Showing papers in "Molecular Physics in 2013"

Using collective variables to drive molecular dynamics simulations

Abstract: A software framework is introduced that facilitates the application of biasing algorithms to collective variables of the type commonly employed to drive massively parallel molecular dynamics (MD) simulations. The modular framework that is presented enables one to combine existing collective variables into new ones, and combine any chosen collective variable with available biasing methods. The latter include the classic time-dependent biases referred to as steered MD and targeted MD, the temperature-accelerated MD algorithm, as well as the adaptive free-energy biases called metadynamics and adaptive biasing force. The present modular software is extensible, and portable between commonly used MD simulation engines.

Manipulation of molecules with electromagnetic fields

Abstract: The goal of the present article is to review the major developments that have led to the current understanding of molecule–field interactions and experimental methods for manipulating molecules with electromagnetic fields. Molecule–field interactions are at the core of several, seemingly distinct areas of molecular physics. This is reflected in the organisation of this article, which includes sections on field control of molecular beams, external field traps for cold molecules, control of molecular orientation and molecular alignment, manipulation of molecules by non-conservative forces, ultracold molecules and ultracold chemistry, controlled many-body phenomena, entanglement of molecules and dipole arrays, and stability of molecular systems in high-frequency super-intense laser fields. The article contains 852 references.

A simple and effective Verlet-type algorithm for simulating Langevin dynamics

Abstract: We present a revision to the well known Stormer–Verlet algorithm for simulating second order differential equations. The revision addresses the inclusion of linear friction with associated stochastic noise, and we analytically demonstrate that the new algorithm correctly reproduces diffusive behaviour of a particle in a flat potential. For a harmonic oscillator, our algorithm provides the exact Boltzmann distribution for any value of damping, frequency and time step for both underdamped and overdamped behaviour within the usual stability limit of the Verlet algorithm. Given the structure and simplicity of the method, we conclude that this approach can trivially be adapted for contemporary applications, including molecular dynamics with extensions such as molecular constraints.

Multireference explicitly correlated F12 theories

Abstract: We review our recent developments in multireference explicitly correlated F12 theories (explicitly correlated internally contracted multireference perturbation and multireference configuration interaction theories) that achieve near-basis-set-limit accuracy of the underlying multireference electron correlation methods with basis sets of medium size. The applicability of the multireference F12 theories is the same as that of their non-F12 counterpart, and therefore it is a computational tool with predictive accuracy for complicated electronic structures with strong correlation. A comparison with the earlier developments by others is also discussed.

Probing weak force-induced parity violation by high-resolution mid-infrared molecular spectroscopy

Abstract: To date no experiment has reached the level of sensitivity required to observe weak nuclear force-induced parity violation (PV) energy differences in chiral molecules. In this paper, we present the approach, adopted at Laboratoire de Physique des Lasers (LPL), to measure frequency differences in the vibrational spectrum of enantiomers. We review different spectroscopic methods developed at LPL leading to the highest resolutions, as well as 20 years of CO2 laser stabilisation work enabling such precise measurements. After a first attempt to observe PV vibrational frequency shifts using sub-Doppler saturated absorption spectroscopy in a cell, we are currently aiming at an experiment based on Doppler-free two-photon Ramsey interferometry on a supersonic beam. We report on our latest progress towards observing PV with chiral organo-metallic complexes containing a heavy rhenium atom.

Ab initio potential energy surface for the nitrogen molecule pair and thermophysical properties of nitrogen gas

Abstract: A four-dimensional potential energy hypersurface (PES) for the interaction of two rigid nitrogen molecules was determined from high-level quantum-chemical ab initio computations. A total of 408 points for 26 distinct angular configurations were calculated utilizing the counterpoise-corrected supermolecular approach at the CCSD(T) level of theory and basis sets up to aug-cc-pV5Z supplemented with bond functions. The calculated interaction energies were extrapolated to the complete basis set limit and complemented by corrections for core–core and core–valence correlations, relativistic effects and higher coupled-cluster levels up to CCSDT(Q). An analytical site–site potential function with five sites per nitrogen molecule was fitted to the interaction energies. The PES was validated by computing second and third pressure virial coefficients as well as shear viscosity and thermal conductivity in the dilute-gas limit. An improved PES was obtained by scaling the CCSDT(Q) corrections for all 408 points by a con...

Failures of TDDFT in describing the lowest intramolecular charge-transfer excitation in para-nitroaniline

Abstract: We investigate the failure of time-dependent density functional theory (TDDFT) with the CAM-B3LYP exchange-correlation (xc) functional coupled to the polarisable embedding (PE) scheme (PE-CAM-B3LYP) in reproducing the solvatochromic shift of the lowest intense charge-transfer excitation in para-nitroaniline (pNA) in water by comparing with results obtained with the coupled cluster singles and doubles (CCSD) model also coupled to the polarisable embedding scheme (PE-CCSD). We determine the amount of charge separation in the ground and excited charge-transfer state with both methods by calculating the electric dipole moments in the gas phase and for 100 solvent configurations. We find that CAM-B3LYP overestimates the amount of charge separation inherent in the ground state and TDDFT/CAM-B3LYP drastically underestimates this amount in the excited charge-transfer state. As the errors in the solvatochromatic shift are found to be inverse proportional to the change in dipole moment upon excitation, we conclude ...

DFT studies of Si- and Al-doping effects on the acetone sensing properties of BC3 graphene

Abstract: In order to find a novel sensor, reactivity and sensitivity of the intrinsic, Al- and Si-doped BC3 graphene-like sheets to an acetone molecule were investigated by using B3LYP and ωB97X-D density functional calculations. Adsorption of acetone on the intrinsic, Al- and Si-doped BC3 sheets releases energies of about 7.2, 36.5 and 24.8 kcal/mol, respectively, using ωB97X-D. The Si-doped sheet presents high sensitivity to acetone compared with the intrinsic and Al-doped sheets indicated by the calculated geometrical structures and electronic properties for these systems. The HOMO/LUMO energy gap of Si-doped BC3 sheet is significantly decreased from 2.20 to 1.65 eV (B3LYP), which would result in electrical conductance increment. Thus, Si-doped sheet are expected to be a potential candidate for detecting the presence of acetone.

Combining spin-adapted open-shell TD-DFT with spin-orbit coupling

Abstract: The recently proposed spin-adapted time-dependent density functional theory (S-TD-DFT) is extended to the relativistic domain for fine-structure splittings of excited states of open-shell systems. Scalar-relativistic effects are treated to infinite order via the spin-free (sf) part of the exact two-component (X2C) Hamiltonian, whereas the spin–orbit couplings (SOC) between the scalar-excited states are treated perturbatively via an effective one-electron spin–orbit operator derived from the same X2C Hamiltonian. The calculated results for prototypical open-shell systems containing heavy elements reveal that the composite approach sf-X2C-S-TD-DFT-SOC is very promising. The fine-structure splitting of a spatially degenerate ground state can also be described properly by taking a non-degenerate excited state as the reference.

Local vibrational modes of the formic acid dimer – the strength of the double hydrogen bond

Abstract: The 24 normal and 24 local vibrational modes of the formic acid dimer formed by two trans formic acid monomers to a ring (TT1) are analysed utilising preferentially experimental frequencies, but also CCSD(T)/CBS and ωB97X-D harmonic vibrational frequencies. The local hydrogen bond (HB) stretching frequencies are at 676 cm−1 and by this 482 and 412 cm−1 higher compared to the measured symmetric and asymmetric HB stretching frequencies at 264 and 194 cm−1. The adiabatic connection scheme between local and normal vibrational modes reveals that the lowering is due to the topology of dimer TT1, mass coupling, and avoided crossings involving the H⋅⋅⋅OC bending modes. The HB local mode stretching force constant is related to the strength of the HB whereas the normal mode stretching force constant and frequency lead to an erroneous underestimation of the HB strength. The HB in TT1 is stabilised by electron delocalisation in the O=C–O units fostered by forming a ring via double HBs. This implies that the CO apart ...

Calculation of fundamental frequencies for small polyatomic molecules: a comparison between correlation consistent and atomic natural orbital basis sets

Abstract: The performance of the NASA Ames atomic natural orbital (ANO) basis sets for calculating fundamental vibrational frequencies is examined, using the CCSD(T) treatment of electron correlation and second-order vibrational perturbation theory. Particular attention is paid to the performance of the small, cost-effective truncations ([3s 2p 1d] and [4s 3p 2d 1f] on second-row atoms) known as ANO0 and ANO1, as similarly sized basis sets must necessarily be used for high-level correlation treatment of ‘large’ molecules. It is found that the ANO0 and ANO1 basis sets – particularly the former – outperform comparably sized correlation consistent basis sets for the calculation of vibrational frequencies, suggesting that the ANO0 basis is a useful tool for this area of computational chemistry.

Interatomic potentials, electric properties and spectroscopy of the ground and excited states of the Rb2 molecule: ab initio calculations and effect of a non-resonant field*

Abstract: We formulate the theory for a diatomic molecule in a spatially degenerate electronic state interacting with a non-resonant laser field and investigate its rovibrational structure in the presence of the field. We report on ab initio calculations employing the double electron attachment intermediate Hamiltonian Fock space coupled cluster method restricted to single and double excitations for all electronic states of the Rb2 molecule up to 5s+5d dissociation limit of about 26,000 cm−1. In order to correctly predict the spectroscopic behaviour of Rb2, we have also calculated the electric transition dipole moments, non-adiabatic coupling and spin-orbit coupling matrix elements, and static dipole polarisabilities, using the multireference configuration interaction method. When a molecule is exposed to strong non-resonant light, its rovibrational levels get hybridised. We study the spectroscopic signatures of this effect for transitions between the X1Σ+ g electronic ground state and the A1Σ+ u and b3Π u excited ...

Light-assisted cold chemical reactions of barium ions with rubidium atoms

Abstract: Light-assisted reactive collisions between laser-cooled Ba+ ions and Rb atoms were studied in an ion–atom hybrid trap. The reaction rate was found to strongly depend on the electronic state of the reaction partners with the largest rate constant [7(2) × 10−11 cm3 s−1] obtained for the excited Ba+(6s)+Rb(5p) reaction channel. Similar to the previously studied Ca++Rb system, charge transfer and radiative association were found to be the dominant reactive processes. The generation of molecular ions by radiative association could directly be observed by their sympathetic cooling into a Coulomb crystal. Potential energy curves up to the Ba+(6s)+Rb(5p) asymptote and reactive-scattering cross sections for the radiative processes were calculated. The theoretical rate constant obtained for the lowest reaction channel Ba+(6s)+Rb(5s) is compatible with the experimental estimates obtained thus far.

Triple zeta quality basis sets for atoms Rb through Xe: application in CCSD(T) atomic and molecular property calculations

Abstract: Segmented all-electron contracted triple zeta valence plus polarization function (TZP) basis sets for the elements from Rb to Xe were constructed to be used in conjunction with the non-relativistic and Douglas–Kroll–Hess (DKH) Hamiltonians. This extends earlier work on segmented contracted TZ basis set for the atoms H-Kr. At the coupled cluster level of theory, ionization energy of some atoms as well as spectroscopic constants of a sample of diatomics were calculated and compared with benchmark theoretical values. One verifies that the benchmark bond length, dissociation energy, and harmonic vibrational frequency can be reproduced well with the TZP-DKZ set.

The role of the exchange-correlation response kernel and scaling corrections in relativistic density functional nuclear magnetic shielding calculations with the zeroth-order regular approximation

Abstract: The relativistic NMR module of the Amsterdam Density Functional (ADF) package, which is frequently utilised in studies of heavy atom NMR chemical shifts, is extended to calculate a hitherto neglected term from the response of the exchange-correlation (XC) potential. The term vanishes in the absence of spin-orbit coupling. Further, corrections to the shielding arising from scaling factors in the zeroth-order regular approximation (zora) relativistic framework are investigated. The XC response markedly improves calculated proton chemical shifts for hydrogen halides. Mercury chemical shifts for mercury dihalides are also noticeably altered. Contributions from density-gradient dependent terms in the response kernel contribute about 30–40%. New fully relativistic density functional theory (DFT) benchmark data are compared with zora and literature reference values. In line with previous work, it is found that absolute shielding constants for Hg are not accurately predicted with zora. However, chemical shifts ag...

Ion-neutral chemistry at ultralow energies: dynamics of reactive collisions between laser-cooled Ca+ ions and Rb atoms in an ion-atom hybrid trap

Abstract: Cold chemical reactions between laser-cooled Ca+ ions and Rb atoms were studied in an ion-atom hybrid trap. Reaction rate constants were determined in the range of collision energies ⟨E coll⟩/k B=20 mK-20 K. The lowest energies were achieved in experiments using single localised Ca+ ions. Product branching ratios were studied using resonant-excitation mass spectrometry. The dynamics of the reactive processes in this system (non-radiative and radiative charge transfer as well as radiative association leading to the formation of CaRb+ molecular ions) have been analysed using high-level quantum-chemical calculations of the potential energy curves of CaRb+ and quantum-scattering calculations for the radiative channels. For the present low-energy scattering experiments, it is shown that the energy dependence of the reaction rate constants is governed by long-range interactions in line with the classical Langevin model, but their magnitude is determined by short-range non-adiabatic and radiative couplings which...

Electrokinetics: insights from simulation on the microscopic scale

Abstract: Electrokinetic effects, i.e. the coupled hydrodynamic and electric phenomena which occur near charged interfaces, constitute a challenge to theorists due to the variety of length and time scales involved. We discuss recent advances in the modelling of these phenomena, emphasising the interplay between the molecular specificity and the collective induced flows that emerge. We discuss the complementary simulation methodologies that have been developed either to focus on the molecular aspects of electrokinetics or on their effective properties on larger scales, as well as the proposed hybrid schemes that can incorporate both aspects. We highlight the insights that molecular studies have brought on the nature of interfacial charges and their implications for kinetic phenomena in confined fluids and also discuss advances in a number of relevant contexts.

W-band ELDOR-detected NMR (EDNMR) spectroscopy as a versatile technique for the characterisation of transition metal–ligand interactions

Abstract: ELDOR-detected NMR (EDNMR) spectra for a series of hydrated transition metal complexes: MnII(H2O)6, CuII(H2O)6 and VIVO(H2O)5 are reported. All EDNMR experiments were performed at W-band (94 GHz) employing two independent microwave frequencies. A purpose-built broadband microwave resonator (spectral range 300 MHz) was used, sufficient to detect all single quantum nuclear transitions of the three model systems. The EDNMR spectral lineshape observed is essentially the same as in conventional ENDOR (Electron-Nuclear Double Resonance). EDNMR presents two technical advantages over ENDOR for transition metal complexes: (i) enhanced sensitivity, reducing acquisition times by at least one order of magnitude; and (ii) simultaneous detection of transitions from all magnetic nuclei. This includes ligand (1H, 2H, 17O) and metal centred hyperfine couplings. For the latter, both isotropic couplings in the case of the 55Mn complex and highly anisotropic couplings in the case of 51V and 63,65Cu complexes could be resolve...

Stochastic resonance-free multiple time-step algorithm for molecular dynamics with very large time steps

Abstract: Molecular dynamics is one of the most commonly used approaches for studying the dynamics and statistical distributions of physical, chemical, and biological systems using atomistic or coarse-grained models. It is often the case, however, that the interparticle forces drive motion on many time scales, and the efficiency of a calculation is limited by the choice of time step, which must be sufficiently small that the fastest force components are accurately integrated. Multiple time-stepping algorithms partially alleviate this inefficiency by assigning to each time scale an appropriately chosen step-size. As the fast forces are often computationally cheaper to evaluate than the slow forces, this results in a significant gain in efficiency. However, such approaches are limited by resonance phenomena, wherein motion on the fastest time scales limits the step sizes associated with slower time scales. In atomistic models of biomolecular systems, for example, resonances limit the largest time step to around 5-6 f...

A scaling PNO–MP2 method using a hybrid OSV–PNO approach with an iterative direct generation of OSVs†

Abstract: We present an implementation of pair natural orbital second-order Moller–Plesset perturbation theory with computational costs that scale only cubically with the system size. The low cost-scaling is achieved by combining a hybrid approach, where the pair natural orbitals are build from orbital-specific virtuals OSVs, with an iterative block Davidson algorithm for solving the equations for OSVs. We thereby avoid a complete diagonalisation of amplitude matrices and the explicit construction of the corresponding exchange integral matrices. This reduces the cost-scaling for the generation of the OSVs and of the pair natural orbitals to without a priori assumptions about locality. The costs can be further reduced by combining the approach with a local resolution-of-the-identity approximation for the exchange integrals. The errors introduced by these approximations are negligible and do not affect the final accuracy of the correlation energy. Test calculations on a set of organic and inorganic molecules demonstr...

A coupled cluster treatment of intramonomer electron correlation within symmetry-adapted perturbation theory: benchmark calculations and a comparison with a density-functional theory description

Abstract: Symmetry-adapted perturbation theory (SAPT) with intramonomer electron correlation described by coupled cluster theory limited to single and double excitations was applied to 21 noncovalent complexes in their minimum geometries. The resulting benchmark contributions to the interaction energy were utilized to examine the accuracy of a more approximate variant of the SAPT method, where interacting molecules are described by density functional theory (DFT) with different functionals, like LDA, PBE, B3LYP, PBE0, M05, M05-2X, M06, and M06-2X (in all cases the asymptotic correction for the exchange-correlation functional has been utilized). Average errors for individual energy components of SAPT(DFT) are not larger than 10% for best functionals under study. Among the tested functionals PBE0, M05, and B3LYP should be especially recommended for the SAPT(DFT) approach. The M06 functional gives the largest errors with respect to SAPT(CCSD) and should not be used for describing intramonomer correlation in SAPT.

Experimental and molecular modeling investigation of (E)-N-{2-[(2-hydroxybenzylidene)amino]phenyl}benzenesulfonamide

Abstract: The Schiff base compound (E)-N-{2-[(2-hydroxybenzylidene)amino]phenyl}benzenesulfonamide has been synthesized and characterized by IR, NMR and Uv-vis spectroscopies, and single-crystal X-ray diffraction technique. In addition, quantum chemical calculations employing density functional theory (DFT) method with the 6–311++G(d,p) basis set were performed to study the molecular, spectroscopic and some electronic structure properties of the title compound, and the results were compared with the experimental findings. There exists a good correlation between experimental and theoretical data. Enol-imine/keto-amine tautomerization mechanism was investigated in the gas phase and in solution phase using the polarizable continuum model (PCM) approximation. The energetic and thermodynamic parameters of the enol-imine → keto-amine transfer process show that the single proton exchange is thermodynamically unfavored both in the gas phase and in solution phase. However, the reverse reaction seems to be feasible with a lo...

Mixed quantum-classical dynamics on the exact time-dependent potential energy surface: a fresh look at non-adiabatic processes

Abstract: The exact nuclear time-dependent potential energy surface arises from the exact decomposition of the electronic and nuclear motions, recently presented in [A. Abedi, N.T. Maitra, and E.K.U. Gross, Phys. Rev. Lett. 105, 123002 (2010)]. Such time-dependent potential drives nuclear motion and fully accounts for the coupling to the electronic subsystem. We investigate the features of the potential in the context of electronic non-adiabatic processes and employ it to study the performance of the classical approximation on nuclear dynamics. We observe that the potential, after the nuclear wave packet splits at an avoided crossing, develops dynamical steps connecting different regions, along the nuclear coordinate, in which it has the same slope as one or the other adiabatic surface. A detailed analysis of these steps is presented for systems with different non-adiabatic coupling strength. The exact factorisation of the electron-nuclear wave function is at the basis of the decomposition. In particular, the nucle...

The alkaline earth dimer cations (Be2 +, Mg2 +, Ca2 +, Sr2 +, and Ba2 +). Coupled cluster and full configuration interaction studies†

Abstract: Although all of the neutral alkaline earth dimers have been studied experimentally, only for the beryllium and strontium systems have the diatomic radical cations been subjected to modern spectroscopic techniques. In the present research, both coupled cluster and full configuration interaction methods were used to describe the M2 + systems. Basis sets as large as aug-cc-pCV5Z were chosen. For both Be2 + and Sr2 + agreement with the experiments is outstanding. Final predictions for the unknown dissociation energies are 10,651 (Mg2 +), 9605 (Ca2 +), and 8980 cm−1 (Ba2 +). The M2 + dissociation energies decrease monotonically going down the periodic except for the Sr2 + - Ba2 + pair. The unknown bond distances re are 3.015 (Mg2 +), 3.814 (Ca2 +), 4.194 (Sr2 +), and 4.587 A (Ba2 +).

On the triplet instability in TDDFT

Abstract: The utility of a Hartree–Fock triplet stability threshold, for identifying time-dependent density functional theory triplet excitations for which the inclusion of exact orbital exchange is detrimental, is illustrated for a benchmark set of 63 excitations in 20 organic molecules. Following earlier spin–spin coupling observations that suggest a relatively small triplet instability problem, the accuracy of triplet excitation energies from the B97-2 hybrid functional is also quantified. As anticipated, the results are relatively accurate and this is readily understood in terms of the stabilities. Application of the Tamm–Dancoff approximation dramatically improves all the triplet excitation energies corresponding to low stabilities, whilst also providing a modest improvement in the corresponding singlet states.

mtsslSuite: In silico spin labelling, trilateration and distance-constrained rigid body docking in PyMOL.

Abstract: Nanometer distance measurements based on electron paramagnetic resonance methods in combination with site-directed spin labelling are powerful tools for the structural analysis of macromolecules. The software package mtsslSuite provides scientists with a set of tools for the translation of experimental distance distributions into structural information. The package is based on the previously published mtsslWizard software for in silico spin labelling. The mtsslSuite includes a new version of MtsslWizard that has improved performance and now includes additional types of spin labels. Moreover, it contains applications for the trilateration of paramagnetic centres in biomolecules and for rigid-body docking of subdomains of macromolecular complexes. The mtsslSuite is tested on a number of challenging test cases and its strengths and weaknesses are evaluated.

Computation of pair distribution functions and three-dimensional densities with a reduced variance principle

Abstract: No fancy statistical objects here, we go back to the computation of one of the most basic and fundamental quantities in the statistical mechanics of fluids, namely the pair distribution functions. Those functions are usually computed in molecular simulations by using histogram techniques. We show here that they can be estimated using a global information on the instantaneous forces acting on the particles, and that this leads to a reduced variance compared to the standard histogram estimators. The technique is extended successfully to the computation of three-dimensional solvent densities around tagged molecular solutes, quantities that are noisy and very long to converge, using histograms.

X-band rapid-scan EPR of samples with long electron spin relaxation times: A comparison of continuous wave, pulse and rapid-scan EPR

Abstract: X-band room temperature spectra obtained by rapid-scan, continuous wave, field-swept echo-detected and Fourier transform electron paramagnetic resonance (FTEPR) were compared for three samples with long electron spin relaxation times: amorphous hydrogenated silicon (T1 = 11 μs, T2 = 3.3 μs), 0.2% N@C60 solid (T1 = 120–160 μs, T2 = 2.8 μs) and neutral single substitutional nitrogen centres (NS0) in diamonds (T1 = 2300 μs, T2 = 230 μs). For each technique, experimental parameters were selected to give less than 2% broadening of the lineshape. For the same data acquisition times, the signal-to-noise for the rapid-scan spectra was one-to-two orders of magnitude better than for continuous wave or field-swept echo-detected spectra. For amorphous hydrogenated silicon, T2* (∼ 10 ns) is too short to perform FTEPR. For 0.2% N@C60, the signal-to-noise ratio for rapid scan is about five times better than for FTEPR. For NS0 the signal-to-noise ratio is similar for rapid scan and FTEPR.

Strongly aligned and oriented molecular samples at a kHz repetition rate

Abstract: We demonstrate strong adiabatic laser alignment and mixed-field orientation at kHz repetition rates. We observe the degrees of alignment as large as ⟨cos2θ⟩2D=0.94 at 1 kHz operation for iodobenzene. The experimental setup consists of a kHz laser system simultaneously producing pulses of 30 fs (1.3 mJ) and 450 ps (9 mJ). A cold 1-K state-selected molecular beam is produced at the same rate by appropriate operation of an Even–Lavie valve. Quantum state selection has been obtained using an electrostatic deflector. A camera and data acquisition system records and analyses the images on a single-shot basis. The system is capable of producing, controlling (translation and rotation) and analysing cold molecular beams at kHz repetition rates and is therefore ideally suited for the recording of ultrafast dynamics in so-called ‘molecular movies’.

Fully adaptive algorithms for multivariate integral equations using the non-standard form and multiwavelets with applications to the Poisson and bound-state Helmholtz kernels in three dimensions

Abstract: We have developed and implemented a general formalism for fast numerical solution of time-independent linear partial differential equations as well as integral equations through the application of numerically separable integral operators in d ≥ 1 dimensions using the non-standard (NS) form. The proposed formalism is universal, compact and oriented towards the practical implementation into a working code using multiwavelets. The formalism is applied to the case of Poisson and bound-state Helmholtz operators in d = 3. Our algorithms are fully adaptive in the sense that the grid supporting each function is obtained on the fly while the function is being computed. In particular, when the function g = O f is obtained by applying an integral operator O, the corresponding grid is not obtained by transferring the grid from the input function f. This aspect has significant implications that will be discussed in the numerical section. The operator kernels are represented in a separated form with finite but arbitra...