Self-consistent Field Calculations Research Articles

An Efficient and Accurate SCF Algorithm for Block Copolymer Films and Brushes Using Adaptive Discretizations.

Self-consistent field (SCF) theory serves as a robust tool for unraveling the intricate behavior exhibited by soft polymeric materials. However, the accuracy and efficiency of SCF calculations are crucially dependent on the numerical methods employed for system discretization and equation-solving. Here, we introduce a simple three dimensional SCF algorithm that uses real-space methods and adaptive discretization, offering improved accuracy and efficiency for simulating polymeric systems at surfaces. Our algorithm's efficacy is demonstrated through simulations of two distinct polymeric systems, namely, block copolymer (BCP) films and polymer brushes. By enhancing spatial resolution in regions influenced by external forces and employing finer contour discretization at grafting chain ends, we achieve significantly more accurate results at very little additional cost, enabling the study of 3D polymeric systems that were previously computationally challenging. To facilitate the widespread use of the algorithm, we have made our 1D-3D SCF code publicly available.

The effect of machine learning predicted anharmonic frequencies on thermodynamic properties of fluid hydrogen fluoride.

Anharmonic effects play a crucial role in determining thermochemical properties of liquids and gases. For such extended phases, the inclusion of anharmonicity in reliable electronic structure methods is computationally extremely demanding, and hence, anharmonic effects are often lacking in thermochemical calculations. In this study, we apply the quantum cluster equilibrium method to transfer density functional theory calculations at the cluster level to the macroscopic, liquid, and gaseous phase of hydrogen fluoride. This allows us to include anharmonicity, either via vibrational self-consistent field calculations for smaller clusters or using a regression model for larger clusters. We obtain the structural composition of the fluid phases in terms of the population of different clusters as well as isobaric heat capacities as an example for thermodynamic properties. We study the role of anharmonicities for these analyses and observe that, in particular, the dominating structural motifs are rather sensitive to the anharmonicity in vibrational frequencies. The regression model proves to be a promising way to get access to anharmonic features, and the extension to more sophisticated machine-learning models is promising.

Structural, electronic and thermoelectric properties of monolayer TiSe2.

In this work the first-principles calculations of the structural, electronic and thermoelectric properties of monolayer TiSe2 are presented. The optimized lattice parameter of monolayer TiSe2 shows excellent agreement with the experimental value. The computed band structure and density of states calculations predict metallic nature of monolayer TiSe2 with overlapping of 0.44eV between the lowest conduction band and top valance band at high symmetry point M. The position of pseudogap formed by Ti-3d orbitals near the Fermi level confirms the mechanical stability of monolayer TiSe2. Due to the influence of positive strain (tensile strain), the Ti-Se bond length increases and the layer height decreases. The applied tensile strain changes the metallic nature of TiSe2 into a semiconductor with opening of bandgap. It has also been observed that the positions of conduction band minima and valance band maxima change with strain. The charge analysis shows that charge transfer from Ti to Se atom increases when tensile strain is applied, while an opposite trend is observed with compression. The computed thermoelectric coefficientsi.e. Seeback coefficient, power factor and figure of merit are in good agreement with the experimental data.The temperature dependence of these coefficientsis also reported. The density functional theory based calculations are reported employing the PBE-GGA ansatz using the plane wave-pseudopotential method embodied in the Quantum ESPRESSO package. The self-consistent field calculations are performed over a dense Monkhorst-Pack net of 12 × 12 × 1k-points. The energy convergence criteria for the self-consistent field calculation were set to 10-6 Ry/atom with a cutoff energy of 90 Ry. The thermoelectric properties are computed by combining the band structure calculations with the Boltzmann transport equation using Boltztrap2 peckage.

Spectroscopic and Theoretical Investigation of High-Spin Square-Planar and Trigonal Fe(II) Complexes Supported by Fluorinated Alkoxides.

The electronic structures and spectroscopic behavior of three high-spin FeII complexes of fluorinated alkoxides were studied: square-planar {K(DME)2}2[Fe(pinF)2] (S) and quasi square-planar {K(C222)}2[Fe(pinF)2] (S') and trigonal-planar {K(18C6)}[Fe(OC4F9)3] (T) where pinF = perfluoropinacolate and OC4F9 = tris-perfluoro-t-butoxide. The zero-field splitting (ZFS) and hyperfine structure parameters of the S = 2 ground states were determined using field-dependent 57Fe Mössbauer and high-field and -frequency electron paramagnetic resonance (HFEPR) spectroscopies. The spin Hamiltonian parameters were analyzed with crystal field theory and corroborated by density functional theory (DFT) and ab initio complete active space self-consistent field (CASSCF) calculations. Whereas the ZFS tensor of S has a small rhombicity, E/D = 0.082, and a positive D = 15.17 cm-1, T exhibits a negative D = -9.16 cm-1 and a large rhombicity, E/D = 0.246. Computational investigation of the structural factors suggests that the ground-state electronic configuration and geometry of T's Fe site are determined by the interaction of [Fe(OC4F9)3]- with {K(18C6)}+. In contrast, two distinct countercations of S/S' have a negligible influence on their [Fe(pinF)2]2- moieties. Instead, the distortions in S' are likely induced by the chelate ring conformation change from δλ, observed for S, to the δδ conformation, determined for S'.

Dinitrogen Activation Mediated by the (P2PPh)Fe Complex: Electronic Structure, Dimerization Mechanism, and Magnetic Coupling.

Herein, we report the estimation of the extent of dinitrogen activation by different charged and structural forms of (P2PPh)Fe biomimetic catalysts, which, in the presence of light, exhibit significant yield in the N2-to-NH3 conversion. Complete active space self-consistent field (CASSCF) calculations have been used to determine the electronic structure of different reduced forms of the mononuclear complexes: the neutral (P2PPh)Fe(N2)2 adduct and the anionic [(P2PPh)Fe(N2)]- and [(P2PPh)Fe(N2)]2- complexes. These calculations also revealed that the extent of reduction of a dinitrogen molecule reaches up to one electron (N21-) due to the back-bonding from the Fe center, in agreement with the changes observed in the vibration frequency of the N-N bond in these complexes. In addition, the energy profile of the dimerization of the mononuclear (P2PPh)Fe(N2)2 complex to the dinuclear mono-N2-bridged [(P2PPh)Fe]2(μ-N2) complex has been determined by means of density functional theory (DFT) calculations. A three-step mechanism has been proposed for the dimerization, favored by both kinetics and thermodynamics criteria. Finally, the magnetic coupling constant in the diiron (μ-N2) complex is estimated from CASSCF/NEVPT2 calculations. Such a dinuclear complex presents a strong antiferromagnetic coupling resulting from the interaction between two S = 1 d6 Fe2+ ions, bridged by a highly activated dinitrogen molecule (N22-) with two electrons on the π* orbitals.

Mapping spin contamination-free potential energy surfaces using restricted open-shell methods with Grassmannians.

The Lagrange-based Grassmann interpolation (G-Int) method has been extended for open-shell systems using restricted open-shell (RO) methods. The performance of this method was assessed in constructing potential energy surfaces (PESs) for vanadium(II) oxide, benzyl radical, and methanesulfenyl chloride radical cation. The density matrices generated by G-Int when used as initial guesses for self-consistent field (SCF) calculations, exhibit superior performance compared to other traditional SCF initial guess schemes, such as SADMO, GWH, and CORE. Additionally, the energy obtained from the G-Int scheme satisfies the variational principle and outperforms the direct energy-based Lagrange interpolation approach. In the case of methanesulfenyl chloride radical cation, a unique example with a flat PES at the end region along the H-C-S-Cl dihedral angle, the use of an equally-spaced grid sampling leads to significant oscillations near the end of the interval due to the effects of Runge's phenomenon. Introducing an unequally-spaced grid sampling based on a scaled Gauss-Chebyshev quadrature effectively mitigated the Runge's phenomenon, making it suitable for combining with G-Int in constructing PESs for general applications. Thus, G-Int provides an efficient and robust strategy for building spin contamination-free PESs with consistent accuracy.

How delocalized are the polyacenes?

In an attempt to quantify electron delocalization in polyacenes with up to 50 carbon atoms, we have performed self-consistent field calculations in which the electrons are constrained to occupy highly localized molecular orbitals (HILOs) centered on a maximum of two, six or ten adjacent carbon atoms. We have also performed similar calculations on simple polyacene analogs consisting only of hydrogen atoms and exhibiting electron delocalization in the framework. We find that the energetic cost of localizing the electrons in the polyacenes is roughly 60, 5 or 0.1 kJ/mol per ring atom for the two-, six- and ten-atom HILOs, respectively, and the use of these localized models overestimates the predicted hydrogenation energies of the acenes by roughly 50%, 4% and 0.1%, respectively. We conclude that the chemistry of polyacenes can be modeled well using highly localized descriptions of the electrons.

A magnetic Ni-based metal-organic framework with interesting transformation dynamics

Herein, a flexible system composed of two Ni(II)-based coordination compounds: a 3D framework of {[Ni(μ-3isoani)2]·DMF}n (1) formula and a 0D monomeric [Ni(3isoani)2(H2O)4] (2) complex (where 3isoani = 3-aminoisonicotinato and DMF = dimethylformamide) which show mutual solvent-induced reversible transformations into each other is reported. The system shows reversible 1 ↔ 2 transformations upon the exposure of one compound to the solvent present in the other, that is, the MOF (1) in water and the monomer (2) in DMF. The process is easily followed by the naked eye because it involves a colour change from green (1)-to-brownish green (2), making the process traceable as previously observed for the Co(II)-based system. Moreover, these compounds present very different magnetic properties since 1 shows field-induced single-molecule magnet (SMM) behaviour, which corresponds to one of the few Ni(II)-based compounds showing single-ion behaviour (being Ni(II) the unique spin carrier), whereas 2 behaves as a regular paramagnet, all of which is explained according to a careful study of the magnetic properties by means of experimental direct-current (dc) and alternating-current (ac) measurements. Obtained experimental results are well supported by active space self-consistent field (CASSCF) calculations that allow understanding the slow relaxation occurring in the Ni(II) ion.

Tuning the magnetic properties of doped ZnS using transition metal doping: A multi-scale computational approach

Transition metal (TM)-doped dilute magnetic semiconductors (DMS) have emerged as promising materials for spintronic applications such as spin-polarized transport and information storage. However, achieving robust room-temperature ferromagnetism in DMS remains a key challenge. This work undertakes a comprehensive investigation of the effects of Ti- and Cr-doping and (Ti,Cr)-codoping on the structural, electronic, and magnetic properties of wurtzite ZnS using first-principles pseudopotential plane-wave self-consistent field calculations and Monte Carlo simulations. The first-principles DFT calculations were performed using the spin-polarized GGA+U approach to account for strong electron–electron interactions. Structural relaxations revealed expanded lattice parameters and bond lengths for the doped systems compared to pure ZnS, attributed to the larger ionic radii of the dopants. Formation energy calculations confirmed the thermodynamic stability of doping. The band structure and density of states analysis demonstrated the half-metallic nature of the doped ZnS systems with 100% spin polarization induced by strong hybridization between the TM-3d and S-3p states. This mediates robust ferromagnetic coupling, with total magnetic moments around 4-8 μB/cell depending on dopant type and concentration. To complement the zero-temperature DFT results, temperature-dependent Monte Carlo simulations using the single-spin flip Heat Bath algorithm were implemented. The modeling of magnetization, susceptibility, specific heat, and hysteresis loops enabled extracting Curie temperatures up to 427.6 K for 12.5% Cr-doped ZnS. The synergistic combination of first-principles DFT and Monte Carlo computational techniques provides significant insights into tailoring the magnetic properties of TM-doped ZnS dilute magnetic semiconductors. The tunability of structural, electronic, and magnetic characteristics through control of dopant selection and concentration demonstrates the promising potential of transition metal-doped ZnS for spintronic devices operable at room-temperature.

Pitfalls in the n-mode representation of vibrational potentials.

Simulations of anharmonic vibrational motion rely on computationally expedient representations of the governing potential energy surface. The n-mode representation (n-MR)-effectively a many-body expansion in the space of molecular vibrations-is a general and efficient approach that is often used for this purpose in vibrational self-consistent field (VSCF) calculations and correlated analogues thereof. In the present analysis, a lack of convergence in many VSCF calculations is shown to originate from negative and unbound potentials at truncated orders of the n-MR expansion. For cases of strong anharmonic coupling between modes, the n-MR can both dip below the true global minimum of the potential surface and lead to effective single-mode potentials in VSCF that do not correspond to bound vibrational problems, even for bound total potentials. The present analysis serves mainly as a pathology report of this issue. Furthermore, this insight into the origin of VSCF non-convergence provides a simple, albeit ad hoc, route to correct the problem by "painting in" the full representation of groups of modes that exhibit these negative potentials at little additional computational cost. Somewhat surprisingly, this approach also reasonably approximates the results of the next-higher n-MR order and identifies groups of modes with particularly strong coupling. The method is shown to identify and correct problematic triples of modes-and restore SCF convergence-in two-mode representations of challenging test systems, including the water dimer and trimer, as well as protonated tropine.

Ab initio study of elastic, electronic, and vibrational properties of SnTe and PbTe.

The elastic, electronic, and vibrational properties of the ground state of the rocksalt SnTe and PbTe are investigated. The deduced elastic constants, namely, shear modulus, Young's modulus, and Poisson's ratio are in very good agreement with the experimental and other theoretical data. The electronic band structure and density of states are obtained with and without considering the spin-orbit coupling. The bandgaps of SnTe and PbTe with (without) spin-orbit coupling are 0.11 (0.05) eV and 0.01 (0.78) eV, respectively. The bandgaps with spin-orbit interactions are nearer to experimental data. The hybrid functionals give higher values of bandgaps for both the SnTe and PbTe. In both compounds, the bandgap increases with volume. The valence bandwidths, however, decrease with increasing volume. The vibrational frequencies are found in reasonable agreement with the experiment. The frequencies increase with pressure. In this work, the ab initio calculations of SnTe and PbTe crystals are carried out applying plane wave pseudopotential method using the QUANTUM ESPRESSO package. The PBE exchange and correlation functional based on GGA is considered. The fully relativistic norm-conserving pseudopotentials for Sn, Pb, and Te are used. The self-consistent field calculations are performed over a dense MP net of 18 × 18 × 18k-points. The energy cut-off of 70 Ryd was found sufficient to achieve convergence of 10-6 Ryd in total energy of the crystals.

Field- and Temperature-Dependent Paramagnetic Relaxation Enhancements in Co(II) Trispyrazolylmethanes.

A comprehensive field- and temperature-dependent examination of nuclear magnetic resonance paramagnetic relaxation enhancements (PREs) for the constitutive protons of [Co(Tpm)2][BF4]2 is presented. Data for an apically substituted derivative clearly establish that bis-Tpm complexes of Co(II) undergo Jahn-Teller dynamics about the molecular threefold axis. PREs from the parent Tpm complex were used to numerically extract the electron relaxation times (T1e). The Tpm complex showed field-dependent behavior, with an approximately 40% higher activation barrier than the related trispyrazolylborate (Tp) complex, based on fits to the T1e vs T, B0 data. Analysis of the field-dependent line widths revealed a surprisingly large contribution from susceptibility (Curie) relaxation (20-35% at the highest field), and a molecular radius (9.5 Å) that is consistent with a tightly associated counterion slowing rotation in solution. Density functional theory showed a shared vibration that is consistent with the Jahn-Teller and appears proportionately higher in energy in [Co(Tpm)2]2+. Complete active-space self-consistent field calculations support ascribing electron relaxation to enhanced mixing of the two Eg orbital sets that accompanies the tetragonal distortion and the differences in electron correlation times to the higher Jahn-Teller activation barrier in [Co(Tpm)2]2+.

RPA, an Accurate and Fast Method for the Computation of Static Nonlinear Optical Properties.

The accurate computation of static nonlinear optical properties (SNLOPs) in large polymers requires accounting for electronic correlation effects with a reasonable computational cost. The Random Phase Approximation (RPA) used in the adiabatic connection fluctuation theorem is known to be a reliable and cost-effective method to render electronic correlation effects when combined with density-fitting techniques and integration over imaginary frequencies. We explore the ability of the RPA energy expression to predict SNLOPs by evaluating RPA electronic energies in the presence of finite electric fields to obtain (using the finite difference method) static polarizabilities and hyperpolarizabilities. We show that the RPA based on hybrid functional self-consistent field calculations yields accurate SNLOPs as the best-tuned double-hybrid functionals developed today, with the additional advantage that the RPA avoids any system-specific adjustment.

Accelerating and stabilizing the convergence of vibrational self-consistent field calculations via the direct inversion of the iterative subspace (vDIIS) algorithm.

The vibrational self-consistent field (VSCF) method yields anharmonic states and spectra for molecular vibrations, and it serves as the starting point for more sophisticated correlated-vibration methods. Convergence of the iterative, non-linear optimization in VSCF calculations can be erratic or altogether unsuccessful, particularly for chemical systems involving low-frequency motions. In this work, a vibrational formulation of the Direct Inversion of the Iterative Subspace method of Pulay is presented and investigated. This formulation accounts for distinct attributes of the vibrational and electronic cases, including the expansion of each single-mode vibrational wavefunction in its own basis set. The resulting Direct Inversion of the Iterative Subspace method is shown to substantially accelerate VSCF convergence in all convergent cases as well as rectify many cases where Roothaan-based methods fail. Performance across systems ranging from small, rigid molecules to weakly bound molecular clusters is investigated in this analysis.

Surface adsorption properties of peptides produced by non-optimum pH pepsinolysis of proteins: A combined experimental and self-consistent-field calculation study

HypothesisPartial hydrolysis of large molecular weight (Mw), highly aggregated plant proteins is frequently used to improve their solubility. However, if this hydrolysis is extensive, random or nonselective, it is unlikely to improve functional properties such as surface activity, emulsion, or foam-stabilising capacity. Experiments and simulationSoy protein isolate (SPI) was hydrolysed by pepsin under optimal (pH 2.1) and non-optimal (pH 4.7) conditions. The surface activity and emulsion stabilising capacity of the resultant peptides were measured and compared. The colloidal interactions between a pair of emulsion droplets were modelled via Self-Consistent-Field Calculations (SCFC). FindingsHydrolysis at pH 2.1 and 4.7 resulted in a considerable increase in measured surface activity compared to the native (non-hydrolysed) SPI, but the hydrolysate from pH 2.1 was not as good an emulsion stabiliser as the hydrolysate (particularly the fraction Mw > 10 kDa) at pH 4.7. Furthermore, peptide analysis of the latter suggested it was dominated by a fragment of one of the major soy proteins β-conglycinin, with Mw ≈ 25 kDa. SCFC calculations confirmed that interactions mediated by adsorbed layers of this peptide point to it being an excellent emulsion stabiliser.

Accelerating Anharmonic Spectroscopy Simulations via Local-Mode, Multilevel Methods.

Ab initio computer simulations of anharmonic vibrational spectra provide nuanced insight into the vibrational behavior of molecules and complexes. The computational bottleneck in such simulations, particularly for ab initio potentials, is often the generation of mode-coupling potentials. Focusing specifically on two-mode couplings in this analysis, the combination of a local-mode representation and multilevel methods is demonstrated to be particularly symbiotic. In this approach, a low-level quantum chemistry method is employed to predict the pairwise couplings that should be included at the target level of theory in vibrational self-consistent field (and similar) calculations. Pairs that are excluded by this approach are "recycled" at the low level of theory. Furthermore, because this low-level pre-screening will eventually become the computational bottleneck for sufficiently large chemical systems, distance-based truncation is applied to these low-level predictions without substantive loss of accuracy. This combination is demonstrated to yield sub-wavenumber fidelity with reference vibrational transitions when including only a small fraction of target-level couplings; the overhead of predicting these couplings, particularly when employing distance-based, local-mode cutoffs, is a trivial added cost. This combined approach is assessed on a series of test cases, including ethylene, hexatriene, and the alanine dipeptide. Vibrational self-consistent field (VSCF) spectra were obtained with an RI-MP2/cc-pVTZ potential for the dipeptide, at approximately a 5-fold reduction in computational cost. Considerable optimism for increased accelerations for larger systems and higher-order couplings is also justified, based on this investigation.

Interpenetration and Friction of Brush-Coated Surfaces under External Load: Analytical Theory and SCF Calculations

We studied the compression and interpenetration properties of two opposing monodisperse polymer brushes under external load by analytical theory and by a numerical self-consistent field (SCF) approach. Analytical expressions are proposed for the brush density profiles in the interpenetration zone and verified by numerical SCF calculations. We quantify the interpenetration of two opposing brushes by the characteristic penetration length and by two integral parameters: the overlap integral, Γ, representing the number of interbush contacts, and the number of brush monomer units in the foreign half-space, Σ. The interpenetration parameters are studied in two conjugate ensembles as functions of the brush separation and of the external pressure. We propose a theoretical description of the solvent-mediated friction force in the low shearing rate regime on the basis of the Brinkman equation for two compressed brushes sliding against each other. We demonstrate that the total friction force which also includes direct brush–brush friction is expressed in terms of Γ and Σ. The SCF data for the interpenetration parameters Γ and Σ and hence for the total sliding friction force in the pressure ensemble collapse onto universal master curves when rescaled by the factor (N/σ)1/3 as suggested by the theory, where N is the chain length and σ is the surface grafting density. Finally, we define the kinetic friction coefficient as a function of the external pressure and analyze its universal rescaled behavior in the two limits of nondraining and free-draining brushes.

Computational Description of Alkylated Iron-Sulfur Organometallic Clusters.

The radical S-adenosyl methionine (SAM) enzyme superfamily has widespread roles in hydrogen atom abstraction reactions of crucial biological importance. In these enzymes, reductive cleavage of SAM bound to a [4Fe-4S]1+ cluster generates the 5'-deoxyadenosyl radical (5'-dAdo•) which ultimately abstracts an H atom from the substrate. However, overwhelming experimental evidence has surprisingly revealed an obligatory organometallic intermediate Ω exhibiting an Fe-C5'-adenosyl bond, whose properties are the target of this theoretical investigation. We report a readily applied, two-configuration version of broken symmetry DFT, denoted 2C-DFT, designed to allow the accurate description of the hyperfine coupling constants and g-tensors of an alkyl group bound to a multimetallic iron-sulfur cluster. This approach has been validated by the excellent agreement of its results both with those of multiconfigurational complete active space self-consistent field computations for a series of model complexes and with the results from electron nuclear double-resonance/electron paramagnetic resonance spectroscopic studies for the crystallographically characterized complex, M-CH3, a [4Fe-4S] cluster with a Fe-CH3 bond. The likewise excellent agreement between spectroscopic results and 2C-DFT computations for Ω confirm its identity as an organometallic complex with a bond between an Fe of the [4Fe-4S] cluster and C5' of the deoxyadenosyl moiety, as first proposed.

The Grassmann interpolation method for spin-unrestricted open-shell systems.

The recently reported Grassmann interpolation (G-Int) method [J. A. Tan and K. U. Lao, J. Chem. Phys. 158, 051101 (2023)] has been extended to spin-unrestricted open-shell systems. In contrast to closed-shell systems, where G-Int has to be performed only once since the α and β density matrices are the same, spin-unrestricted open-shell systems require G-Int to be performed twice-one for the α spin and another for the β spin density matrix. In this work, we tested the performance of G-Int to the carbon monoxide radical cation CO●+ and nickelocene complex, which have the doublet and triple ground states, respectively. We found that the Frobenius normerrors associated with the interpolations for the α and β spin density matrices are comparable for a given molecular geometry. These G-Int density matrices, when used as an initial guess for a self-consistent field (SCF) calculation, outperform the conventional SCF guess schemes, such as the superposition of atomic densities, purified superposition of atomic densities, core Hamiltonian, and generalized Wolfsberg-Helmholtz approximation. Depending on the desired accuracy, these G-Int density matrices can be used to directly evaluate the SCF energy without performing SCF iterations. In addition, the spin-unrestricted G-Int density matrices have been used for the first time to directly calculate the atomic charges using the Mulliken and ChElPG population analysis.

Effect of polymer architecture on the adsorption behaviour of amphiphilic copolymers: A theoretical study

HypothesisPolymer architecture is known to have significant impact on its adsorption behaviour. Most studies have been concerned with the more concentrated, “close to surface saturation” regime of the isotherm, where complications such as lateral interactions and crowding also additionally affect the adsorption. We compare a variety of amphiphilic polymer architectures by determining their Henry’s adsorption constant (kH), which, as with other surface active molecules, is the proportionality constant between surface coverage and bulk polymer concentration in a sufficiently dilute regime. It is speculated that not only the number of arms or branches, but also the position of adsorbing hydrophobes influence the adsorption, and that by controlling the latter the two can counteract each other. MethodologyThe Self-consistent field calculation of Scheutjens and Fleer was implemented to calculate the adsorbed amount of polymer for many different polymer architectures including linear, star and dendritic. Using the adsorption isotherms at very low bulk concentrations, we determined the value of kH for these. FindingsIt is found that the branched structures (star polymers and dendrimers) can be viewed as analogues of linear block polymers based on the location of their adsorbing units. Polymers containing consecutive trains of adsorbing hydrophobes in all cases showed higher level of adsorption compared to their counterparts, where the hydrophobes were more uniformly distributed on the chains. While increasing the number of branches (or arms for star polymers) also confirmed the known result that the adsorption decreased with the number of arms, this trend can be partially offset by the appropriate choice of the location of anchoring groups.