cd m-2, approaching commercial-level performance without the assistance of phosphors.

Alternative CNDOL Fockians for fast and accurate description of molecular exciton properties.

CNDOL is an a priori, approximate Fockian for molecular wave functions. In this study, we employ several modes of singly excited configuration interaction (CIS) to model molecular excitation properties by using four combinations of the one electron operator terms. Those options are compared to the experimental and theoretical data for a carefully selected set of molecules. The resulting excitons are represented by CIS wave functions that encompass all valence electrons in the system for each excited state energy. The Coulomb-exchange term associated to the calculated excitation energies is rationalized to evaluate theoretical exciton binding energies. This property is shown to be useful for discriminating the charge donation ability of molecular and supermolecular systems. Multielectronic 3D maps of exciton formal charges are showcased, demonstrating the applicability of these approximate wave functions for modeling properties of large molecules and clusters at nanoscales. This modeling proves useful in designing molecular photovoltaic devices. Our methodology holds potential applications in systematic evaluations of such systems and the development of fundamental artificial intelligence databases for predicting related properties.

Hückel molecular orbital theory on a quantum computer: A scalable system-agnostic variational implementation with compact encoding.

Hückel molecular orbital (HMO) theory provides a semi-empirical treatment of the electronic structure in conjugated π-electronic systems. A scalable system-agnostic execution of HMO theory on a quantum computer is reported here based on a variational quantum deflation (VQD) algorithm for excited state quantum simulation. A compact encoding scheme is proposed here that provides an exponential advantage over the direct mapping and allows for quantum simulation of the HMO model for systems with up to 2n conjugated centers with n qubits. The transformation of the Hückel Hamiltonian to qubit space is achieved by two different strategies: an iterative refinement transformation and the Frobenius-inner-product-based transformation. These methods are tested on a series of linear, cyclic, and hetero-nuclear conjugated π-electronic systems. The molecular orbital energy levels and wavefunctions from the quantum simulation are in excellent agreement with the exact classical results. However, the higher excited states of large systems are found to suffer from error accumulation in the VQD simulation. This is mitigated by formulating a variant of VQD that exploits the symmetry of the Hamiltonian. This strategy has been successfully demonstrated for the quantum simulation of C60 fullerene containing 680 Pauli strings encoded on six qubits. The methods developed in this work are easily adaptable to similar problems of different complexity in other fields of research.

Improved treatment of the T2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document} molecular final-states uncertainties for the KATRIN neutrino-mass measurement

The KArlsruhe TRItium Neutrino experiment (KATRIN) aims to determine the effective mass of the electron antineutrino via a high-precision measurement of the tritium β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upbeta $$\\end{document}-decay spectrum in its end-point region. The target neutrino-mass sensitivity of 0.2eV/c2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${0.2}~\ ext {eV}/\ ext {c}^2$$\\end{document} at 90% CL can only be achieved in the case of high statistics and good control of the systematic uncertainties. One key systematic effect originates from the calculation of the molecular final states of T2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document}β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upbeta $$\\end{document} decay. In the first neutrino-mass analyses of KATRIN the contribution of the uncertainty of the molecular final-states distribution (FSD) was estimated via a conservative phenomenological approach to be 2×10-2eV2/c4.\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2 \ imes 10^{-2}~\ ext {eV}^{2}/\ ext {c}^{4}.$$\\end{document} In this work a new procedure is presented for estimating the FSD-related uncertainties by considering the details of the final-states calculation, i.e. the uncertainties of constants, parameters, and functions used in the calculation as well as its convergence itself as a function of the basis-set size used in expanding the molecular wave functions. The calculated uncertainties are directly propagated into the experimental observable, the squared neutrino mass mν2,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m_\ u ^2,$$\\end{document} and thus have to be determined individually for each experimental configuration. For the experimental conditions of the first KATRIN measurement campaign the new procedure is presented in detail, allowing for the application of this procedure to other experiments. This specific calculation leads to a constraint of the FSD-related uncertainty of 1.3×10-3eV2/c4,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1.3 \ imes 10^{-3}~\ ext {eV}^{2}/\ ext {c}^{4},$$\\end{document} well below the design limit of 7.5×10-3eV2/c4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$7.5 \ imes 10^{-3}~\ ext {eV}^{2}/\ ext {c}^{4}$$\\end{document} for any individual systematic contribution.

Density functional theory beyond the Born–Oppenheimer approximation: exact mapping onto an electronically non-interacting Kohn–Sham molecule

This work presents an alternative, general, and in-principle exact extension of electronic Kohn–Sham density functional theory (KS-DFT) to the fully quantum-mechanical molecular problem. Unlike in existing multi-component or exact-factorization-based DFTs of electrons and nuclei, both nuclear and electronic densities are mapped onto a fictitious electronically non-interacting molecule (referred to as KS molecule), where the electrons still interact with the nuclei. Moreover, in the present molecular KS-DFT, no assumption is made about the mathematical form (exactly factorized or not) of the molecular wavefunction. By expanding the KS molecular wavefunction à la Born–Huang, we obtain a self-consistent set of ‘KS beyond Born–Oppenheimer’ electronic equations coupled to nuclear equations that describe nuclei interacting among themselves and with non-interacting electrons. An exact adiabatic connection formula is derived for the Hartree-exchange-correlation energy of the electrons within the molecule and, on that basis, a practical adiabatic density-functional approximation is proposed and discussed.

χ(2) and χ(3) enhancement by arylamine substituents in aromatic conjugated polyenyne polymers

In this work, we have determined the χ(1), χ(2), and χ(3) NLO properties of NH2substituted aromatic polyenynes in ortho, meta, and para positions. It is worth noting that Mednis-Genkin’s approximation takes into account the intraband contribution with a derivate of the dipole valence-conduction band moment transition, unlike, for example, Ward’s summation-over-sates (SOS) methodology, which considers the difference of these states. Indeed, we have selected these polymers because of the high asymmetry in their molecular wavefunction. In this way, the calculated χ(3) values of the para-NH2 substituted aromatic polyenyne with a higher degree of polymerization are near 1 X 10−7 esu. For its part, the ortho polymer has higher values, of the order of 1 X 10−6 esu, due to its high transition dipole moment. We have also found that the energy band distribution in the para position of these polymers produces van Hove points, which have a negligible proportion of the NLO properties, compared with singularity regions 1 and 2, which have a contribution of 100 %. These regions are due to the wavefunction coefficients’ first and second-order derivatives. Besides, without considering border effects nor correlation effects, and only the variation of excitation energy, we have calculated that the quaternary monomeric oligomers of these polymers have almost similar values of χ(2) and χ(3). Then, it implies building a methodology to synthesize the polymers to avoid canceling the NLO-χ(2) and -χ(3) values.

Interference effects in Compton scattering of keV photons at H 2+ : a nonrelativistic analytical approach

In this paper we study interference effects in Compton scattering at molecule by keV photons. As a test case we investigate the molecular system H 2+ at the equilibrium internuclear distance and in the dissociative channel. The initial molecular wavefunction is described as a linear combination of atomic orbitals centered on each nucleus. The final continuum state is a two-centre continuum Coulomb wavefunction. Using these approximations, we obtain an analytical form for the Compton scattering fully differential cross section. We investigate the molecular effects at various internuclear distance for an incident photon energy close to 2.1 keV. The relative contribution of the A⋅P and A 2 coupling terms in the Compton scattering magnitude is discussed (where P is the electron momentum operator and A the vector potential of the field). We focus on Cohen-Fano type interference effects, as the ones observed in the photoionization of molecules.

Fragment-Based Deep Learning for Simultaneous Prediction of Polarizabilities and NMR Shieldings of Macromolecules and Their Aggregates.

Simultaneous prediction of the molecular response properties, such as polarizability and the NMR shielding constant, at a low computational cost is an unresolved issue. We propose to combine a linear-scaling generalized energy-based fragmentation (GEBF) method and deep learning (DL) with both molecular and atomic information-theoretic approach (ITA) quantities as effective descriptors. In GEBF, the total molecular polarizability can be assembled as a linear combination of the corresponding quantities calculated from a set of small embedded subsystems in GEBF. In the new GEBF-DL(ITA) protocol, one can predict subsystem polarizabilities based on the corresponding molecular wave function (thus electron density and ITA quantities) and DL model rather than calculate them from the computationally intensive coupled-perturbed Hartree-Fock or Kohn-Sham equations and finally obtain the total molecular polarizability via a linear combination equation. As a proof-of-concept application, we predict the molecular polarizabilities of large proteins and protein aggregates. GEBF-DL(ITA) is shown to be as accurate enough as GEBF, with mean absolute percentage error <1%. For the largest protein aggregate (>4000 atoms), GEBF-DL(ITA) gains a speedup ratio of 3 compared with GEBF. It is anticipated that when more advanced electronic structure methods are used, this advantage will be more appealing. Moreover, one can also predict the NMR chemical shieldings of proteins with reasonably good accuracy. Overall, the cost-efficient GEBF-DL(ITA) protocol should be a robust theoretical tool for simultaneously predicting polarizabilities and NMR shieldings of large systems.

Coupled Electron-Nuclear Dynamics Induced and Monitored with Femtosecond Soft X-ray Pulses in the Amino Acid Glycine.

The coupling of electronic and nuclear motion in polyatomic molecules is at the heart of attochemistry. The molecular properties, transient structures, and reaction mechanism of these many-body quantum objects are defined on the level of electrons and ions by molecular wave functions and their coherent superposition, respectively. In the present contribution, we monitor nonadiabatic quantum wave packet dynamics during molecular charge motion by reconstructing both the oscillatory charge density distribution and the characteristic time-dependent nuclear configuration coordinate from time-resolved Auger electron spectroscopic data recorded in previous studies on glycine molecules [Schwickert et al. Sci. Adv. 2022, 8, eabn6848]. The electronic and nuclear motion on the femtosecond time scale was induced and probed in kinematically complete soft X-ray experiments at the FLASH free-electron laser facility. The detailed analysis of amplitude, instantaneous phase, and instantaneous frequency of the propagating many-body wave packet during its lifecycle provides unprecedented insight into dynamical processes beyond the Born-Oppenheimer approximation. We are confident that the refined experimental data evaluation helps to develop new theoretical tools to describe time-dependent molecular wave functions in complicated but ubiquitous non-Born-Oppenheimer photochemical conditions.

Nonadiabatic dynamics with classical trajectories: The problem of an initial coherent superposition of electronic states.

Advances in coherent light sources and development of pump-probe techniques in recent decades have opened the way to study electronic motion in its natural time scale. When an ultrashort laser pulse interacts with a molecular target, a coherent superposition of electronic states is created and the triggered electron dynamics is coupled to the nuclear motion. A natural and computationally efficient choice to simulate this correlated dynamics is a trajectory-based method where the quantum-mechanical electronic evolution is coupled to a classical-like nuclear dynamics. These methods must approximate the initial correlated electron-nuclear state by associating an initial electronic wavefunction to each classical trajectory in the ensemble. Different possibilities exist that reproduce the initial populations of the exact molecular wavefunction when represented in a basis. We show that different choices yield different dynamics and explore the effect of this choice in Ehrenfest, surface hopping, and exact-factorization-based coupled-trajectory schemes in a one-dimensional two-electronic-state model system that can be solved numerically exactly. This work aims to clarify the problems that standard trajectory-based techniques might have when a coherent superposition of electronic states is created to initialize the dynamics, to discuss what properties and observables are affected by different choices of electronic initial conditions and to point out the importance of quantum-momentum-induced electronic transitions in coupled-trajectory schemes.